Quantitative Aptitude Mock Test 4 Practice

1. How many positive factors does 72 have?

• A. 10
• B. 12 (Correct)
• C. 14
• D. 16

Explanation: $72 = 2^3 x 3^2$. Number of factors = $(3+1)(2+1) = 4 x 3 = 12$.

2. A student gets 55% of 800 marks. Marks obtained =

• A. 420
• B. 430
• C. 440 (Correct)
• D. 450

Explanation: 0.55 x 800 = 440.

3. 11 kg of rice worth Rs 42/kg is mixed with 9 kg of rice worth Rs 56/kg. The mean price of the mixture is:

• A. Rs 48.3/kg (Correct)
• B. Rs 49.3/kg
• C. Rs 47.3/kg
• D. Rs 49/kg

Explanation: Weighted mean = (42 x 11 + 56 x 9) / 20 = Rs 48.3/kg.

4. A boat's speed in still water is 12 km/hr and the current speed is 3 km/hr. Its downstream speed is:

• A. 9 km/hr
• B. 12 km/hr
• C. 15 km/hr (Correct)
• D. 18 km/hr

Explanation: Downstream speed = still water speed + stream speed = 12 + 3 = 15 km/hr.

5. Evaluate $\log_5 125$

• A. 2
• B. 3 (Correct)
• C. 4
• D. 5

Explanation: $5^3 = 125$, so $\log_5 125 = 3$.

6. How many proper subsets does a 5-element set have?

• A. 16
• B. 30
• C. 31 (Correct)
• D. 32

Explanation: Total subsets = $2^5 = 32$. Excluding the set itself leaves 31 proper subsets.

7. Two similar cylinders have radii 2 cm and 5 cm. What is the ratio of their curved surface areas?

• A. 4:25 (Correct)
• B. 2:5
• C. 8:125
• D. 4:10

Explanation: For similar solids, corresponding heights scale in the same ratio as radii, so curved surface area scales as the square of the linear ratio. Therefore the ratio is 2^2 : 5^2 = 4:25.

8. Find the amount on Rs 16,000 for 1 year at 10% p.a. compounded half-yearly.

• A. Rs 17,600
• B. Rs 17,640 (Correct)
• C. Rs 17,680
• D. Rs 17,700

Explanation: Half-yearly rate = 5%, periods = 2. Amount $=16000(1.05)^2=17640$.

9. A shopkeeper buys a calculator for Rs 800 and sells it for Rs 920. What is the profit percentage?

• A. 12%
• B. 15% (Correct)
• C. 18%
• D. 20%

Explanation: Profit $=120$. Profit\% $=\frac{120}{800}\times100=15\%$.

10. 485deg lies in which quadrant?

• A. 1st
• B. 2nd (Correct)
• C. 3rd
• D. 4th

Explanation: $485^\circ = 360^\circ + 125^\circ$. Since $125^\circ$ lies between $90^\circ$ and $180^\circ$, it is in the second quadrant.

11. How many positive factors does 144 have?

• A. 12
• B. 14
• C. 15 (Correct)
• D. 18

Explanation: $144 = 2^4 x 3^2$. Number of factors = $(4+1)(2+1) = 5 x 3 = 15$.

12. GST of 8% on Rs 340 equals:

• A. Rs 24.2
• B. Rs 27.2 (Correct)
• C. Rs 28.4
• D. Rs 30.6

Explanation: 8% of 340 = 27.2.

13. Tea worth Rs 32/kg is mixed with tea worth Rs 44/kg to obtain a blend worth Rs 38/kg. The ratio of cheaper to dearer tea is:

• A. 6:6 (Correct)
• B. 7:6
• C. 8:6
• D. 6:7

Explanation: By alligation, cheaper:dearer = (44 - 38):(38 - 32) = 6:6.

14. A boat covers 32 km upstream in 4 hours and 40 km downstream in 4 hours. The speed of the stream is:

• A. 1 km/hr (Correct)
• B. 2 km/hr
• C. 3 km/hr
• D. 4 km/hr

Explanation: Upstream speed = 32/4 = 8 km/hr and downstream speed = 40/4 = 10 km/hr. Stream speed = (10 - 8)/2 = 1 km/hr.

15. Find the 8th term of the A.P. 5, 8, 11, 14, ...

• A. 23
• B. 24
• C. 25
• D. 26 (Correct)

Explanation: Here $a = 5$ and $d = 3$. So $a_8 = a + 7d = 5 + 21 = 26$.

16. A set with no element is called:

• A. singleton set
• B. finite set
• C. empty set (Correct)
• D. universal set

Explanation: A set with zero elements is the empty or null set.

17. Two parallel lines are cut by a transversal. One pair of co-interior angles is in the ratio 2:3. Find the larger angle.

• A. 72deg
• B. 108deg (Correct)
• C. 80deg
• D. 100deg

Explanation: Co-interior angles add up to 180deg. Let them be 2x and 3x. Then 5x = 180deg, so x = 36deg and the larger angle is 3x = 108deg.

18. A laptop worth Rs 72,000 depreciates by 20% in the first year and 10% in the second year. Its value after 2 years is:

• A. Rs 50,840
• B. Rs 51,840 (Correct)
• C. Rs 52,840
• D. Rs 53,840

Explanation: Value factor $=0.8\times0.9=0.72$. Value $=72000\times0.72=51840$.

19. A lamp is sold for Rs 1,260 at a loss of 10%. What was its cost price?

• A. Rs 1,300
• B. Rs 1,350
• C. Rs 1,400 (Correct)
• D. Rs 1,450

Explanation: $CP=1260\times\frac{100}{90}=1400$.

20. Find sin²45deg + sin²30deg + sin²60deg + sin²90deg.

• A. 4
• B. 3
• C. 2.5 (Correct)
• D. 2

Explanation: $1/2 + 1/4 + 3/4 + 1 = 2.5$.

21. Which of the following is a factor of 48?

• A. 7
• B. 9
• C. 12 (Correct)
• D. 14

Explanation: A factor divides the number exactly. $48 / 12 = 4$, so 12 is a factor of 48.

22. Population of a colony rises from 25,000 to 31,250. Increase % =

• A. 20%
• B. 25% (Correct)
• C. 30%
• D. 35%

Explanation: Increase = 6250. Then 6250/25000 x 100 = 25%.

23. A container has 30 L of milk. 6 L is removed and replaced with water, and the process is repeated 3 times. Milk left is:

• A. 15.36 L (Correct)
• B. 14.64 L
• C. 16.36 L
• D. 14.36 L

Explanation: Fraction left each time = 24/30 = 4/5. Milk left = 30 x (4/5)^3 = 15.36 L.

24. A boat can travel 20 km in 2 hours downstream and the same distance in 5 hours upstream. Its speed in still water is:

• A. 6 km/hr
• B. 7 km/hr (Correct)
• C. 8 km/hr
• D. 9 km/hr

Explanation: Downstream speed = 10 km/hr and upstream speed = 4 km/hr. Still water speed = (10 + 4)/2 = 7 km/hr.

25. Find the sum of the first 10 terms of the A.P. with $a = 4$ and $d = 3$.

• A. 165
• B. 175 (Correct)
• C. 185
• D. 195

Explanation: $S_n = \frac{n}{2}[2a + (n-1)d]$. So $S_{10} = 5[8 + 27] = 175$.

26. The universal set in a problem is chosen to:

• A. avoid formulas
• B. contain all objects under discussion (Correct)
• C. replace subsets
• D. force disjoint sets

Explanation: The universal set defines the full collection relevant to the problem.

27. Two adjacent angles are (4x + 10)deg and (2x + 50)deg. Find x.

• A. 20 (Correct)
• B. 25
• C. 15
• D. 30

Explanation: Adjacent angles on a straight line are supplementary. (4x + 10) + (2x + 50) = 180 gives 6x = 120, so x = 20.

28. A sum becomes Rs 13,310 in 3 years at annual compound interest. If the principal is Rs 10,000, the annual rate is:

• A. 8%
• B. 9%
• C. 10% (Correct)
• D. 11%

Explanation: $13310/10000=1.331$. Since $1.1^3=1.331$, the annual rate is 10%.

29. The cost price of 18 articles equals the selling price of 15 articles. The profit percentage is:

• A. 16%
• B. 18%
• C. 20% (Correct)
• D. 25%

Explanation: Profit\% $=\frac{18-15}{15}\times100=20\%$.

30. From the top of a 100 m tower, the angle of depression of a car is 30deg. Find the horizontal distance of the car.

• A. 100sqrt(3) m (Correct)
• B. 100 m
• C. 50sqrt(3) m
• D. 100/sqrt(3) m

Explanation: Angle of depression equals angle of elevation. So $\tan 30^\circ = 100/x$, giving $x = 100\sqrt{3}$ m.

31. The highest power of 2 that exactly divides 96 is:

• A. 8
• B. 16
• C. 32 (Correct)
• D. 64

Explanation: $96 = 2^5 x 3$. So the highest power of 2 that divides 96 is $2^5 = 32$.

32. If a number is increased by 15% and becomes 345, original number is:

• A. 280
• B. 290
• C. 300 (Correct)
• D. 310

Explanation: 115% = 345, so 100% = 345/1.15 = 300.

33. Find the average of 22, 28, 31, 35, 44.

• A. 32 (Correct)
• B. 33
• C. 31
• D. 160

Explanation: Average = (22 + 28 + 31 + 35 + 44) / 5 = 160/5 = 32.

34. A boat goes 75 km downstream in the same time it goes 45 km upstream. If the speed of the current is 3 km/hr, the speed in still water is:

• A. 10 km/hr
• B. 12 km/hr (Correct)
• C. 14 km/hr
• D. 16 km/hr

Explanation: Let still water speed be u. Then 75/(u+3) = 45/(u-3). Solving gives u = 12 km/hr.

35. What is the common difference of the A.P. 12, 17, 22, 27, ...?

• A. 3
• B. 4
• C. 5 (Correct)
• D. 6

Explanation: Subtract consecutive terms: $17 - 12 = 5$, so the common difference is 5.

36. From 5 letters and 4 digits, one letter or one digit is chosen. Number of ways?

• A. 9 (Correct)
• B. 20
• C. 45
• D. 1

Explanation: Use the addition principle because the choice is one letter or one digit. So total ways = $5 + 4 = 9$.

37. What is the sum of interior angles of a hexagon?

• A. 540deg
• B. 720deg (Correct)
• C. 900deg
• D. 1080deg

Explanation: For an n-gon, sum of interior angles = (n - 2) x 180deg. For n = 6, the sum is 4 x 180deg = 720deg.

38. What is the simple interest on Rs 14,000 at 15% for 3 years?

• A. Rs 5,800
• B. Rs 6,000
• C. Rs 6,300 (Correct)
• D. Rs 6,500

Explanation: $SI=\frac{PRT}{100}=\frac{14000\times15\times3}{100}=6300$.

39. An article is sold at 25% gain. If its cost price is Rs 640, the selling price is:

• A. Rs 760
• B. Rs 780
• C. Rs 800 (Correct)
• D. Rs 820

Explanation: $SP=640\times\frac{125}{100}=800$.

40. A kite is flying with a 150 m thread making a 30deg angle with the horizontal. Find the height of the kite.

• A. 100 m
• B. 75 m (Correct)
• C. 50 m
• D. 80 m

Explanation: Thread is the hypotenuse. Height $=150\sin 30^\circ = 150\times1/2 = 75$ m.

41. How many numbers between 1 and 50 are divisible by 6?

• A. 7
• B. 8 (Correct)
• C. 9
• D. 10

Explanation: Count multiples of 6 up to 50: $\lfloor 50/6 \rfloor = 8$.

42. 125% of 3060 minus 85% of x equals 408. Then x =

• A. 3960
• B. 4000
• C. 4020 (Correct)
• D. 4080

Explanation: 1.25 x 3060 - 0.85x = 408. Solving gives x = 4020.

43. The average of 7 numbers is 36. If the sum of 6 of them is 210, the missing number is:

• A. 42 (Correct)
• B. 44
• C. 40
• D. 36

Explanation: Total sum = 36 x 7 = 252. Missing number = 252 - 210 = 42.

44. Two friends run on a 400 m track in opposite directions at 5 m/s and 3 m/s. Their first meeting at the starting point happens after:

• A. 200 sec
• B. 300 sec
• C. 400 sec (Correct)
• D. 500 sec

Explanation: Lap times are 400/5 = 80 sec and 400/3 sec. Their first common return to start is after the LCM, which is 400 seconds.

45. If $\log_a m + \log_a n =$

• A. $\log_a(m+n)$
• B. $\log_a(mn)$ (Correct)
• C. $\log_a(m-n)$
• D. $\log_a(m/n)$

Explanation: The product law says $\log_a m + \log_a n = \log_a(mn)$.

46. Evaluate $\frac{8!}{6!}$.

• A. 42
• B. 48
• C. 56 (Correct)
• D. 64

Explanation: Cancel $6!$ to get $8 \times 7 = 56$.

47. Each interior angle of a regular polygon is 135deg. How many sides does the polygon have?

• A. 6
• B. 8 (Correct)
• C. 10
• D. 12

Explanation: Exterior angle = 180deg - 135deg = 45deg. Number of sides = 360deg / 45deg = 8.

48. A sum earns Rs 1,920 as SI in 4 years at 8%. Find the principal.

• A. Rs 5,000
• B. Rs 6,000 (Correct)
• C. Rs 7,000
• D. Rs 8,000

Explanation: $P=\frac{SI\times100}{RT}=\frac{1920\times100}{8\times4}=6000$.

49. A trader sells two items at the same selling price. On one he gains 20% and on the other he loses 20%. His overall result is:

• A. No profit no loss
• B. 4% loss (Correct)
• C. 4% gain
• D. 2% loss

Explanation: Equal $\pm x\%$ gives loss $=\frac{20^2}{100}=4\%$.

50. A 200 m tower has shadow lengths corresponding to sun elevations 45deg and 60deg. By how much does the shadow shorten?

• A. 200(sqrt(3)-1)/sqrt(3)
• B. 200(3-sqrt(3))/3 (Correct)
• C. 200sqrt(3)
• D. 200/sqrt(3)

Explanation: At $45^\circ$, shadow = 200 m. At $60^\circ$, shadow = $200/\sqrt{3}$. Difference = $200 - 200/\sqrt{3} = 200(3-\sqrt{3})/3$.