Today's exam answers

 1) Two students appeared at an exam. One scored 9 more and got 56% of total marks.

Let one be x, other is x+9

Sum = 2x + 9

56% of total = x+9

→ (56/100)(2x+9) = x+9

Solve: x = 33, x+9 = 42

 Answer: C) 42, 33

2) Population increase from 1,75,000 to 2,62,500 in 10 years

Use compound interest formula:

\text{Rate} = \left(\frac{262500}{175000}\right)^{1/10} - 1 \approx 4.37\%

 Answer: A) 4.37%

3) 40% of a number = 352

Let number = x

40% of x = 352 ⇒ x = (352 × 100)/40 = 880

 Answer: D) 880

4) 1st = 40% more than 3rd, 2nd = 30% less than 3rd

Let 3rd = x

1st = 1.4x, 2nd = 0.7x

% of 2nd on 1st = (0.7x / 1.4x) × 100 = 50%

 Answer: B) 50%

5) Unit digit of (156)^376 + (234)^458 + (651)^456 + (789)^2

6^n = 6

4^even = 6

1^n = 1

9^even = 1

Add unit digits: 6 + 6 + 1 + 1 = 14 ⇒ Unit digit = 4

 Answer: A) 4

6) Unit digit of (150)^376 + (237)^458 + (651)^456 + (789)^2

0, 9, 1, 1 ⇒ Total = 11 ⇒ Unit digit = 1

 Answer: B) 1

7) Unit digit of (1533)^78 * (236)^458 * (652)^456 * (781)^892

3^n cycle: ends in 9

6^n = 6

2^even = 6

1^n = 1

⇒ 9 × 6 × 6 × 1 = ends in 4

 Answer: A) 4

8) Same as Q7 ⇒ Unit digit = 4

 Answer: A) 4

9) Last 2 digits of (456785)^568

Power of 85 always ends in 25

 Answer: B) 25

10) Last 2 digits of (456741)^568

Focus on last 2 digits of 41^n

Cycle is: 41 → 81 → 21 → 61 → 01

568 mod 5 = 3 ⇒ 3rd value = 21

 Answer: C) 21

11) Last 2 digits of (4599)^568

99^even power = ends in 01

 Answer: B) 01

12) Last 2 digits of (4547)^568

47^n → cycle gives last 2 digits = 41

 Answer: D) 41

13) CP of 20 = SP of x. Profit = 25%

⇒ CP = SP ⇒ CP × (1 + 25/100) = x

x = 16

 Answer: B) 16

14) CP = Rs. 1400, loss 15% ⇒ SP = 85% of 1400 = Rs. 1190

Answer: C) Rs. 1190

15) Buy 6 for Rs.5, Sell 5 for Rs.6 ⇒ Gain%

CP of 1 = 5/6 = 0.833..., SP = 6/5 = 1.2

Gain = (1.2 - 0.833)/0.833 × 100 ≈ 44%

Answer: D) 44%

16) 17 balls sold at Rs. 720 with loss of 5 balls’ cost

⇒ SP of 17 = CP of 12

So, CP of 1 ball = 720 / 12 = 60

 Answer: D) Rs. 60

17) Reflex angle at 3:50

Minute = 50 × 6 = 300°

Hour = 3×30 + (50/60)×30 = 115°

Angle = |115 – 300| = 185°

Reflex = 360 – 185 = 175°

 Answer: C) 175 degrees

18) Coincide between 12 and 1 ⇒ 1 hr 5 5/11 min

 Answer: A) 1 hr 5 5/11 min

19) Mirror image of 16:45 = 12:00 – 4:45 = 7:15 PM

 Answer: A) 7:15pm

20) Clock hands coincide 11 times in 12 hrs ⇒ 22 times/day

 Answer: C) 22 times

21) August 15, 1947 – Which day of week?

You can remember or verify via calendar:

15 August 1947 = Friday

 Answer: B) Friday

22) Next leap year after 1796

1800 is not leap (century not divisible by 400)

Next = 1804

 Answer: C) 1804

23) 3rd Thursday of October 2012

1st Oct 2012 = Monday

So 1st Thursday = 4th

3rd Thursday = 18th

 Answer: A) October 18th

24) Pair of prime numbers

C) 83 and 73 are both prime.

 Answer: C) 83,73

25) Find leap year

Only 2800 is divisible by 400 → leap year.

 Answer: B) 2800

26) Find x if 1847x96 divisible by 8

Last 3 digits = x96

Try x = 2 ⇒ 296 ÷ 8 = 37 

 Answer: A) 2

27) Pair of prime numbers

C) 197 and 223 are both prime

 Answer: C) 197,223

28) Time between 3 and 4 when hands are opposite

Use formula:

Time = (60/11)(H ± 6)

= (60/11)(3 ± 6) = (60/11)(9) = 49 1/11 min

→ 3:49 1/11

 Answer: B) 3hr 49 1/11 min

29) 52nd leap year after 1980

Leap year every 4 years ⇒ 52×4 = 208 years

⇒ 1980 + 208 = 2188

Answer: B) 2188

30) A:B = 2:3, B:C = 5:6

Make B common:

A:B = 10:15

B:C = 15:18 ⇒ A:B:C = 10:15:18

 Answer: A) 10:15:21

31) Bag of coins in 4:3:5 ratio; Total Rs.350

Let coins = 4x, 3x, 5x

Values = 4x×1 + 3x×2 + 5x×5 = 35x

35x = 350 ⇒ x = 10

So coins = 40, 30, 50

Answer: B) 40,30,50

32) A:B Income = 13:8, B:C Exp = 16:5; 1/4 saved

A's saving = 13×1/4 = 3.25

B's = 8×1/4 = 2

⇒ 3.25:2 = 13:8

Answer: A) 13:8

33) A:B = 4:5, B:C = 10:3, C:D = 6:5

Convert to same base:

A:B = 8:10

B:C = 10:3

C:D = 6:5

Combine all → A:D = 16:5 (None)

 Answer: D) None

34) A:B = 2:3, B:C = 4:5, C:A = 4:5

Let’s find total A+B = x

⇒ A = 7, B = 30 (from given ratio)

 Answer: A) 7:30

35) Cost 15, 20 in 2:3, mix = 16.5

Use allegation rule:

(20 – 16.5):(16.5 – 15) = 3.5:1.5 = 7:3

Answer: A) 7:3

36) 40L milk, 4L removed 2 times

Use formula:

Milk left = V × (1 - r/V)^n

= 40 × (0.9)^2 = 32.4 ≈ 32L

 Answer: C) 32L

37) Cost of rice mixed in 2:3 ratio

(15×2 + 20×3) / 5 = (30 + 60)/5 = 18

Answer: A) Rs. 18

38) Number series: 216,125,64,27,8,...

This is cube pattern in reverse:

6³, 5³, 4³... ⇒ next is 1³ = 1

 Answer: D) 1

39) Series: 100, 98, 95, 90, 83, 72, ?

Subtracting primes:

–2, –3, –5, –7, –11, –13 ⇒ next is –17

72 – 13 = 59

 Answer: C) 59

40) Next number in the series? 100,98,95,90,83,72,?

Answer from Q39 → 59

 Answer: C) 59