Quantitative Aptitude Mock Test 8 Practice

1. Which set correctly represents integers?

• A. {1, 2, 3, ...}
• B. {0, 1, 2, 3, ...}
• C. {..., -2, -1, 0, 1, 2, ...} (Correct)
• D. {3/4, 5/6, 7/8}

Explanation: Integers include negative whole numbers, zero, and positive whole numbers. So the correct set is $\{..., -2, -1, 0, 1, 2, ...\}$.

2. If 35% of a number is 280, the number is:

• A. 700
• B. 750
• C. 800 (Correct)
• D. 840

Explanation: 0.35x = 280, so x = 280/0.35 = 800.

3. Riya and Kabir invest Rs 32000 and Rs 48000 for the same time. Total profit is Rs 25000. Riya's share is:

• A. Rs 10000 (Correct)
• B. Rs 15000
• C. Rs 11000
• D. Rs 9000

Explanation: Profit ratio follows capital ratio 32000:48000 = 2:3. Riya gets 2/5 of 25000 = Rs 10000.

4. Two pipes fill a tank in 20 and 30 hours respectively. A waste pipe empties it in 40 hours. If all three are opened together, time taken to fill the tank is:

• A. 17.1 hours (Correct)
• B. 18 hours
• C. 19.2 hours
• D. 20 hours

Explanation: Net rate = 1/20 + 1/30 - 1/40 = 7/120. Time = 120/7 = 17.14 hours, about 17.1 hours.

5. If the discriminant of a quadratic is negative, the roots are:

• A. equal and real
• B. distinct and real
• C. non-real (Correct)
• D. zero

Explanation: When $D

6. Two dice are thrown. What is the probability that the sum is prime?

• A. $1/3$
• B. $5/12$ (Correct)
• C. $1/2$
• D. $7/12$

Explanation: Prime sums are 2, 3, 5, 7, and 11, with total count 15. Hence probability $= \frac{15}{36} = \frac{5}{12}$.

7. A circular ring has outer radius 10 cm and inner radius 6 cm. Find the area of the ring. Use pi = 3.14.

• A. 200.96 cm^2 (Correct)
• B. 251.2 cm^2
• C. 113.04 cm^2
• D. 400 cm^2

Explanation: Area of annulus = pi(R^2 - r^2). So 3.14 x (100 - 36) = 200.96 cm^2.

8. What is the effective annual rate of 12% p.a. compounded half-yearly?

• A. 12.00%
• B. 12.25%
• C. 12.36% (Correct)
• D. 12.50%

Explanation: Effective rate = $(1.06)^2 - 1 = 0.1236 = 12.36\%$.

9. A merchant sells 80% items at 15% gain and 20% items at 20% loss. Net result:

• A. 8% gain (Correct)
• B. 8% loss
• C. 7% gain
• D. 6% gain

Explanation: Overall\% $=0.8\times15+0.2\times(-20)=8\%$ gain.

10. Which of the following equals cos 30deg?

• A. 1/2
• B. 1/sqrt(2)
• C. sqrt(3)/2 (Correct)
• D. sqrt(3)

Explanation: $\cos 30^\circ = \sqrt{3}/2$.

11. The number 738 is divisible by:

• A. Only 3
• B. Only 9
• C. Both 3 and 9 (Correct)
• D. Neither 3 nor 9

Explanation: Sum of digits = 7 + 3 + 8 = 18. Since 18 is divisible by 3 and also by 9, 738 is divisible by both.

12. Which of the following equals 16 2/3%?

• A. 1/5
• B. 1/6 (Correct)
• C. 1/7
• D. 1/8

Explanation: 16 2/3% = 16.66.../100 = 1/6.

13. Ayaan invests Rs 22000 for 12 months and Meera invests Rs 18000 for 10 months. Their profit ratio is:

• A. 22:15 (Correct)
• B. 11:9
• C. 12:10
• D. 15:22

Explanation: Profit ratio = 22000 x 12 : 18000 x 10 = 264000:180000 = 22:15.

14. Pipe A fills a tank in 9 hours. Pipe B fills it in 12 hours. Pipe A is opened at 6 AM and Pipe B at 9 AM. At approximately what time will the tank be full?

• A. 12:00 PM
• B. 12:26 PM (Correct)
• C. 12:45 PM
• D. 1:00 PM

Explanation: By 9 AM, Pipe A fills 3/9 = 1/3 of the tank. Remaining tank = 2/3. Combined rate = 1/9 + 1/12 = 7/36. Time for remaining = (2/3)/(7/36) = 24/7 hours = about 3 hours 26 minutes. So the tank is full at about 12:26 PM.

15. Find the remainder when $x^2 + 3x + 2$ is divided by $x + 1$.

• A. 0 (Correct)
• B. 1
• C. 2
• D. 3

Explanation: By the Remainder Theorem, remainder = $f(-1) = 1 - 3 + 2 = 0$.

16. A bag has 5 red and 3 blue balls. Two balls are drawn without replacement. Probability both are red?

• A. $1/4$
• B. $5/14$ (Correct)
• C. $3/8$
• D. $5/8$

Explanation: Use combinations: $\frac{^5C_2}{^8C_2} = \frac{10}{28} = \frac{5}{14}$.

17. A triangle has sides 9 cm, 12 cm, and 15 cm. Find its area using Heron's formula.

• A. 54 cm^2 (Correct)
• B. 72 cm^2
• C. 36 cm^2
• D. 48 cm^2

Explanation: Semi-perimeter s = (9 + 12 + 15)/2 = 18. Area = sqrt[18 x 9 x 6 x 3] = sqrt(2916) = 54 cm^2.

18. The amount on Rs 40,000 for 9 months at 12% p.a. compounded quarterly is:

• A. Rs 43,272
• B. Rs 43,708 (Correct)
• C. Rs 43,927
• D. Rs 44,000

Explanation: Quarterly rate = 3% and periods = 3. $A=40000(1.03)^3=43708.36$, approximately Rs 43,708.

19. A trader bought 120 items at Rs 110 each. He earned Rs 360 on 30 items, Rs 1,050 on 75 items, and lost Rs 105 on the rest. Average profit per item is:

• A. Rs 9
• B. Rs 10.875 (Correct)
• C. Rs 11.25
• D. Rs 12

Explanation: Net profit $=1305$. Average per item $=\frac{1305}{120}=10.875$.

20. In which quadrant are tan and cot both positive?

• A. Quadrant I only
• B. Quadrant II only
• C. Quadrant III only
• D. Quadrants I and III (Correct)

Explanation: Tan and cot are positive wherever sin and cos have the same sign: Quadrants I and III.

21. 4516 is divisible by:

• A. 4 only (Correct)
• B. 8 only
• C. Both 4 and 8
• D. Neither 4 nor 8

Explanation: For divisibility by 4, last two digits are 16, which is divisible by 4. For divisibility by 8, last three digits are 516, and 516 is not divisible by 8.

22. 75% of 84 is:

• A. 60
• B. 63 (Correct)
• C. 66
• D. 69

Explanation: 75% = 3/4, so 3/4 of 84 = 63.

23. Neel starts a business with Rs 50000. After 6 months, Ishaan joins with Rs 30000. At year end, their profit ratio is:

• A. 10:3 (Correct)
• B. 5:3
• C. 12:6
• D. 3:10

Explanation: Neel: 50000 x 12 = 600000. Ishaan: 30000 x 6 = 180000. Ratio = 10:3.

24. A cistern is 3/5 full. Three pipes fill it in 10, 12 and 15 hours respectively. In how much time will it become full?

• A. 1 hour 20 min
• B. 1 hour 30 min
• C. 1 hour 36 min (Correct)
• D. 2 hours

Explanation: Combined rate = 1/10 + 1/12 + 1/15 = 1/4 tank per hour. Remaining part = 2/5. Time = (2/5)/(1/4) = 8/5 hours = 1 hour 36 minutes.

25. Find the remainder when $2x^2 - 5x + 3$ is divided by $x - 2$.

• A. -1
• B. 0
• C. 1 (Correct)
• D. 2

Explanation: Remainder = $f(2) = 2(4) - 10 + 3 = 1$.

26. A box has 4 green and 6 yellow balls. Two draws are made with replacement. Probability both are green?

• A. $1/5$
• B. $4/25$ (Correct)
• C. $2/5$
• D. $8/25$

Explanation: Each draw has probability $\frac{4}{10} = \frac25$. Independent draws give $\frac25 \times \frac25 = \frac{4}{25}$.

27. The perimeter of a square equals the perimeter of a rectangle with sides 8 cm and 6 cm. Find the area of the square.

• A. 49 cm^2 (Correct)
• B. 36 cm^2
• C. 64 cm^2
• D. 25 cm^2

Explanation: Perimeter of the rectangle = 2(8 + 6) = 28 cm. So the square has side 7 cm and area 49 cm^2.

28. A sum at 8% compounded annually becomes Rs 11,664 in 2 years. Find SI on the same principal, same rate, same time.

• A. Rs 1,520
• B. Rs 1,600 (Correct)
• C. Rs 1,680
• D. Rs 1,760

Explanation: First find the principal: $P=11664/(1.08)^2=10000$. Then SI = $10000\times8\times2/100 = 1600$.

29. An article sold for Rs 4,250 gives the same numerical profit as the loss when sold for Rs 3,650. Find the cost price.

• A. Rs 3,850
• B. Rs 3,900
• C. Rs 3,950 (Correct)
• D. Rs 4,000

Explanation: $CP=\frac{4250+3650}{2}=3950$.

30. If A=(0,0) and B=(8,15), then AB is:

• A. 15
• B. 16
• C. 17 (Correct)
• D. 23

Explanation: $AB=\sqrt{8^2+15^2}=\sqrt{289}=17$.

31. The smallest digit that can replace x in 43x2 so that the number is divisible by 3 is:

• A. 0 (Correct)
• B. 1
• C. 2
• D. 3

Explanation: Sum of digits = 4 + 3 + x + 2 = 9 + x. For divisibility by 3, $9 + x$ must be divisible by 3. So x can be 0, 3, 6, or 9. The smallest is 0.

32. A is 25% more than B. B is what percent less than A?

• A. 15%
• B. 18%
• C. 20% (Correct)
• D. 25%

Explanation: Use x/(100+x) x 100 = 25/125 x 100 = 20%.

33. Vani invests Rs 42000 at the start of the year. After 4 months, she changes it to Rs 54000. Kunal keeps Rs 36000 for 12 months. Their profit ratio is:

• A. 25:18 (Correct)
• B. 42000:36000
• C. 18:25
• D. 8:12

Explanation: Vani = 42000 x 4 + 54000 x 8 = 600000. Kunal = 36000 x 12 = 432000. Ratio = 25:18.

34. A leak at the bottom empties a full tank in 8 hours. An inlet fills it in 6 hours. If the tank is full and both start together, what happens?

• A. It empties in 24 hours
• B. It empties in 12 hours
• C. It never empties (Correct)
• D. It empties in 48 hours

Explanation: Inlet rate = 1/6, leak rate = 1/8. Net rate = 1/24 filling, not emptying. So the tank never empties while both operate.

35. Form the quadratic equation whose roots have sum 8 and product 15.

• A. $x^2 - 8x + 15 = 0$ (Correct)
• B. $x^2 + 8x + 15 = 0$
• C. $x^2 - 8x - 15 = 0$
• D. $x^2 + 8x - 15 = 0$

Explanation: If the roots have sum $S$ and product $P$, the equation is $x^2 - Sx + P = 0$. So it becomes $x^2 - 8x + 15 = 0$.

36. On a die roll, let A = odd number and B = even number. Find $P(A \cup B)$.

• A. 0
• B. $1/2$
• C. $3/4$
• D. 1 (Correct)

Explanation: Odd and even outcomes cover the entire sample space and do not overlap. So the probability is 1.

37. Find the volume of a sphere with radius 21 cm. Use pi = 22/7.

• A. 38808 cm^3 (Correct)
• B. 19404 cm^3
• C. 9702 cm^3
• D. 77616 cm^3

Explanation: Volume of sphere = (4/3)pi r^3. Substituting r = 21 and pi = 22/7 gives 38808 cm^3.

38. The difference between half-yearly and annual amount on Rs 20,000 for 1 year at 10% is:

• A. Rs 25
• B. Rs 50 (Correct)
• C. Rs 75
• D. Rs 100

Explanation: Half-yearly amount = 20000(1.05)^2 = 22050. Annual amount = 22000. Difference = 50.

39. A product goes from manufacturer to wholesaler to retailer at gains of 10%, 20%, and 25% respectively. If final price is Rs 3,300, manufacturing cost was:

• A. Rs 2,000 (Correct)
• B. Rs 2,100
• C. Rs 2,200
• D. Rs 2,250

Explanation: Original cost $=\frac{3300}{1.1\times1.2\times1.25}=2000$.

40. Which formula is used to test whether three coordinate points are collinear?

• A. Slope = 0
• B. Area of triangle = 0 (Correct)
• C. Distance from origin
• D. Midpoint formula

Explanation: Three points are collinear if the area of the triangle formed by them is zero.

41. The greatest digit that can replace y in 57y4 so that the number is divisible by 9 is:

• A. 1
• B. 2 (Correct)
• C. 4
• D. 8

Explanation: Sum of digits = 5 + 7 + y + 4 = 16 + y. For divisibility by 9, $16 + y$ must be a multiple of 9. The next multiple is 18, so y = 2.

42. A is 40% less than B. B is what percent more than A?

• A. 50%
• B. 60%
• C. 66 2/3% (Correct)
• D. 80%

Explanation: Take B = 100, then A = 60. Increase = 40/60 x 100 = 66 2/3%.

43. Aarav invests Rs 36000 for 12 months and Meera invests Rs 24000 for 9 months. Total profit is Rs 18000. Aarav's share is:

• A. Rs 12000 (Correct)
• B. Rs 6000
• C. Rs 13200
• D. Rs 10800

Explanation: Capital-months = 432000 and 216000. Aarav gets 432000/648000 of 18000 = Rs 12000.

44. Pipe A fills 1/3 of a tank in 5 hours. In how many hours will Pipe A fill the whole tank?

• A. 10 hours
• B. 12 hours
• C. 15 hours (Correct)
• D. 18 hours

Explanation: If 1/3 tank is filled in 5 hours, the full tank is filled in 5 x 3 = 15 hours.

45. Solve: $2x - 5 > 9$

• A. $x > 5$
• B. $x > 6$
• C. $x > 7$ (Correct)
• D. $x > 8$

Explanation: Add 5: $2x > 14$. Divide by 2 to get $x > 7$.

46. A card is drawn. What is the probability it is a king or a diamond?

• A. $3/13$
• B. $4/13$ (Correct)
• C. $5/13$
• D. $16/52$

Explanation: Kings = 4, diamonds = 13, overlap = 1. So probability $= \frac{4+13-1}{52} = \frac{16}{52} = \frac4{13}$.

47. A cylinder has diameter 14 cm and height 20 cm. Find its total surface area. Use pi = 22/7.

• A. 1188 cm^2 (Correct)
• B. 594 cm^2
• C. 968 cm^2
• D. 1056 cm^2

Explanation: Radius = 7 cm. TSA = 2pi r(r + h). So TSA = 2 x (22/7) x 7 x 27 = 1188 cm^2.

48. At 10% annual CI, in how many years will a sum become 1.331 times?

• A. 1
• B. 2
• C. 3 (Correct)
• D. 4

Explanation: Since $1.1^3=1.331$, the time is 3 years.

49. A dealer quotes Rs 45 for an article costing Rs 30. A fake Rs 50 note is used and Rs 5 change is returned. Total loss is:

• A. Rs 35 (Correct)
• B. Rs 45
• C. Rs 50
• D. Rs 80

Explanation: Loss consists of article cost and returned change, so total loss is Rs 35.

50. What is the value of sin²θ + cos²θ?

• A. 0
• B. 1 (Correct)
• C. 2
• D. Depends on θ

Explanation: This is the basic Pythagorean identity. For every angle, $\sin^2\theta + \cos^2\theta = 1$.

51. 53724 is divisible by 11 because:

• A. Sum of digits is 21
• B. Difference of alternate digit sums is 11 (Correct)
• C. Last digit is 4
• D. It is divisible by 2 and 9

Explanation: Using the divisibility rule of 11: $5 - 3 + 7 - 2 + 4 = 11$. Since 11 is divisible by 11, the number is divisible by 11.

52. If P is 20% more than Q and Q = 250, then P =

• A. 280
• B. 290
• C. 300 (Correct)
• D. 320

Explanation: 20% of 250 = 50, so P = 300.

53. Aarav invests Rs 20000 for 8 months and Meera invests Rs 30000 for 12 months. Total profit is Rs 15600. Meera's share is:

• A. Rs 10800 (Correct)
• B. Rs 4800
• C. Rs 12000
• D. Rs 9600

Explanation: Capital-months = 160000 and 360000. Meera gets 360000/520000 of 15600 = Rs 10800.

54. Pipe A fills 1/3 of a tank in 5 hours and Pipe B fills 2/5 of the same tank in 8 hours. Working together, they fill the tank in:

• A. 8 4/7 hours (Correct)
• B. 9 hours
• C. 9 1/2 hours
• D. 10 hours

Explanation: Pipe A fills full tank in 15 hours, Pipe B fills full tank in 20 hours. Combined rate = 1/15 + 1/20 = 7/60. Time = 60/7 = 8 4/7 hours.

55. Solve: $3x + 4 \le 19$

• A. $x \le 4$
• B. $x \le 5$ (Correct)
• C. $x \le 6$
• D. $x \le 7$

Explanation: Subtract 4: $3x \le 15$. Divide by 3 to get $x \le 5$.

56. A coin and a die are used together. Probability of head and a number greater than 4?

• A. $1/12$
• B. $1/6$ (Correct)
• C. $1/4$
• D. $1/3$

Explanation: The events are independent. So probability $= \frac12 \times \frac26 = \frac16$.

57. A cone has base radius 7 cm and slant height 25 cm. Find its lateral surface area. Use pi = 22/7.

• A. 550 cm^2 (Correct)
• B. 1100 cm^2
• C. 275 cm^2
• D. 154 cm^2

Explanation: Lateral surface area of cone = pi r l. So (22/7) x 7 x 25 = 550 cm^2.

58. The population of a village is 80,000 and grows by 5% every year. Find the population after 2 years.

• A. 88,000
• B. 88,200 (Correct)
• C. 88,400
• D. 88,600

Explanation: Population after 2 years = $80000(1.05)^2=88200$.

59. A trader sells 40% of his stock at 20% loss. At what markup on the remaining stock should he sell to gain 25% overall?

• A. 45%
• B. 50%
• C. 55% (Correct)
• D. 60%

Explanation: Take total CP $=100$. 40% sold at 20% loss gives SP $=32$. Needed total SP $=125$. So remaining 60 must sell for 93, giving gain $=\frac{33}{60}\times100=55\%$.

60. What is tan 45deg?

• A. 0
• B. 1/sqrt(2)
• C. 1 (Correct)
• D. sqrt(3)

Explanation: $\tan 45^\circ = 1$ because $\sin 45^\circ = \cos 45^\circ$.