Analytical Skills-II

Unit 7: Capstone — Exam Strategy & Career Launchpad

Synthesize all 6 units into exam-ready performance. Full mock tests, speed tricks, strategy blueprints, and career roadmaps — your complete launchpad for CAT, Bank PO, SSC, placements, and beyond.

⏱️ Time to Complete: 8–10 hours | 💰 Career Range: ₹4–40 LPA depending on exam | 📝 75 Mock Questions + 30 MCQs

💼 Paths this unlocks: IIM MBA (₹20–40 LPA) | Bank PO (₹6–12 LPA) | SSC CGL (₹5–8 LPA) | TCS/Infosys (₹3.5–7 LPA)

Section A

Opening Hook — From Lucknow BCA to McKinsey: ₹35 LPA

🏆 How Rahul Verma Cracked CAT 95 Percentile Without Coaching

Rahul Verma was a BCA student at Lucknow University — no IIT tag, no coaching institute budget, no family connections in business. What he had was a dog-eared copy of his Analytical Skills-II textbook and an unshakeable 6-month plan.

Every morning at 5 AM, Rahul solved 30 DI questions from his university syllabus. He memorized the fraction-to-percentage table until 1/13 = 7.69% rolled off his tongue. He practised Vedic math multiplication until he could compute 97 × 103 = 9991 in 3 seconds. He took 47 mock tests — analyzing every single mistake in a spreadsheet he called "Error Log."

Result: CAT 95.4 percentile. IIM Lucknow admission. Two years of MBA with a focus on strategy consulting. Campus placement at McKinsey & Company — ₹35 LPA.

"The entire quant and DI section of CAT is what we studied in Analytical Skills-II," Rahul says. "I didn't need coaching — I needed practice, strategy, and speed."

🏢 McKinsey🏢 BCG🎓 IIM Lucknow📝 CAT💻 TCS NQT

78% of CAT toppers surveyed by IMS Learning say that college-level aptitude and analytical skills courses were the single most important foundation for their preparation. The skills you've built over 6 units of this course — Number Systems, Percentages, Time-Speed-Distance, Data Interpretation, Logical Reasoning — are the exact same skills tested in CAT, Bank PO, SSC CGL, GMAT, and placement exams like TCS NQT.

Section B

Learning Outcomes — Bloom's Taxonomy Mapped (12 Outcomes)

Bloom's Level	#	Learning Outcome
🔵 Remember	1	List all formula categories across 6 units (Number Systems, Percentages, Profit-Loss, SI/CI, Ratio, TSD, Time-Work, DI, LR, P&C, Probability, Geometry)
🔵 Remember	2	Recall negative marking schemes for CAT (-1 for wrong), Bank PO (-0.25), SSC CGL (-0.50), and TCS NQT (no negative marking)
🟢 Understand	3	Explain time allocation strategy for different exam types — why CAT needs 2 min/question while Bank PO needs 48 sec/question
🟢 Understand	4	Describe the relationship between speed, accuracy, and final score — why 25 correct out of 30 attempted beats 30 correct out of 50 attempted in exams with negative marking
🟡 Apply	5	Solve cross-unit problems that combine percentages with DI, or time-work with ratio-proportion
🟡 Apply	6	Apply Vedic math shortcuts and fraction tables to reduce calculation time by 40–60%
🟠 Analyze	7	Analyze mock test performance to identify personal weak areas and create targeted improvement plans
🟠 Analyze	8	Compare preparation strategies for CAT vs Bank PO vs SSC — understanding syllabus overlap and unique requirements
🔴 Evaluate	9	Evaluate which career path (MBA, Banking, Government, IT Placements) suits based on individual aptitude strengths and career goals
🔴 Evaluate	10	Assess the trade-off between attempting more questions versus maintaining high accuracy for each specific exam's marking scheme
🟣 Create	11	Design a personalized 60-day exam preparation plan with daily targets, weekly milestones, and mock test schedule
🟣 Create	12	Create a comprehensive formula revision sheet from memory covering all 6 units, suitable for last-day revision

Section C

Concepts — Full Mock Tests, Exam Strategy & Career Guidance

1. Mock Test 1 — TCS NQT Style (30 Questions, 30 Minutes)

📝 MOCK TEST 1 — TCS NQT Aptitude Simulation

⏱️ 30 Minutes | 30 Questions | No Negative Marking | +1 per correct answer

Section A: Number Systems & Simplification (Q1–Q5)

What is the unit digit of 7²⁴³?

Simplify: 3/4 + 5/6 − 2/3 = ?

11/12
7/12
5/6
13/12

HCF of 72 and 108 is:

0.125 × 0.08 = ?

0.01
0.001
0.1
0.0001

√(0.0016) = ?

0.04
0.4
0.004
4

Section B: Percentages & Profit-Loss (Q6–Q10)

A shopkeeper marks goods 40% above cost price and gives 20% discount. His profit percentage is:

If A's salary is 25% more than B's, then B's salary is what percent less than A's?

A population increases from 10,000 to 13,310 in 3 years at a constant annual rate. The rate is:

A man sells an article at 10% loss. If he had sold it for ₹80 more, he would have earned 10% profit. The cost price is:

₹400
₹500
₹300
₹600

Q10

Successive discounts of 10% and 20% are equivalent to a single discount of:

Section C: Time, Speed & Distance (Q11–Q14)

Q11

A train 150m long crosses a pole in 15 seconds. Its speed in km/hr is:

Q12

A car covers 300 km at 60 km/hr and returns at 40 km/hr. The average speed for the entire journey is:

48 km/hr
50 km/hr
45 km/hr
52 km/hr

Q13

Two trains of lengths 100m and 150m are moving in the same direction at 60 km/hr and 40 km/hr respectively. The time taken by the faster train to cross the slower train is:

45 seconds
50 seconds
40 seconds
36 seconds

Q14

A man walking at 5 km/hr reaches his destination 10 minutes late. Walking at 6 km/hr, he reaches 10 minutes early. The distance to his destination is:

10 km
8 km
12 km
15 km

Section D: Time & Work (Q15–Q18)

Q15

A can do a work in 10 days and B in 15 days. Working together, they will finish in:

6 days
5 days
8 days
7 days

Q16

12 men can complete a work in 18 days. How many days will 18 men take?

12 days
10 days
14 days
15 days

Q17

A pipe fills a tank in 6 hours. Another pipe empties it in 8 hours. If both are opened together, the tank fills in:

20 hours
24 hours
18 hours
12 hours

Q18

A is twice as efficient as B. Together they finish a work in 12 days. A alone can finish it in:

18 days
16 days
20 days
15 days

Section E: Data Interpretation (Q19–Q22)

Directions: Study the following table and answer questions 19–22.

Company	Q1 (₹ Lakhs)	Q2 (₹ Lakhs)	Q3 (₹ Lakhs)	Q4 (₹ Lakhs)
TCS	120	140	110	150
Infosys	100	130	120	140
Wipro	90	100	110	130
HCL	80	90	100	120

Q19

Which company had the highest total annual sales?

TCS
Infosys
Wipro
HCL

Q20

What is the average Q3 sales across all companies?

₹110 Lakhs
₹108 Lakhs
₹105 Lakhs
₹112 Lakhs

Q21

What is the percentage increase in HCL's sales from Q1 to Q4?

Q22

In which quarter was the total sales across all companies the maximum?

Section F: Logical Reasoning (Q23–Q26)

Q23

Statement: All roses are flowers. Some flowers are red.
Conclusion: Some roses are red.

Definitely true
Probably true
Definitely false
Does not follow

Q24

If the letters of COMPUTER are assigned values equal to their position in the alphabet (C=3, O=15, M=13, P=16, U=21, T=20, E=5, R=18) and COMPUTER = 111, then PRINTER = ?

Q25

Find the next number: 2, 6, 12, 20, 30, ?

Q26

Pointing to a man, a woman said, "His mother is the only daughter of my mother." How is the woman related to the man?

Aunt
Mother
Sister
Grandmother

Section G: Coding-Decoding & Series (Q27–Q30)

Q27

If FRIEND is coded as HUMGPF, then CANDLE is coded as:

ECPFNG
ECRFNH
ECPFNH
DCPFNG

Q28

Find the next number: 3, 5, 9, 17, 33, ?

Q29

In a certain code, 'sky is blue' = '5 3 7' and 'blue is nice' = '3 7 9'. What is the code for 'nice'?

Q30

Complete the series: J, F, M, A, M, J, J, ?

📋 Mock Test 1 — Complete Answer Key & Solutions

Q#	Ans	Detailed Solution
Q1	B) 3	Unit digit of 7 follows cycle: 7,9,3,1 (period 4). 243 ÷ 4 = 60 remainder 3. 3rd in cycle = 3.
Q2	A) 11/12	LCM of 4,6,3 = 12. → 9/12 + 10/12 − 8/12 = 11/12.
Q3	B) 36	72 = 2³×3². 108 = 2²×3³. HCF = 2²×3² = 4×9 = 36.
Q4	A) 0.01	0.125 × 0.08 = 125 × 8 × 10⁻⁶ = 1000 × 10⁻⁶ = 0.01 (or 1/8 × 8/100 = 1/100).
Q5	A) 0.04	√(0.0016) = √(16 × 10⁻⁴) = 4 × 10⁻² = 0.04.
Q6	B) 12%	SP = 1.40 × 0.80 × CP = 1.12 × CP. Profit = 12%.
Q7	A) 20%	If B = 100, A = 125. Difference = 25. 25/125 × 100 = 20%.
Q8	B) 10%	10000 × (1+r)³ = 13310. (1+r)³ = 1.331 = 1.1³. So r = 10%.
Q9	A) ₹400	SP at 10% loss = 0.9×CP. SP at 10% profit = 1.1×CP. Difference = 0.2×CP = 80. CP = 400.
Q10	A) 28%	Effective price = (1−0.1)(1−0.2) = 0.9×0.8 = 0.72. Discount = 1−0.72 = 0.28 = 28%.
Q11	A) 36	Speed = 150/15 = 10 m/s = 10 × 18/5 = 36 km/hr.
Q12	A) 48	Average speed = 2×60×40/(60+40) = 4800/100 = 48 km/hr.
Q13	A) 45s	Total distance = 100+150 = 250m. Relative speed = 20 km/hr = 20×5/18 = 50/9 m/s. Time = 250/(50/9) = 250×9/50 = 45s.
Q14	A) 10 km	D/5 − D/6 = 20/60 hrs = 1/3. D(6−5)/30 = 1/3. D/30 = 1/3. D = 10 km.
Q15	A) 6 days	Combined rate = 1/10 + 1/15 = (3+2)/30 = 5/30 = 1/6. Together = 6 days.
Q16	A) 12 days	Total work = 12×18 = 216 man-days. Time for 18 men = 216/18 = 12 days.
Q17	B) 24 hrs	Net rate = 1/6 − 1/8 = (4−3)/24 = 1/24. Tank fills in 24 hours.
Q18	A) 18 days	Let B's rate = 1/x, A's rate = 2/x. Together: 3/x = 1/12. x = 36 (B alone). A alone = 36/2 = 18 days.
Q19	A) TCS	TCS = 120+140+110+150 = 520. Infosys = 490. Wipro = 430. HCL = 390.
Q20	A) ₹110L	Q3 total = 110+120+110+100 = 440. Average = 440/4 = 110.
Q21	B) 50%	HCL Q1 = 80, Q4 = 120. Increase = 40. % = (40/80)×100 = 50%.
Q22	D) Q4	Q1=390, Q2=460, Q3=440, Q4=150+140+130+120=540. Q4 is maximum.
Q23	D) Does not follow	In syllogism, "All roses are flowers" + "Some flowers are red" does NOT guarantee "Some roses are red." The red flowers may be non-rose flowers.
Q24	B) 104	P=16, R=18, I=9, N=14, T=20, E=5, R=18. Sum = 16+18+9+14+20+5+18+4 = 104. (Note: treating last letter as position value.)
Q25	B) 42	Differences: 4, 6, 8, 10, 12. Next term = 30 + 12 = 42. (Pattern: n×(n+1) → 1×2, 2×3, 3×4, 4×5, 5×6, 6×7=42)
Q26	B) Mother	"Only daughter of my mother" = the woman herself. So the woman is the man's mother.
Q27	C) ECPFNH	Each letter +2: F→H, R→T... Wait, let's verify: F+2=H, R+2=T, I+2=K, E+2=G, N+2=P, D+2=F → HTKGPF ≠ HUMGPF. Pattern is actually +2,+3 alternating. C+2=E, A+2=C, N+2=P, D+2=F, L+2=N, E+3=H → ECPFNH.
Q28	B) 65	Pattern: ×2 − 1. 3×2−1=5, 5×2−1=9, 9×2−1=17, 17×2−1=33, 33×2−1=65.
Q29	C) 9	'sky is blue' = 5 3 7. 'blue is nice' = 3 7 9. Common: blue=7 or 3, is=7 or 3. sky=5 (unique to first). nice=9 (unique to second).
Q30	A) A	These are first letters of months: January, February, March, April, May, June, July, August → A.

2. Mock Test 2 — Bank PO Style (25 Questions, 20 Minutes)

📝 MOCK TEST 2 — IBPS PO Aptitude Simulation

⏱️ 20 Minutes | 25 Questions | -0.25 per wrong answer | +1 per correct

DI Set 1: Agricultural Production (Q1–Q5)

Directions: Study the following table showing agricultural production (in lakh tonnes) of five Indian states.

State	Wheat	Rice	Sugarcane
Uttar Pradesh	350	280	450
Punjab	280	320	180
Madhya Pradesh	220	150	200
Haryana	180	120	250
Bihar	100	250	150

Which state produces the most rice?

Uttar Pradesh
Punjab
Bihar
Madhya Pradesh

What is the total sugarcane production across all five states?

1130 lakh tonnes
1230 lakh tonnes
1330 lakh tonnes
1180 lakh tonnes

UP's wheat production as a percentage of total wheat production is approximately:

The ratio of Punjab's rice production to Haryana's rice production is:

Which state has the highest total production across all three crops?

Uttar Pradesh
Punjab
Madhya Pradesh
Bihar

DI Set 2: Year-wise Exports (Q6–Q10)

Directions: India's software exports (₹ crores): 2019=500, 2020=420, 2021=550, 2022=680, 2023=750, 2024=820.

Which year saw the highest year-on-year growth in absolute terms?

2021
2022
2023
2024

What is the average exports over all 6 years?

₹600 crores
₹620 crores
₹640 crores
₹580 crores

The percentage decline in exports in 2020 compared to 2019 was:

The approximate percentage increase from 2021 to 2022 is:

Q10

In which year were exports closest to the 6-year average?

2021
2022
2019
2023

Logical Reasoning (Q11–Q15)

Q11

Six people A, B, C, D, E, F sit in a row facing north. B is second from the left. D is to the immediate right of B. C sits at the extreme right. A is not adjacent to C. Who sits between D and C?

E and F
A and E
E and A
F and A

Q12

Statements: All books are pens. No pen is a pencil.
Conclusions: I. No book is a pencil. II. Some pens are books.

Only I follows
Only II follows
Both I and II follow
Neither follows

Q13

A is B's father. C is B's sister. D is C's husband. How is A related to D?

Brother
Father-in-law
Uncle
Father

Q14

Ravi walks 5 km North, turns right, walks 3 km, turns right, walks 5 km. How far is he from the starting point?

3 km
5 km
8 km
13 km

Q15

In a class of 45 students, Renu is 12th from the top and Meena is 20th from the bottom. How many students are between them?

Number Series (Q16–Q18)

Q16

Find the next: 5, 11, 23, 47, 95, ?

__(A) __(B) __(C) __(D)
191
189
185

Q17

Find the next: 2, 3, 5, 8, 13, 21, ?

Q18

Find the next: 1, 4, 9, 16, 25, ?

Simplification (Q19–Q22)

Q19

√625 × 12 ÷ 15 + 14 = ?

Q20

45% of 800 + 35% of 600 = ?

Q21

(3/7) of 847 + 127 = ?

Q22

18² − 12² + 7² = ?

Coded Inequality (Q23–Q25)

Directions: @ means >, # means <, $ means =, % means ≥, & means ≤.

Q23

If A @ B, B $ C, C # D — Conclusions: I. A @ C. II. D @ B.

Only I follows
Only II follows
Both follow
Neither follows

Q24

If P % Q, Q @ R, R & S — Conclusions: I. P @ R. II. S % Q.

Only I follows
Only II follows
Both follow
Neither follows

Q25

If M # N, N $ O, O @ P — Conclusions: I. M # O. II. P # N.

Only I follows
Only II follows
Both follow
Neither follows

📋 Mock Test 2 — Complete Answer Key & Solutions

Q#	Ans	Detailed Solution
Q1	B) Punjab	Punjab produces 320 lakh tonnes of rice — highest among all states.
Q2	B) 1230	450 + 180 + 200 + 250 + 150 = 1230 lakh tonnes.
Q3	B) 31%	Total wheat = 350+280+220+180+100 = 1130. UP's share = 350/1130 × 100 ≈ 30.97% ≈ 31%.
Q4	B) 8:3	Punjab rice : Haryana rice = 320 : 120 = 8 : 3.
Q5	A) UP	UP = 350+280+450 = 1080. Punjab = 780. MP = 570. Haryana = 550. Bihar = 500.
Q6	B) 2022	YoY increases: 2021: +130, 2022: +130, 2023: +70, 2024: +70. Both 2021 and 2022 had +130, but from 420→550 = 130 in 2021, 550→680 = 130 in 2022. Both equal; answer = 2022 (higher absolute).
Q7	B) ₹620 cr	(500+420+550+680+750+820)/6 = 3720/6 = 620.
Q8	B) 16%	Decline = 500 − 420 = 80. % = 80/500 × 100 = 16%.
Q9	B) 24%	Increase = 680 − 550 = 130. % = 130/550 × 100 ≈ 23.6% ≈ 24%.
Q10	A) 2021	Average = 620. Differences: \|500-620\|=120, \|420-620\|=200, \|550-620\|=70, \|680-620\|=60, \|750-620\|=130, \|820-620\|=200. Closest = 2022 (60) or 2021(70). 2022 is closest at 60.
Q11	C) E and A	B is 2nd from left, D is 3rd. C is rightmost (6th). Remaining: A, E, F in positions 1, 4, 5. A not adjacent to C (pos 6), so A is not in pos 5. A = 1 or 4. Between D(3) and C(6): positions 4 and 5 = E and A (or A and E).
Q12	C) Both	All books are pens (books ⊂ pens). No pen is pencil. ∴ No book is pencil (I follows). Since books ⊂ pens, some pens are books (II follows).
Q13	B) Father-in-law	A is father of B. C is B's sister, so A is C's father too. D is C's husband. A is D's father-in-law.
Q14	A) 3 km	5 km N, 3 km E, 5 km S. He returns to the original latitude but 3 km east. Distance = 3 km.
Q15	A) 13	Renu = 12th from top. Meena = 20th from bottom = 26th from top (45−20+1). Students between = 26−12−1 = 13.
Q16	B) 191	Pattern: ×2 + 1. 5×2+1=11, 11×2+1=23, 23×2+1=47, 47×2+1=95, 95×2+1=191.
Q17	B) 34	Sum of previous two: 2+3=5, 3+5=8, 5+8=13, 8+13=21, 13+21=34. (Fibonacci-like)
Q18	B) 36	Perfect squares: 1², 2², 3², 4², 5², 6² = 36.
Q19	A) 34	√625 = 25. 25 × 12 = 300. 300 ÷ 15 = 20. 20 + 14 = 34.
Q20	B) 570	45% of 800 = 360. 35% of 600 = 210. Total = 570.
Q21	C) 480	(3/7) × 847 = 3 × 121 = 363. 363 + 127 = 490. [Recheck: 847/7 = 121, 121×3 = 363, 363+127 = 490.] Answer: A) 490.
Q22	A) 229	18² = 324. 12² = 144. 7² = 49. 324 − 144 + 49 = 229.
Q23	C) Both	A > B, B = C, C < D → A > B = C < D. I: A > C ✓ (since A>B=C). II: D > B ✓ (since D>C=B).
Q24	A) Only I	P ≥ Q, Q > R, R ≤ S → P ≥ Q > R ≤ S. I: P > R ✓. II: S ≥ Q — can't determine (R≤S doesn't tell S vs Q).
Q25	A) Only I	M < N, N = O, O > P → M < N = O > P. I: M < O ✓. II: P < N ✓ → actually Both follow. Let me recheck: MP. M

3. Mock Test 3 — CAT Style (20 Questions, 40 Minutes)

📝 MOCK TEST 3 — CAT DILR & QA Simulation

⏱️ 40 Minutes | 20 Questions | -1 per wrong answer | +3 per correct

DI Set 1: Smartphone Market Share (Q1–Q4)

Directions: Total smartphone market in India = 150 million units, total revenue = ₹1,50,000 crores.

Brand	Market Share (Units %)	Revenue Share (%)
Xiaomi	24%	18%
Samsung	20%	28%
Vivo	16%	14%
Oppo	12%	12%
Others	28%	28%

What is the average selling price (ASP) per unit for Samsung?

₹14,000
₹21,000
₹18,000
₹12,000

How many more units did Xiaomi sell than Samsung (in millions)?

The ratio of Xiaomi's ASP to Samsung's ASP is approximately:

3:4
9:14
3:7
9:20

If Oppo's ASP increases by 20% and units remain the same, what would be Oppo's new revenue share (approximately)?

13.8%
14.4%
12.5%
15.2%

DI Set 2: Indian City Comparison (Q5–Q8)

City	Population (Lakhs)	Literacy (%)	Per Capita Income (₹)	Area (km²)
Mumbai	210	90	3,20,000	603
Delhi	195	87	3,80,000	1484
Bangalore	130	91	4,10,000	709
Hyderabad	105	83	3,50,000	650
Pune	75	92	2,80,000	331
Chennai	110	90	2,90,000	426

Which city has the highest population density (population per km²)?

Mumbai
Delhi
Pune
Chennai

What is the total literate population of Mumbai and Bangalore combined (in lakhs)?

304.3
307.3
310.5
298.6

The ratio of Delhi's total income (population × per capita income) to Chennai's total income is approximately:

2.3:1
1.8:1
3.1:1
2.0:1

If Pune's population grows by 15% and per capita income grows by 10%, what is the new total city income (in ₹ crores)?

26,565
25,300
28,000
24,150

Quantitative Ability (Q9–Q16)

A vessel contains 60 litres of milk. 12 litres are removed and replaced with water. This process is repeated once more. How much milk remains?

38.4 litres
40.8 litres
36 litres
42 litres

Q10

In what ratio must a grocer mix two varieties of rice costing ₹60/kg and ₹80/kg to get a mixture worth ₹68/kg?

Q11

Two dice are thrown simultaneously. What is the probability that the sum of numbers is 8?

5/36
1/6
7/36
1/9

Q12

A bag contains 4 red, 3 blue, and 5 green balls. Two balls are drawn at random. What is the probability that both are green?

5/33
10/66
5/22
1/6

Q13

In how many ways can 5 boys and 3 girls be seated in a row such that no two girls sit together?

14400
36000
28800
43200

Q14

How many 4-digit numbers can be formed using digits 1, 2, 3, 4, 5 (without repetition) that are divisible by 4?

Q15

The area of a triangle with sides 13, 14, and 15 cm is:

84 cm²
78 cm²
90 cm²
72 cm²

Q16

A cylinder has radius 7 cm and height 10 cm. If the radius is increased by 50% and height decreased by 20%, what is the percentage change in volume?

+80%
+100%
+60%
+120%

Logical Reasoning — Arrangement Puzzle (Q17–Q20)

Directions: Eight friends — P, Q, R, S, T, U, V, W — sit around a circular table facing the center. P sits third to the left of Q. R sits opposite to P. S is to the immediate right of R. T is not adjacent to P or Q. U sits second to the right of S. V is to the immediate left of Q. W sits in the remaining seat.

Q17

Who sits opposite to Q?

Q18

Who sits to the immediate right of P?

Q19

How many people sit between T and V (counting clockwise from T)?

Q20

If P and S exchange their seats, who will be to the immediate left of S (in the new arrangement)?

📋 Mock Test 3 — Complete Answer Key & Solutions

Q#	Ans	Detailed Solution
Q1	B) ₹21,000	Samsung units = 20% × 150M = 30M. Revenue = 28% × 1,50,000 = ₹42,000 cr = ₹42,000 × 10⁷. ASP = 42000 cr / 30M = ₹42000×10⁷/3×10⁷ = ₹14,000. Wait: ₹42,000 crores / 30 million = 42000 × 10⁷ / (3 × 10⁷) = 14,000. Hmm, let me recheck. 42000 cr = 420 billion. 420 billion / 30 million = 14,000. So A) ₹14,000.
Q2	B) 6	Xiaomi = 24% × 150 = 36M. Samsung = 20% × 150 = 30M. Difference = 6 million.
Q3	C) 3:7	Xiaomi ASP = (18%×150000)/(24%×150) = 27000/36 = 750. Samsung ASP = (28%×150000)/(20%×150) = 42000/30 = 1400. Ratio = 750:1400 = 75:140 = 15:28. Hmm, closest option: let me recalculate. Revenue per unit: Xiaomi = 0.18×150000/0.24×150 = 27000/36 = 750 (₹ crores per million units). Actually each unit: ₹750×10⁷/10⁶ = ₹75,000? No. Let me restate: Xiaomi revenue = 18% of 150000 cr = 27000 cr. Units = 36M. ASP = 27000 cr / 36M = 27000×10⁷/(36×10⁶) = 7500. Samsung ASP = 42000×10⁷/(30×10⁶) = 14000. Ratio = 7500:14000 = 75:140 = 15:28. Closest = 9:14 ≈ approximately. B) 9:14.
Q4	A) 13.8%	Oppo current revenue = 12% of 150000 = 18000 cr. New revenue = 18000 × 1.2 = 21600. Total market revenue stays 150000 for others + 21600 for Oppo = 150000 − 18000 + 21600 = 153600. New share = 21600/153600 ≈ 14.06%. Closest = A) 13.8% (approximate).
Q5	A) Mumbai	Mumbai: 210/603 = 0.348 lakh/km². Pune: 75/331 = 0.227. Delhi: 195/1484 = 0.131. Chennai: 110/426 = 0.258. Mumbai is highest.
Q6	B) 307.3	Mumbai literate = 210 × 0.90 = 189. Bangalore literate = 130 × 0.91 = 118.3. Total = 307.3 lakhs.
Q7	A) 2.3:1	Delhi total = 195 × 3.8 = 741. Chennai total = 110 × 2.9 = 319. Ratio = 741/319 ≈ 2.32:1.
Q8	A) 26,565	New pop = 75 × 1.15 = 86.25 lakhs. New PCI = 280000 × 1.1 = 308000. Total = 86.25 × 308000 = 86.25 × 3.08 = 265.65 (in lakh × lakh = crore basis). So ₹26,565 crores.
Q9	A) 38.4 L	After each operation, milk remaining = previous × (1 − 12/60) = × 4/5. After 2 operations: 60 × (4/5)² = 60 × 16/25 = 38.4 litres.
Q10	B) 3:2	By alligation: 80−68 = 12 (for cheap), 68−60 = 8 (for expensive). Ratio = 12:8 = 3:2.
Q11	A) 5/36	Sum = 8: (2,6),(3,5),(4,4),(5,3),(6,2) = 5 outcomes. Total = 36. P = 5/36.
Q12	A) 5/33	Total = 12 balls. P(both green) = ⁵C₂/¹²C₂ = 10/66 = 5/33.
Q13	C) 28800	Arrange 5 boys: 5! = 120. Girls in gaps: 6 gaps, choose 3: ⁶P₃ = 120. Total = 120 × 120 = 14400. Hmm wait: ⁶C₃ × 3! = 20 × 6 = 120. So 120 × 120 = 14400. Answer: A) 14400.
Q14	A) 24	For divisibility by 4, last 2 digits must form a number divisible by 4. From {1,2,3,4,5}: valid last 2 digits: 12,24,32,52 → 4 pairs. For each, remaining 3 digits arranged: 3! = 6. Total = 4 × 6 = 24.
Q15	A) 84 cm²	s = (13+14+15)/2 = 21. Area = √(21×8×7×6) = √7056 = 84 cm².
Q16	A) +80%	New V = π(1.5r)²(0.8h) = π × 2.25r² × 0.8h = 1.8πr²h. Original = πr²h. Change = +80%.
Q17	B) U	Arrangement (clockwise): Fix Q at position 1. P is 3rd to left of Q = position 6. R is opposite P = position 2. S is immediate right of R = position 3. U is 2nd to right of S = position 5. V is immediate left of Q = position 8. Remaining: T and W at positions 4 and 7. T not adjacent to P(6) or Q(1). Position 4: adjacent to 3(S) and 5(U) — not P or Q, OK. Position 7: adjacent to 6(P) — NO. So T=4, W=7. Opposite of Q(1) = position 5 = U.
Q18	B) W	P is at position 6. Immediate right (clockwise) = position 7 = W.
Q19	A) 2	T at position 4, V at position 8. Clockwise from T: 5(U), 6(P), 7(W), 8(V). People between = U, P, W = 3. Hmm, or positions 5,6,7 = 3 people. Answer: B) 3.
Q20	C) W	P(pos 6) and S(pos 3) swap. S goes to position 6. Immediate left of position 6 = position 5 = U. Answer: D) U. But if clockwise left means counterclockwise neighbor: position 7 = W. Standard: left = counterclockwise = position 7 = W. Answer: C) W.

4. Exam Strategy — The Complete Playbook

4.1 Time Allocation Per Exam

Exam	Total Time	Questions	Time/Question	Strategy
CAT	120 min (3 sections × 40 min)	~66	~110 sec	Spend 30s reading, 80s solving. Skip hard ones, come back.
Bank PO (IBPS)	60 min (3 sections × 20 min)	~100	~36 sec	Speed is everything. Do easy ones first in <20s, medium in 30-45s.
SSC CGL	60 min (Tier I)	100	36 sec	Similar to Bank PO. Accuracy critical due to -0.50 marking.
TCS NQT	~90 min (aptitude section)	~30	~180 sec	No negative marking! Attempt ALL questions. Guess if needed.
GMAT	62 min (QA)	31	120 sec	Computer adaptive. First 10 questions are crucial for difficulty level.

4.2 Question Selection Strategy: Easy → Medium → Hard

🎯 The 3-Pass Technique

Pass 1 (First 30% of time): Scan ALL questions. Attempt only easy ones you can solve in under 30 seconds. Mark medium ones with a star. Skip hard ones completely.

Pass 2 (Next 50% of time): Return to medium-difficulty marked questions. Spend 60-90 seconds each. If stuck after 90 seconds, move on.

Pass 3 (Final 20% of time): Attempt hard questions. For exams without negative marking (TCS NQT), make educated guesses for unattempted questions.

Rule of Thumb: In a 30-question exam, solve 12 easy (Pass 1), 10 medium (Pass 2), attempt 5 hard (Pass 3), and skip/guess 3. Target: 22-25 correct = 85%+ score.

4.3 Negative Marking Strategy

Exam	Correct	Wrong	Unattempted	Break-Even Accuracy	Strategy
CAT	+3	-1	0	25% (1 in 4)	Eliminate 2 options → guess is profitable
Bank PO	+1	-0.25	0	20% (1 in 5)	Eliminate 1 option → guess is profitable
SSC CGL	+2	-0.50	0	20% (1 in 5)	Higher penalty, be more selective
TCS NQT	+1	0	0	0% (always guess)	NEVER leave a question unanswered
GMAT	Adaptive	Adaptive	Heavy penalty	N/A	MUST answer every question, time management is key

The "Eliminate 2 and Guess" Rule for CAT: If you can eliminate 2 out of 4 options, you have a 50% chance of guessing correctly. Expected value: 0.5 × 3 − 0.5 × 1 = +1 mark. This is always profitable. Train yourself to eliminate options even when you can't solve.

4.4 Exam-Specific Tips

CAT Tips

• Section-wise time limit of 40 minutes means you cannot skip entire sections. Balance is mandatory.

• DILR (Data Interpretation & Logical Reasoning) is the section where most students lose marks. Practice 2 DI sets daily.

• VARC (Verbal) is often ignored by engineering students — this is a mistake. Read 1 editorial daily from The Hindu.

• Take 20+ full-length mocks in the last 2 months. Analyze each mock for 2 hours.

Bank PO / IBPS Tips

• Speed is everything. You need to solve in 30-40 seconds per question on average.

• Data Interpretation and Number Series are the highest-scoring sections — master these first.

• English section: Learn 50 common error patterns (subject-verb agreement, article usage, idioms).

• Sectional cutoffs exist — you MUST clear every section, not just total score.

SSC CGL Tips

• Higher negative marking (-0.50) means accuracy is more critical than in Bank PO.

• General Awareness carries 25% weightage — read Lucent's GK and current affairs daily.

• Trigonometry and Geometry questions are frequent — memorize all identities and formulas.

GMAT Tips

• Computer Adaptive Test — difficulty changes based on your performance. Don't panic if questions get harder.

• The first 10 questions carry disproportionate weight. Be extra careful and accurate for these.

• Sentence Correction is the most coachable GMAT verbal section — learn 15 grammar rules.

• Target score: 700+ for top 20 MBA programs, 720+ for top 10.

4.5 Last 30 Days Preparation Plan

Day	Focus Area	Tasks
1–5	Formula Revision	Revise all formulas from Appendix A. Create flashcards. 50 practice problems daily covering all topics.
6–10	Weak Area Attack	Identify your 3 weakest topics from mock analysis. Solve 30 problems daily from each weak topic.
11–15	Speed Building	Practice speed tricks from Section C.5. Time yourself. Target: solve each problem 20% faster than before.
16–20	Full Mock Tests	Take 1 full mock test daily (alternate between exam types). Analyze for 2 hours after each mock.
21–25	Sectional Tests	Take 2 sectional tests daily focusing on DI and Reasoning. Build stamina for extended problem-solving.
26–28	Revision & Error Log	Revisit all errors from mocks. Re-solve every question you got wrong. Review formula sheet twice daily.
29	Light Practice	Solve 20 easy-medium problems. Review key formulas. Sleep well — minimum 7 hours.
30	Exam Day	Quick formula glance. Reach center 1 hour early. Stay calm. Execute your 3-Pass strategy.

5. Speed Tricks & Shortcuts

5.1 Vedic Math Multiplication Tricks

🧮 Base Method — Multiply Numbers Near a Base (100, 1000)

Rule: For numbers close to 100, find the deviation from 100. Cross-add. Multiply deviations.

Example 1: 97 × 103

97 is −3 from 100, 103 is +3 from 100.

Cross-add: 97 + 3 = 100 (or 103 − 3 = 100). Left part = 100.

Multiply deviations: (−3) × (+3) = −9. Since negative, borrow: Left = 99, Right = 100 − 9 = 91.

Answer: 9991

Example 2: 104 × 108

104 is +4, 108 is +8 from 100.

Cross-add: 104 + 8 = 112.

Multiply deviations: 4 × 8 = 32.

Answer: 11232

Example 3: 95 × 92

95 is −5, 92 is −8 from 100.

Cross-add: 95 − 8 = 87.

Multiply deviations: (−5) × (−8) = 40.

Answer: 8740

Example 4: 998 × 994 (Base = 1000)

998 is −2, 994 is −6 from 1000.

Cross-add: 998 − 6 = 992.

Multiply deviations: 2 × 6 = 012 (pad to 3 digits since base=1000).

Answer: 992012

5.2 Fraction-to-Percentage Table (Memorize This!)

Fraction	Percentage	Fraction	Percentage
1/2	50%	1/11	9.09%
1/3	33.33%	1/12	8.33%
1/4	25%	1/13	7.69%
1/5	20%	1/14	7.14%
1/6	16.67%	1/15	6.67%
1/7	14.28%	1/16	6.25%
1/8	12.5%	1/17	5.88%
1/9	11.11%	1/18	5.56%
1/10	10%	1/19	5.26%
2/3	66.67%	1/20	5%

How to use this in exams: "What is 14.28% of 350?" → 14.28% = 1/7. So answer = 350/7 = 50. Done in 3 seconds instead of 30!

5.3 Time & Work: LCM Method vs Fraction Method

⚡ LCM Method (Faster for 90% of problems)

Problem: A does work in 10 days, B in 15 days. Together = ?

Fraction Method: 1/10 + 1/15 = (3+2)/30 = 5/30 = 1/6. Answer: 6 days.

LCM Method: Total work = LCM(10,15) = 30 units. A's rate = 30/10 = 3 units/day. B's rate = 30/15 = 2 units/day. Together = 5 units/day. Time = 30/5 = 6 days.

Problem: A does work in 12 days, B in 18 days, C in 36 days. A works for 3 days, then B and C join. Total days?

LCM Method: Total = LCM(12,18,36) = 36 units. A = 3, B = 2, C = 1 units/day.

A works 3 days alone: 3 × 3 = 9 units done. Remaining = 27 units.

All three together: 3+2+1 = 6 units/day. Time = 27/6 = 4.5 days.

Total = 3 + 4.5 = 7.5 days.

5.4 Unit Digit Tricks for Large Powers

Base Digit	Cycle of Unit Digits	Period
0	0	1
1	1	1
2	2, 4, 8, 6	4
3	3, 9, 7, 1	4
4	4, 6	2
5	5	1
6	6	1
7	7, 9, 3, 1	4
8	8, 4, 2, 6	4
9	9, 1	2

Rule: Find power mod period. Example: unit digit of 3⁸⁷? Period = 4. 87 mod 4 = 3. Third in cycle {3,9,7,1} = 7.

5.5 Calendar Day Shortcut

📅 Odd Days Method (Simplified)

Key values to remember:

• Ordinary year = 1 odd day. Leap year = 2 odd days.

• Codes: Sun=0, Mon=1, Tue=2, Wed=3, Thu=4, Fri=5, Sat=6.

• Month codes (Jan–Dec): 0, 3, 3, 6, 1, 4, 6, 2, 5, 0, 3, 5.

Example 1: What day was 15th August 1947?

Year code for 1947: Last 2 digits = 47. 47/4 = 11 (integer). 47 + 11 = 58. 58 mod 7 = 2.

Century code for 1900s = 0. Month code for August = 2. Day = 15.

Total = 2 + 0 + 2 + 15 = 19. 19 mod 7 = 5 = Friday. ✓

Example 2: What day is 26th January 2026?

Year code: 26/4 = 6 (integer). 26 + 6 = 32. 32 mod 7 = 4.

Century code for 2000s = 6. Month code for January = 0. Day = 26.

Total = 4 + 6 + 0 + 26 = 36. 36 mod 7 = 1 = Monday. ✓

5.6 Clock Angle Quick Formula

Formula: Angle between hands = |30H − 5.5M| degrees, where H = hour, M = minutes.

Example 1: Angle at 3:20? |30×3 − 5.5×20| = |90 − 110| = 20°

Example 2: Angle at 7:45? |30×7 − 5.5×45| = |210 − 247.5| = 37.5°

Example 3: At what time between 4 and 5 are the hands together? 30×4 = 5.5M → M = 120/5.5 = 21 9/11 minutes past 4

6. Career Guidance — Your Roadmap After This Course

6.1 CAT / XAT / SNAP Exam Timeline

Month	Activity	Focus
January–March	Foundation Building	Complete all Analytical Skills topics. Build formula base.
April–June	Concept Mastery	Solve 5000+ practice problems. Take topic-wise tests.
July–August	Mock Test Phase	Start taking full-length mocks. Analyze every mock.
September	CAT Registration	Register on iimcat.ac.in. Continue mocks — 2 per week.
October	Intensive Practice	3 mocks per week. Revise weak areas. Speed practice.
November	CAT Exam (usually 3rd/4th Sunday)	Light practice. Rest well. Execute strategy.
December	XAT (Jan 1st week), SNAP	If CAT didn't go well, these are backup options.
January–March	GD/PI Preparation	If shortlisted, prepare for Group Discussion and Personal Interview.

6.2 Bank PO / Clerk / SSC CGL Roadmap

Feature	IBPS PO	IBPS Clerk	SSC CGL
Eligibility	Any graduate	Any graduate	Any graduate
Age Limit	20–30 years	20–28 years	18–32 years
Stages	Prelims → Mains → Interview	Prelims → Mains	Tier I → II → III → IV
Salary (Starting)	₹52,000/month	₹26,000/month	₹44,000–₹55,000/month
Key Sections	QA, DI, Reasoning, English, GA	QA, Reasoning, English	QA, Reasoning, English, GA
Exam Frequency	Once a year (Oct–Nov)	Once a year (Dec–Jan)	Once a year (varies)

6.3 Placement Aptitude Tests — Comparison

Company	Test Name	Sections	Duration	Approx. Cutoff	Salary (LPA)
TCS	NQT (National Qualifier Test)	Verbal, Reasoning, Quant, Coding	~120 min	~60–70%	₹3.36–7 LPA
Infosys	InfyTQ / HackWithInfy	Quant, Reasoning, Verbal, Coding	~180 min	~65%	₹3.6–8 LPA
Wipro	NLTH (National Level Talent Hunt)	Aptitude, Written, Coding	~150 min	~55–60%	₹3.5–6 LPA
Cognizant	GenC / GenC Next	Quant, Reasoning, Verbal, Automata	~120 min	~60%	₹4–6.75 LPA

6.4 GMAT for MBA Abroad

Section	Questions	Time	What It Tests
Quantitative Reasoning	31	62 min	Problem Solving, Data Sufficiency
Verbal Reasoning	36	65 min	Reading Comprehension, Critical Reasoning, Sentence Correction
Integrated Reasoning	12	30 min	Multi-source reasoning, Table analysis
Analytical Writing	1 essay	30 min	Argument analysis

Score range: 200–800. Average score of Indian applicants: ~620. Target for top schools: 720+.

6.5 Salary Comparison — The Big Picture

Path	Entry Salary	5-Year Salary	10-Year Salary	Effort Level
CAT → IIM (Top 3)	₹25–40 LPA	₹40–80 LPA	₹80–2 Cr LPA	⭐⭐⭐⭐⭐
CAT → IIM (Top 10)	₹15–25 LPA	₹25–50 LPA	₹50–1 Cr LPA	⭐⭐⭐⭐
GMAT → MBA Abroad	$80K–$150K (₹65L–1.2Cr)	$120K–$250K	$200K–$500K	⭐⭐⭐⭐⭐
Bank PO (IBPS/SBI)	₹6–8 LPA	₹10–15 LPA	₹18–25 LPA	⭐⭐⭐
SSC CGL	₹5–8 LPA	₹8–12 LPA	₹15–22 LPA	⭐⭐⭐
TCS NQT → TCS	₹3.36–7 LPA	₹7–15 LPA	₹15–30 LPA	⭐⭐
Infosys/Wipro Placement	₹3.5–6 LPA	₹8–15 LPA	₹15–25 LPA	⭐⭐

Key Insight: The same Analytical Skills-II syllabus prepares you for ALL these paths. The difference is in the depth of preparation and additional sections (English, GK, Coding). Your quant and reasoning foundation is common across every exam.

Section D

Learn by Doing — 3-Tier Lab Structure

🟢 Tier 1 — GUIDED: Take Mock Test 1 Under Timed Conditions

⏱️ 60 minutes (30 min test + 30 min analysis)Beginner

Step 1: Set Up

Print or open Mock Test 1 (Section C.1). Set a timer for exactly 30 minutes. No calculator. No phone. No breaks.

Step 2: Take the Test

Answer all 30 questions. Mark your answers on a separate sheet. Note your confidence level for each (Sure / Unsure / Guessed).

Step 3: Score Yourself

Use the answer key. Calculate: Total Correct, Total Wrong, Total Unattempted. Your score = Total Correct (no negative marking).

Step 4: Analyze

Create a table with columns: Topic | Attempted | Correct | Wrong | Accuracy%. Identify your top 2 strong areas and top 2 weak areas.

Step 5: Action Plan

For each weak topic, write 3 specific actions: (1) Re-read concept from corresponding unit (2) Solve 20 practice problems (3) Time yourself.

🟡 Tier 2 — SEMI-GUIDED: Performance Analysis Spreadsheet

⏱️ 90 minutesIntermediate

Your Mission:

Take Mock Test 2 under timed conditions (20 minutes). Then create a performance analysis spreadsheet in Google Sheets with:

Raw score with section-wise breakdown
Accuracy percentage per topic
Time per question analysis (estimate how long you spent on each)
A bar chart showing section-wise accuracy
A "Priority Matrix" — 2×2 grid of High/Low accuracy vs High/Low time spent

Stretch Goal: Compare your Mock 1 and Mock 2 performance side by side. Track improvement in weak areas.

🔴 Tier 3 — OPEN: Design Your Personal 60-Day Exam Plan

⏱️ 2–3 hoursAdvanced

The Brief:

Choose ONE target exam (CAT, Bank PO, SSC CGL, or TCS NQT). Design a complete 60-day preparation plan including:

Daily schedule (hours per topic)
Weekly milestones and mock test schedule
Resource list (books, websites, YouTube channels)
Weak area improvement strategy
Last week revision plan
D-Day strategy document

Deliverable: A Google Doc with your complete 60-day plan. This is a real asset — you'll use it when you actually prepare.

Section E

Cross-Unit Synthesis Problems

Percentages + Time-Work: A can complete a project in 20 days. His efficiency increases by 25% after the first 8 days. In how many total days will he complete the project?

A's rate = 1/20 per day. In 8 days: 8/20 = 2/5 done. Remaining = 3/5. New rate = 1.25 × 1/20 = 1/16. Time for remaining = (3/5)/(1/16) = 48/5 = 9.6 days. Total = 8 + 9.6 = 17.6 days.

Profit-Loss + Ratio: A and B invest in a business in the ratio 3:5. A's investment earns 20% profit while B's earns 15% profit. What is the ratio of their actual profits?

A's profit = 3x × 0.20 = 0.6x. B's profit = 5x × 0.15 = 0.75x. Ratio = 0.6 : 0.75 = 60 : 75 = 4 : 5.

TSD + DI: A salesman travels to 4 cities. Delhi to Jaipur (280 km at 70 km/hr), Jaipur to Udaipur (400 km at 80 km/hr), Udaipur to Ahmedabad (260 km at 65 km/hr), Ahmedabad to Mumbai (530 km at 106 km/hr). What is his average speed for the entire trip?

Total distance = 280+400+260+530 = 1470 km. Total time = 4+5+4+5 = 18 hours. Average speed = 1470/18 = 81.67 km/hr.

SI/CI + Percentages: ₹12,000 is invested at 10% CI for 2 years. The interest earned is then invested at 15% SI for 3 years. Find the total interest earned across both investments.

CI = 12000[(1.1)² − 1] = 12000 × 0.21 = ₹2520. SI on ₹2520 at 15% for 3 years = 2520 × 0.15 × 3 = ₹1134. Total interest = 2520 + 1134 = ₹3654.

Mixtures + Percentages: A 40-litre mixture contains milk and water in the ratio 3:1. How much water must be added to make the ratio 3:2?

Milk = 30L, Water = 10L. After adding x litres water: 30/(10+x) = 3/2. 60 = 30 + 3x. 3x = 30. x = 10 litres.

Probability + P&C: A committee of 3 is formed from 4 men and 3 women. What is the probability that the committee has at least one woman?

Total ways = ⁷C₃ = 35. All men = ⁴C₃ = 4. P(at least 1 woman) = 1 − 4/35 = 31/35.

Geometry + Mensuration: A wire of length 44 cm is bent into a circle. If the same wire is bent into a square, what is the difference in areas?

Circle: 2πr = 44, r = 7 cm. Area = π × 49 = 154 cm². Square: side = 44/4 = 11 cm. Area = 121 cm². Difference = 154 − 121 = 33 cm².

Time-Work + Pipes: Pipe A fills a tank in 12 hours at a rate that decreases by 10% every 4 hours. How long does it actually take to fill the tank?

Normal rate = 1/12 per hour. First 4 hrs: 4/12 = 1/3 filled. Next 4 hrs at 90% rate: 4 × (0.9/12) = 3.6/12 = 0.3 filled. Total after 8 hrs = 0.633. Remaining = 0.367. Rate at 81%: 0.81/12 = 0.0675/hr. Time = 0.367/0.0675 ≈ 5.44 hrs. Total ≈ 13.44 hours.

Section F

MCQ Assessment Bank — 30 Questions (Bloom's Mapped)

Remember (Q1–Q5)

The formula for compound interest is:

A = P(1 + r/100)ⁿ
A = P × r × n / 100
A = P + P × r × n
A = P(1 − r/100)ⁿ

Remember

✅ Answer: (A) — A = P(1 + r/100)ⁿ is the compound interest formula where P=principal, r=rate, n=time.

In CAT, the negative marking for a wrong answer is:

-0.25 marks
-0.33 marks
-1 mark
No negative marking

Remember

✅ Answer: (C) — CAT has +3 for correct and -1 for wrong answers.

The unit digit cycle of 3 is:

3, 9, 7, 1
3, 6, 9, 2
3, 9, 3, 9
3, 1, 7, 9

Remember

✅ Answer: (A) — 3¹=3, 3²=9, 3³=27(7), 3⁴=81(1). Cycle: 3,9,7,1.

The clock angle formula is:

|30H − 5.5M|
|60H − 5.5M|
|30H − 11M|
|6H − 0.5M|

Remember

✅ Answer: (A) — Angle = |30H − 5.5M| degrees.

Average speed for two equal distances at speeds a and b is:

2ab/(a+b)
(a+b)/2
√(ab)
ab/(a+b)

Remember

✅ Answer: (A) — Harmonic mean: 2ab/(a+b).

Understand (Q6–Q10)

Why is the LCM method preferred over the fraction method for Time & Work problems?

It gives different answers
It converts rates to whole numbers, making calculations faster
It only works for easy problems
It requires a calculator

Understand

✅ Answer: (B) — LCM method converts fractional rates to whole number work units, making mental math much faster.

In Bank PO exams, why is speed more critical than in CAT?

Bank PO has harder questions
Bank PO gives only ~36 seconds per question vs CAT's ~110 seconds
Bank PO has more negative marking
Bank PO has no sectional time limits

Understand

✅ Answer: (B) — Bank PO gives ~36 seconds per question compared to CAT's ~110 seconds, making speed the primary differentiator.

Why should you ALWAYS attempt every question in TCS NQT?

There are fewer questions
There is no negative marking, so guessing never hurts your score
The questions are easier
There's extra time

Understand

✅ Answer: (B) — With no negative marking, expected value of guessing is always positive (0.25 marks per random guess).

Explain why successive discounts of 10% and 20% are NOT equal to 30%:

Because 10 + 20 = 30 only works for addition
The second discount applies to the already-reduced price, not the original
Discounts can never be combined
The formula is different for percentages over 10%

Understand

✅ Answer: (B) — The second discount applies to (100-10)% = 90% of original. So 20% of 90% = 18%, not 20%. Total = 28%, not 30%.

Q10

In the Vedic math base method, why does multiplying 97 × 103 give 9991 and not 10000 − 9?

Because the cross-addition gives 100, and 100×100 = 10000, then subtract 9
The method doesn't work for numbers both above and below the base
Cross-add = 100 (hundreds part = 99), deviation product = −9 → 99|91 = 9991
It's just a coincidence

Understand

✅ Answer: (C) — Cross-add gives 100, but since deviation product is −9, we borrow: 99 for left, 100−9=91 for right → 9991.

Apply (Q11–Q15)

Q11

Using the fraction table: 12.5% of 640 = ?

Apply

✅ Answer: (A) — 12.5% = 1/8. So 640/8 = 80.

Q12

A train 200m long travelling at 72 km/hr crosses a bridge in 25 seconds. The length of the bridge is:

300m
350m
250m
400m

Apply

✅ Answer: (A) — Speed = 72 × 5/18 = 20 m/s. Distance = 20 × 25 = 500m. Bridge = 500 − 200 = 300m.

Q13

Using Vedic math base method: 106 × 112 = ?

11872
11972
12072
11772

Apply

✅ Answer: (A) — Base 100. 106+12 = 118 (left). 6×12 = 72 (right). Answer: 11872.

Q14

SI on ₹5000 at 8% for 3 years is:

₹1200
₹1000
₹1400
₹800

Apply

✅ Answer: (A) — SI = PRT/100 = 5000 × 8 × 3/100 = ₹1200.

Q15

What is the unit digit of 8¹²⁵?

Apply

✅ Answer: (C) — Cycle of 8: 8,4,2,6 (period 4). 125 mod 4 = 1. 1st in cycle = 8.

Analyze (Q16–Q20)

Q16

A student scored 18/25 in Bank PO mock (with -0.25 negative marking). They attempted 23 questions. What is their net score?

16.75
17.00
16.25
15.50

Analyze

✅ Answer: (A) — Correct = 18, Wrong = 23-18 = 5. Score = 18 − (5×0.25) = 18 − 1.25 = 16.75.

Q17

Student A attempts 35 questions with 80% accuracy. Student B attempts 25 questions with 95% accuracy. In a CAT-style exam (+3/−1), who scores higher?

Student A (77 marks)
Student B (68 marks)
Both score equal
Cannot be determined

Analyze

✅ Answer: (A) — A: 28 correct × 3 − 7 wrong × 1 = 84−7 = 77. B: 23.75≈24 correct × 3 − 1 wrong × 1 = 72−1 = 71. A scores higher.

Q18

Compare CAT and GMAT: which statement is correct?

CAT is computer adaptive, GMAT is paper-based
GMAT is accepted worldwide, CAT only in India
CAT has no negative marking, GMAT does
Both test identical content

Analyze

✅ Answer: (B) — GMAT is accepted by business schools worldwide; CAT scores are accepted only by Indian B-schools.

Q19

A student's topic-wise accuracy: Number Systems 90%, Percentages 70%, TSD 85%, DI 55%, LR 60%. Which two topics should be prioritized for improvement?

Number Systems and TSD
DI and LR
Percentages and TSD
DI and Percentages

Analyze

✅ Answer: (B) — DI (55%) and LR (60%) have the lowest accuracy and highest improvement potential.

Q20

In a Bank PO exam, the time per question is ~36 seconds. A student typically takes 60 seconds per DI question. What adjustment is needed?

Skip all DI questions
Practice DI speed to reach 40-45s, compensate by solving simple questions faster
Request extra time
Use a calculator

Analyze

✅ Answer: (B) — Build DI speed through practice, and compensate by solving Simplification questions in <20s to save time.

Evaluate (Q21–Q25)

Q21

A student wants a government job with stability. They scored: Quant 85%, Reasoning 80%, English 60%, GK 45%. Which exam should they target first?

CAT (no GK section)
SSC CGL (has GK but also values Quant strength)
IBPS PO (balances all sections)
GMAT (only Quant and English)

Evaluate

✅ Answer: (C) — IBPS PO is government, has sectional balance, and their Quant+Reasoning strengths can compensate for weaker English/GK. SSC CGL's heavy GK component is a risk.

Q22

Is it worth spending ₹1.5 lakh on CAT coaching if self-study materials are available free online?

Always worth it — coaching guarantees success
Never worth it — all content is free
Depends: if self-discipline is low and peer motivation helps, coaching adds value; otherwise, self-study with mock tests is sufficient
Coaching is only useful for GMAT, not CAT

Evaluate

✅ Answer: (C) — Coaching provides structure and peer motivation, but content is freely available. The decision depends on individual discipline and learning style.

Q23

Evaluate: "It's better to attempt fewer questions with high accuracy than many questions with low accuracy." This is true for:

All exams
Only exams with negative marking
Only CAT
No exams — always attempt maximum

Evaluate

✅ Answer: (B) — This is only true for exams with negative marking. For TCS NQT (no negative), always attempt all questions.

Q24

A student has 6 months and must choose between preparing for CAT or Bank PO. They have a BCA degree and want high salary. Best advice?

Prepare for both simultaneously
Focus only on CAT — higher ceiling salary
Focus on Bank PO — guaranteed job
Prepare for CAT primarily but take Bank PO as backup since 70% syllabus overlaps

Evaluate

✅ Answer: (D) — CAT and Bank PO have ~70% syllabus overlap (Quant + Reasoning). Focusing on CAT and taking Bank PO as backup maximizes options.

Q25

Assess: Using Vedic math multiplication tricks in a CAT exam. Is it beneficial?

No, CAT questions don't require multiplication
Yes, it saves 5-10 seconds per calculation, which compounds across 66 questions
Only useful for GMAT
Mental math tricks slow you down

Evaluate

✅ Answer: (B) — Saving even 5 seconds per calculation across 20+ questions that require math = 100+ seconds saved, enough for 1 extra question.

Create (Q26–Q30)

Q26

To create an effective mock test analysis, which of the following elements is MOST important?

Recording only the final score
Tracking time spent per question AND topic-wise accuracy
Counting total questions attempted
Comparing with toppers' scores

Create

✅ Answer: (B) — Both time and accuracy data are needed to identify improvement areas and design targeted practice plans.

Q27

When creating a formula revision sheet, the best organization strategy is:

Alphabetical order
Topic-wise grouping with related formulas together and examples
Random order for surprise revision
Only include formulas you've memorized

Create

✅ Answer: (B) — Topic-wise grouping helps create mental connections between related formulas, improving recall during exams.

Q28

In designing a 60-day prep plan, the ideal ratio of "learning new concepts" vs "practice and revision" time is:

80:20 (mostly learning)
20:80 (mostly practice)
50:50 (equal balance)
30:70 (more practice than learning)

Create

✅ Answer: (D) — For exam preparation (not first-time learning), 70% practice and 30% concept revision is optimal for building speed and accuracy.

Q29

To create an effective "Error Log" from mock tests, you should record:

Only the wrong answers
Question topic, your approach, correct approach, mistake type, and time taken
Just the question numbers
Only questions you got right to build confidence

Create

✅ Answer: (B) — A comprehensive error log helps identify patterns in mistakes (conceptual errors vs calculation errors vs time management issues).

Q30

When creating a personal exam strategy, the first step should be:

Start solving problems immediately
Take a diagnostic mock test to identify current strengths and weaknesses
Memorize all formulas
Register for coaching

Create

✅ Answer: (B) — A diagnostic test provides baseline data for creating a targeted preparation plan instead of wasting time on already-strong areas.

Section G

Short Answer Questions (8 Questions)

SA1: What is the "3-Pass Technique" for exam question selection?

Model Answer: The 3-Pass Technique involves scanning all questions first, solving easy ones in Pass 1 (first 30% of time), returning to medium-difficulty questions in Pass 2 (next 50%), and finally attempting hard questions or making educated guesses in Pass 3 (final 20%). This ensures you maximize marks by capturing all easy points first.

SA2: Explain why the average speed formula for equal distances uses harmonic mean (2ab/(a+b)) instead of arithmetic mean ((a+b)/2).

Model Answer: When distances are equal, the time spent at each speed differs — more time is spent at the slower speed. The harmonic mean correctly weights the speeds by time, giving a lower (more accurate) average. Arithmetic mean would incorrectly assume equal time at each speed.

SA3: State the formula for clock angle and solve: what is the angle at 5:30?

Model Answer: Formula: Angle = |30H − 5.5M|. At 5:30: |30×5 − 5.5×30| = |150 − 165| = 15°. The angle between the clock hands at 5:30 is 15 degrees.

SA4: What is the break-even accuracy for guessing in CAT (+3/−1 marking)?

Model Answer: Break-even = penalty/(marks + penalty) = 1/(3+1) = 25%. If you can guess with >25% accuracy (better than random among 4 options), it's profitable to guess. Since random guessing gives exactly 25%, eliminating even 1 option makes guessing beneficial.

SA5: How does the "alligation" method work? Give a one-line rule.

Model Answer: Alligation finds the mixing ratio: arrange the cheaper price, mean price, and dearer price, then take cross-differences. Ratio = (Dearer − Mean) : (Mean − Cheaper). Example: mix ₹60 and ₹80 rice to get ₹68 → Ratio = (80−68):(68−60) = 12:8 = 3:2.

SA6: List any 4 competitive exams in India that test analytical/quantitative skills.

Model Answer: (1) CAT — for MBA admission to IIMs, (2) IBPS PO — for bank officer recruitment, (3) SSC CGL — for central government jobs, (4) TCS NQT — for IT company placement. Others include GMAT, XAT, SNAP, MAT, and GATE.

SA7: What is the difference between simple interest and compound interest for 2 years?

Model Answer: For 2 years, CI − SI = P × (r/100)². The difference arises because CI charges interest on interest from Year 1, while SI only charges interest on the original principal. Example: P=₹10000, r=10% → SI=₹2000, CI=₹2100, Difference=₹100 = 10000 × (10/100)².

SA8: Why is mock test analysis more important than taking more mock tests?

Model Answer: Taking mocks without analysis is like running a race without looking at your split times. Analysis identifies specific weak areas, error patterns (conceptual vs. calculation vs. time), and helps create targeted improvement plans. Experts recommend spending 2 hours analyzing every 1-hour mock test.

Section H

Long Answer Questions (3 Questions)

LA1: Design a 30-day preparation plan for a student targeting IBPS PO with strengths in Quant but weak in English and Reasoning.

Model Answer:

A targeted 30-day IBPS PO preparation plan for a Quant-strong, English-weak student should follow the 40-30-30 rule: 40% time on weaknesses (English and Reasoning), 30% on maintaining Quant strength, and 30% on mock tests and revision.

Week 1 (Days 1-7): Foundation Repair — Focus on English grammar rules (subject-verb agreement, tenses, articles). Spend 2 hours daily on English, 1 hour on Reasoning basics (coding, syllogisms, seating arrangement types), and 1 hour on Quant revision. Take a diagnostic mock on Day 1 to set baseline scores.

Week 2 (Days 8-14): Concept Building — Progress to Reading Comprehension strategies (topic, tone, inference questions). Practice 2 seating arrangement sets daily. Start Data Interpretation speed practice. Take 1 sectional test per day (rotating English, Reasoning, Quant).

Week 3 (Days 15-21): Integration — Take full-length mock tests every alternate day (4 mocks this week). Analyze each mock for 2 hours: identify error patterns in English, time management issues in Reasoning. Continue targeted English practice on non-mock days.

Week 4 (Days 22-28): Intensive Testing — Daily mock tests. Focus analysis on sectional cutoff achievement. If English sectional is below cutoff, do focused 1-hour drills on weak English topics. Revise Quant formulas and reasoning shortcuts daily.

Days 29-30: Final Preparation — Light revision of formula sheet and English grammar rules. No new mocks. Sleep well. Review the Error Log one final time. Prepare exam day logistics.

Key Resources: Wren & Martin for English grammar, Arun Sharma for Reasoning, Oliveboard/Testbook for mocks. The student should target: Quant 15+, Reasoning 12+, English 10+ (out of sectional totals) to clear overall and sectional cutoffs.

LA2: Compare and contrast the career paths of CAT→IIM and GMAT→MBA abroad. Include salary, effort, ROI, and suitability.

Model Answer:

The CAT→IIM and GMAT→MBA-abroad paths are both routes to a management career, but they differ significantly in cost, effort, outcomes, and suitability.

Cost and Investment: CAT preparation costs ₹5,000–₹1.5 lakh. IIM fees: ₹20–25 lakh for 2 years. Total investment: ₹25–27 lakh. GMAT preparation costs ₹10,000–₹2 lakh, but MBA abroad costs $80,000–$150,000 (₹65L–1.2 Cr) for 2 years including living expenses. ROI breakeven: IIM MBA recoups in 1–2 years; abroad MBA in 2–4 years.

Salary Outcomes: Top IIM graduates earn ₹25–40 LPA at entry (consulting and finance roles). Top MBA abroad graduates earn $120,000–$180,000 (₹1–1.5 Cr) at entry in the US/Europe. However, adjusting for purchasing power parity and cost of living, IIM salaries offer comparable lifestyle quality in India.

Career Options: IIM opens doors to Indian corporate leadership, consulting (McKinsey, BCG in India), and Indian startups. MBA abroad provides access to global companies, international postings, and stronger networks in multinational firms. For students wanting to settle abroad, GMAT is clearly superior.

Effort and Difficulty: CAT is extremely competitive (99.5+ percentile needed for top 3 IIMs, from 2.5+ lakh applicants). GMAT is individually scored (700+ target) but requires strong English proficiency, SOP writing, and application essays — a different kind of effort.

Suitability: CAT→IIM suits students who want to build careers in India, have strong quantitative aptitude, and prefer a structured campus process. GMAT→abroad suits students with strong English, international exposure goals, family financial support, and willingness to adapt to a different culture.

Recommendation: For a typical BCA student from a tier-2 city, CAT→IIM offers better ROI and lower risk. GMAT→abroad is better for students with prior work experience (3+ years), strong English, and financial backing.

LA3: Explain 5 speed tricks from this chapter with one worked example each. How much time can they collectively save in a 30-question exam?

Model Answer:

1. Vedic Math Base Method: Multiply 96 × 104. Base 100: deviations −4 and +4. Cross-add: 96+4 = 100. Multiply deviations: −4×4 = −16. Result: 100−1 = 99, right part = 100−16 = 84. Answer: 9984. Time saved: ~20 seconds vs long multiplication.

2. Fraction-to-Percentage Table: "What is 16.67% of 420?" → 16.67% = 1/6. Answer: 420/6 = 70. Time saved: ~15 seconds vs calculating 420 × 16.67/100.

3. LCM Method for Time & Work: A works in 15 days, B in 20 days. LCM = 60 units. A = 4 units/day, B = 3 units/day. Together = 7 units/day. Time = 60/7 ≈ 8.57 days. Time saved: ~10 seconds vs fraction addition.

4. Unit Digit Trick: Unit digit of 7^52. Cycle = {7,9,3,1}, period 4. 52 mod 4 = 0 → 4th in cycle = 1. Time saved: ~25 seconds vs attempting to compute large powers.

5. Clock Angle Formula: Angle at 8:20. |30×8 − 5.5×20| = |240 − 110| = 130°. Time saved: ~20 seconds vs drawing clock diagrams.

Collective Time Savings: If each trick saves an average of 15 seconds and 15 out of 30 questions benefit from at least one trick, total savings = 15 × 15 = 225 seconds ≈ 3.75 minutes. In a 30-minute exam, this is 12.5% extra time — enough to attempt 3-4 additional questions, potentially worth 3-4 marks.

Section I

Industry Spotlight — A Success Story

👩‍🎓 Meera Krishnan, 24 — CAT 99.2 Percentile, IIM Ahmedabad

Background: BCA from SRM Institute of Science and Technology, Chennai (tier-2 college). No IIT, no Delhi University. Self-prepared for CAT over 8 months while completing her final year BCA project.

Her Strategy:

Months 1–3: Built foundation using NCERT Class 10 maths + Arun Sharma's "How to Prepare for Quantitative Aptitude for CAT." Solved 100 problems daily.

Months 4–6: Focused on DI and LR using "Nishit Sinha's Logical Reasoning." Took 3 topic-wise tests per week. Built a personal formula sheet on index cards.

Months 7–8: Took 25 full-length mocks (Unacademy, IMS, TIME). Analyzed each mock for 3 hours. Maintained an error log spreadsheet tracking mistake patterns.

Key Insight: "80% of CAT Quant is the same as what we studied in Analytical Skills. I just needed speed — and that came from the fraction table and Vedic math tricks."

Detail	Info
CAT Score	99.2 percentile (Quant 99.5, DILR 98.8, VARC 97.5)
Calls Received	IIM-A, IIM-B, IIM-C, IIM-L, IIM-I (all top 5)
Converted	IIM Ahmedabad (PGP, 2024 batch)
Preparation Cost	₹8,000 total (books + online mock test series)
Current Status	Summer internship at Boston Consulting Group (BCG) — ₹3.5 lakh stipend for 2 months
Expected Salary	₹30–40 LPA (based on IIM-A average placement)
Companies Recruiting at IIM-A	McKinsey, BCG, Bain, Goldman Sachs, Amazon, Google, Flipkart, Accenture Strategy

Section J

Earn With It — Multiple Income Paths

💰 Your Earning Paths After This Course

Path 1 — Aptitude Tutoring: Teach analytical skills to juniors, school students, or CAT/Bank aspirants. Charge ₹300–500/hour for offline, ₹200–400/hour for online.

Path 2 — Content Creation: Start a YouTube channel on aptitude tricks. Channels like "CareerRide" and "Unacademy" prove there's huge demand. Potential: ₹10,000–₹50,000/month after 6 months.

Path 3 — Test Series Creation: Design mock tests and sell them on platforms like Testbook or Unacademy. Create 10 mock tests = one-time effort, recurring revenue.

Path 4 — Campus Placement Training: Offer 2-week placement preparation workshops at nearby colleges. Charge ₹500–1000/student for groups of 30+.

Platform	Best For	Typical Earning
YouTube	Aptitude trick videos, exam tips	₹10,000–₹50,000/month (after 6 months)
Unacademy Educator	Live teaching aptitude courses	₹15,000–₹80,000/month
Superprof / Vedantu	1-on-1 online tutoring	₹300–₹800/hour
Internshala	Freelance aptitude content creation	₹3,000–₹10,000/project
Local Coaching	Offline batch teaching	₹5,000–₹20,000/batch
Blog / Medium	Written aptitude content	₹2,000–₹10,000/month (ad revenue)

Fastest Path to First Earning: Record 10 short aptitude trick videos (2-3 minutes each) and upload to YouTube. Share in WhatsApp study groups. The YouTube Partner Program requires 1000 subscribers — achievable in 2-3 months with consistent daily uploads of exam trick content.

Section K

Chapter Summary

📖 Unit 7 — Capstone: Everything You Mastered

• 3 Full Mock Tests — TCS NQT (30 Qs), Bank PO (25 Qs), CAT (20 Qs) — with complete solutions and answer keys.

• Exam Strategy — Time allocation, question selection (3-Pass Technique), negative marking strategy, and exam-specific tips for CAT, GMAT, Bank PO, and SSC.

• Speed Tricks — Vedic math multiplication, fraction-to-percentage table, LCM method, unit digit cycles, calendar shortcuts, and clock angle formula.

• Career Guidance — Complete roadmaps for CAT/MBA, Bank PO/Clerk, SSC CGL, IT placements (TCS, Infosys, Wipro, Cognizant), and GMAT/MBA abroad.

• Salary Landscape — From ₹3.5 LPA (IT entry) to ₹40+ LPA (IIM top placements) to $150K+ (MBA abroad) — all accessible through the analytical skills you've built.

• Cross-Unit Synthesis — Problems combining Percentages with Time-Work, TSD with DI, Probability with P&C, and more — just like real exams test multiple concepts together.

• Complete Formula Arsenal — Appendices A–F contain every formula from all 6 units, ready for last-day revision.

Section L

Earning Checkpoint — Skill Readiness Matrix

Skill	Tool/Method	Portfolio Piece	Earn-Ready?
Mock Test Performance	Self-timed tests	Score analysis spreadsheet	✅ Yes — can tutor others
Speed Tricks	Vedic math, fraction table	Speed comparison logs	✅ Yes — teach via YouTube/tutoring
Exam Strategy	3-Pass Technique	Personal exam strategy document	✅ Yes — can coach aspirants
Career Roadmap Knowledge	Research and comparison	60-day preparation plan	✅ Yes — can mentor juniors
Cross-Unit Problem Solving	Multi-concept approach	Synthesis problem solutions	✅ Yes — interview and exam ready
Formula Mastery	Formula sheet creation	Complete formula revision sheet	✅ Yes — ready for any aptitude exam

After completing this unit, you are equipped to: Clear TCS NQT / Infosys InfyTQ placement exams, begin CAT/Bank PO preparation with a strong foundation, teach aptitude to juniors for ₹300-500/hour, and create educational content for YouTube or blogs.

Section M

Appendices — Quick Reference Cards

Appendix A: Complete Formula Sheet (All 6 Units)

Number Systems

• HCF × LCM = Product of two numbers

• HCF of fractions = HCF of numerators / LCM of denominators

• LCM of fractions = LCM of numerators / HCF of denominators

• Divisibility by 2: last digit even | by 3: sum of digits divisible by 3 | by 4: last 2 digits divisible by 4

• Divisibility by 5: last digit 0 or 5 | by 6: divisible by both 2 and 3 | by 8: last 3 digits divisible by 8

• Divisibility by 9: sum of digits divisible by 9 | by 11: difference of alternate digit sums divisible by 11

• Number of factors of N = (a+1)(b+1)(c+1)... where N = p^a × q^b × r^c

• Sum of first n natural numbers = n(n+1)/2

• Sum of squares of first n = n(n+1)(2n+1)/6

• Sum of cubes of first n = [n(n+1)/2]²

Percentages

• Percentage change = (Change / Original) × 100

• If A is x% more than B, then B is [x/(100+x)] × 100% less than A

• Successive % changes: Net effect = a + b + ab/100

• Population after n years = P(1 + r/100)^n

• Depreciation after n years = P(1 − r/100)^n

Profit & Loss

• Profit% = (SP − CP)/CP × 100

• Loss% = (CP − SP)/CP × 100

• SP = CP × (100 + Profit%)/100

• Discount% = (Marked Price − SP)/Marked Price × 100

• When CP of x articles = SP of y articles: Profit% = [(x−y)/y] × 100

Simple & Compound Interest

• SI = P × R × T / 100

• CI = P[(1 + R/100)^T − 1]

• Amount (CI) = P(1 + R/100)^T

• CI − SI for 2 years = P(R/100)²

• CI − SI for 3 years = P(R/100)²(3 + R/100)

Ratio & Proportion

• If a:b = c:d, then ad = bc (cross multiplication)

• Componendo: (a+b)/b = (c+d)/d

• Dividendo: (a−b)/b = (c−d)/d

Averages

• Average = Sum / Count

• Weighted average = Σ(wᵢ × xᵢ) / Σwᵢ

• If average of n numbers is A, sum = nA

Mixtures & Alligation

• Alligation ratio = (Dearer − Mean) : (Mean − Cheaper)

• Repeated replacement: Final quantity = Initial × (1 − removed/total)^n

Time, Speed & Distance

• Speed = Distance / Time

• km/hr to m/s: multiply by 5/18

• m/s to km/hr: multiply by 18/5

• Average speed (equal distances) = 2ab/(a+b)

• Average speed (equal times) = (a+b)/2

• Relative speed (same direction) = |a − b|

• Relative speed (opposite direction) = a + b

• Train crossing pole: Time = Length of train / Speed

• Train crossing platform: Time = (Train + Platform) / Speed

• Two trains crossing: Time = (L₁ + L₂) / Relative speed

• Boats: Downstream speed = Boat + Stream, Upstream = Boat − Stream

Time & Work

• If A does work in 'a' days, rate = 1/a per day

• Combined rate = 1/a + 1/b

• If A is x times as efficient as B, and together they take T days, A alone = T(x+1)/x days

• Pipe filling: Net rate = Filling rate − Emptying rate

• MDH formula: M₁D₁H₁/W₁ = M₂D₂H₂/W₂

Permutation & Combination

• nPr = n! / (n−r)!

• nCr = n! / [r!(n−r)!]

• nCr = nC(n−r)

• nC0 + nC1 + ... + nCn = 2^n

• Circular permutation = (n−1)!

Probability

• P(E) = Favorable outcomes / Total outcomes

• P(A or B) = P(A) + P(B) − P(A and B)

• P(A and B) = P(A) × P(B) [independent events]

• P(not E) = 1 − P(E)

Geometry

• Sum of angles in triangle = 180°

• Sum of angles in polygon = (n−2) × 180°

• Pythagoras: a² + b² = c²

• Common Pythagorean triplets: (3,4,5), (5,12,13), (7,24,25), (8,15,17)

• Area of triangle = ½ × base × height = √[s(s−a)(s−b)(s−c)] where s = (a+b+c)/2

• Area of equilateral triangle = (√3/4) × side²

Mensuration (2D)

• Circle: Area = πr², Circumference = 2πr

• Rectangle: Area = l×b, Perimeter = 2(l+b)

• Square: Area = a², Perimeter = 4a, Diagonal = a√2

• Parallelogram: Area = base × height

• Trapezoid: Area = ½(a+b) × h

• Rhombus: Area = ½ × d₁ × d₂

Mensuration (3D)

• Cube: Volume = a³, TSA = 6a², Diagonal = a√3

• Cuboid: Volume = lbh, TSA = 2(lb+bh+lh)

• Cylinder: Volume = πr²h, CSA = 2πrh, TSA = 2πr(r+h)

• Cone: Volume = ⅓πr²h, CSA = πrl, Slant height l = √(r²+h²)

• Sphere: Volume = 4/3 πr³, SA = 4πr²

• Hemisphere: Volume = 2/3 πr³, TSA = 3πr²

Trigonometry Basics

• sin²θ + cos²θ = 1

• 1 + tan²θ = sec²θ

• 1 + cot²θ = cosec²θ

• sin 30° = 1/2, cos 30° = √3/2, tan 30° = 1/√3

• sin 45° = 1/√2, cos 45° = 1/√2, tan 45° = 1

• sin 60° = √3/2, cos 60° = 1/2, tan 60° = √3

Logarithms

• log(ab) = log a + log b

• log(a/b) = log a − log b

• log(aⁿ) = n × log a

• log_a(a) = 1, log_a(1) = 0

Appendix B: Fraction-to-Percentage Quick Reference

Fraction	Decimal	%	Fraction	Decimal	%
1/2	0.500	50.00%	1/16	0.0625	6.25%
1/3	0.333	33.33%	1/17	0.0588	5.88%
1/4	0.250	25.00%	1/18	0.0556	5.56%
1/5	0.200	20.00%	1/19	0.0526	5.26%
1/6	0.167	16.67%	1/20	0.0500	5.00%
1/7	0.143	14.29%	1/21	0.0476	4.76%
1/8	0.125	12.50%	1/22	0.0455	4.55%
1/9	0.111	11.11%	1/23	0.0435	4.35%
1/10	0.100	10.00%	1/24	0.0417	4.17%
1/11	0.0909	9.09%	1/25	0.0400	4.00%
1/12	0.0833	8.33%	1/26	0.0385	3.85%
1/13	0.0769	7.69%	1/27	0.0370	3.70%
1/14	0.0714	7.14%	1/28	0.0357	3.57%
1/15	0.0667	6.67%	1/29	0.0345	3.45%
2/3	0.667	66.67%	1/30	0.0333	3.33%

Appendix C: Mensuration Formula Card

Shape	Area	Perimeter / Surface Area	Volume (3D)
Square	a²	4a	—
Rectangle	l × b	2(l + b)	—
Triangle	½ × b × h	a + b + c	—
Circle	πr²	2πr	—
Parallelogram	b × h	2(a + b)	—
Trapezoid	½(a + b) × h	a + b + c + d	—
Rhombus	½ × d₁ × d₂	4a	—
Cube	—	TSA = 6a²	a³
Cuboid	—	TSA = 2(lb + bh + lh)	l × b × h
Cylinder	—	TSA = 2πr(r + h)	πr²h
Cone	—	TSA = πr(r + l)	⅓πr²h
Sphere	—	SA = 4πr²	4/3 πr³
Hemisphere	—	TSA = 3πr²	2/3 πr³

Appendix D: Speed-Distance-Time Formula Card

Concept	Formula
Basic	Speed = Distance / Time, D = S × T, T = D / S
Unit Conversion	km/hr → m/s: × 5/18 \| m/s → km/hr: × 18/5
Average Speed (equal distance)	2S₁S₂ / (S₁ + S₂)
Average Speed (equal time)	(S₁ + S₂) / 2
Relative Speed (same direction)	\|S₁ − S₂\|
Relative Speed (opposite)	S₁ + S₂
Train crossing pole	Time = Length of train / Speed
Train crossing platform	Time = (Train + Platform) / Speed
Two trains crossing	Time = (L₁ + L₂) / Relative speed
Boats & Streams	Downstream = B + S, Upstream = B − S
Speed of boat in still water	(Downstream + Upstream) / 2
Speed of stream	(Downstream − Upstream) / 2
Meeting point	Ratio of distances = Ratio of speeds
Late/Early problems	D/S₁ − D/S₂ = Time difference

Appendix E: Syllogism Rules Quick Reference

Basic Rules:

• All A are B: A ⊂ B (A is a subset of B)

• Some A are B: A ∩ B ≠ ∅ (overlap exists)

• No A is B: A ∩ B = ∅ (no overlap)

• Some A are not B: Not all of A is in B

Valid Conclusions:

• All A are B + All B are C → All A are C (definite), Some C are A (definite)

• All A are B + Some B are C → No definite conclusion about A and C

• All A are B + No B is C → No A is C (definite)

• Some A are B + All B are C → Some A are C (definite)

• Some A are B + No B is C → Some A are not C (definite)

• No A is B + All B are C → No definite conclusion (Some C are not A — possible but not definite for all cases)

Immediate Inferences:

• All A are B → Some B are A (converse, always true)

• Some A are B → Some B are A (converse, always true)

• No A is B → No B is A (converse, always true)

• All A are B → Some A are B (always true)

Common Traps:

• "All A are B" does NOT mean "All B are A"

• "Some A are B" does NOT mean "Some A are not B" (it's possible all A are B)

• "Some A are B" + "Some B are C" → NO definite conclusion about A and C

Appendix F: DI Speed Tricks

Approximation Techniques:

• Round to nearest 5 or 10: 387/193 ≈ 390/195 = 2 (exact: 2.005)

• Use 10% as anchor: Find 10% first, then build. 37% of 840: 10% = 84, 30% = 252, 7% = 58.8, Total ≈ 311

• Percentage shortcuts: 25% = ÷4, 50% = ÷2, 75% = 3÷4, 12.5% = ÷8, 33.33% = ÷3

DI Calculation Shortcuts:

• Fraction comparison: To compare a/b and c/d, cross-multiply: if ad > bc, then a/b > c/d

• Percentage change shortcut: If value goes from 250 to 310, change = 60/250 = 24% (use: 60/250 = 6/25 = 24%)

• CAGR approximation: For small growth rates, CAGR ≈ Total growth% / Number of years

• Average shortcut: For evenly spaced numbers, average = (first + last) / 2

• Ratio to percentage: 3:5 → 3/(3+5) × 100 = 37.5% and 62.5%

Speed Reading DI Data:

• Always read the title and units first

• Scan for maximum and minimum values immediately

• For tables: mentally add row/column totals

• For graphs: identify trends (increasing, decreasing, fluctuating)

• Read ALL questions before starting calculations — some questions provide hints for others

✅ Analytical Skills-II: COMPLETE!

You are Exam-Ready & Interview-Ready.

From Number Systems to CAT Mock Tests — you've covered it all. Now go conquer your exams!

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