Quantitative Aptitude Mock Test 7 Practice

1. If one number is even and another is odd, then their sum is:

• A. Always even
• B. Always odd (Correct)
• C. Always prime
• D. Always composite

Explanation: Even + Odd = Odd. Example: 6 + 5 = 11, which is odd.

2. What is 25% of 240?

• A. 50
• B. 60 (Correct)
• C. 70
• D. 80

Explanation: 25% = 1/4, so 1/4 of 240 = 60.

3. If x:y = 5:8 and y:z = 4:7, then x:y:z is:

• A. 5:8:14 (Correct)
• B. 5:8:7
• C. 10:16:14
• D. 6:8:7

Explanation: Make the common term y equal. Scale 4:7 to 8:14, so x:y:z = 5:8:14.

4. 15 workers can build a road in 24 days. How many workers are needed to build the same road in 18 days?

• A. 18
• B. 20 (Correct)
• C. 22
• D. 24

Explanation: Total work = 15 x 24 = 360 worker-days. Required workers = 360/18 = 20.

5. Solve: $\frac{x}{3} + 5 = 9$

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

Explanation: Subtract 5: $x/3 = 4$. Multiply by 3 to get $x = 12$.

6. How many arrangements of LEVEL are possible?

• A. 24
• B. 30 (Correct)
• C. 36
• D. 60

Explanation: LEVEL has 5 letters with L repeated twice and E repeated twice, so count $= \frac{5!}{2!2!} = 30$.

7. The circumference of a circle exceeds its diameter by 30 cm. Find the radius. Use pi = 22/7.

• A. 7 cm (Correct)
• B. 14 cm
• C. 3.5 cm
• D. 10 cm

Explanation: 2pi r - 2r = 30. So 2r(pi - 1) = 30, and substituting pi = 22/7 gives r = 7 cm.

8. The amount on Rs 30,000 for 2 years at 6% CI is:

• A. Rs 33,708 (Correct)
• B. Rs 33,816
• C. Rs 33,908
• D. Rs 34,020

Explanation: $A=30000(1.06)^2=33708$.

9. A trader uses a weight of 900 g for 1 kg while selling at cost price. His gain percentage is:

• A. 10%
• B. 11.11% (Correct)
• C. 12.5%
• D. 9.09%

Explanation: Gain\% $=\frac{100}{900}\times100=11.11\ldots\%$.

10. A point equidistant from (3,0) and (-3,0) must lie on which line?

• A. x-axis
• B. y-axis (Correct)
• C. line y=x
• D. line y=3

Explanation: The perpendicular bisector of the segment joining $(3,0)$ and $(-3,0)$ is the y-axis.

11. Which is the smallest prime number?

• A. 0
• B. 1
• C. 2 (Correct)
• D. 3

Explanation: A prime number has exactly two distinct positive factors. 2 has factors 1 and 2 only, so it is prime. It is also the only even prime number.

12. Convert 3/4 into percentage.

• A. 70%
• B. 75% (Correct)
• C. 80%
• D. 85%

Explanation: (3/4) x 100 = 75%.

13. If a:b = c:d and a = 12, b = 18, c = 20, then d =

• A. 30 (Correct)
• B. 32
• C. 28
• D. 35

Explanation: Use a/b = c/d. So 12/18 = 20/d, hence d = (18 x 20) / 12 = 30.

14. Priya is twice as efficient as Rohan. Together they complete a project in 18 days. How long would Priya alone take?

• A. 24 days
• B. 27 days (Correct)
• C. 30 days
• D. 36 days

Explanation: Let Rohan's rate be r, then Priya's rate is 2r. Together = 3r. Total work = 3r x 18 = 54r. Priya alone takes 54r/2r = 27 days.

15. If $x + y = 9$ and $x - y = 3$, find $x$.

• A. 5
• B. 6 (Correct)
• C. 7
• D. 8

Explanation: Add the two equations: $2x = 12$, so $x = 6$.

16. How many 4-member committees can be formed from 10 persons if one fixed person must be included?

• A. 84 (Correct)
• B. 126
• C. 210
• D. 252

Explanation: Choose the remaining 3 from the other 9 people: $^9C_3 = 84$.

17. A sector has radius 14 cm and central angle 90deg. Find its area. Use pi = 22/7.

• A. 154 cm^2 (Correct)
• B. 308 cm^2
• C. 77 cm^2
• D. 616 cm^2

Explanation: Area of sector = (theta/360) x pi r^2. So (90/360) x (22/7) x 14^2 = 154 cm^2.

18. A principal becomes Rs 46,656 in 3 years at 8% CI. Find the nearest principal.

• A. Rs 37,000
• B. Rs 37,050 (Correct)
• C. Rs 37,100
• D. Rs 37,150

Explanation: $P=46656/(1.08)^3\approx37050.75$. The nearest option is Rs 37,050.

19. A dealer gains 25% after mixing two varieties of rice costing Rs 18/kg and Rs 22/kg in the ratio 3:2. The selling price per kg is:

• A. Rs 24.50 (Correct)
• B. Rs 25
• C. Rs 25.50
• D. Rs 26

Explanation: Average CP $=19.6$. For 25% gain, $SP=19.6\times1.25=24.5$.

20. If the distance between (x,6) and (3,0) is 10, what are the possible values of x?

• A. 11 only
• B. -5 only
• C. 11 and -5 (Correct)
• D. 3 and 13

Explanation: $\sqrt{(x-3)^2+36}=10$ gives $(x-3)^2=64$. So $x=11$ or $x=-5$.

21. Which statement is true about the number 1?

• A. It is prime
• B. It is composite
• C. It is neither prime nor composite (Correct)
• D. It is irrational

Explanation: A prime number must have exactly two distinct factors. The number 1 has only one positive factor, namely 1, so it is neither prime nor composite.

22. 0.32 equals:

• A. 3.2%
• B. 32% (Correct)
• C. 320%
• D. 0.32%

Explanation: Multiply the decimal by 100 to convert it into percentage.

23. A vehicle covers 150 km in 5 hours. At the same speed, it will cover 270 km in:

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

Explanation: Speed = 150/5 = 30 km/h. Time for 270 km = 270/30 = 9 h.

24. 20 men can dig a trench in 18 days. After 6 days, 8 men leave. How many more days are needed?

• A. 18 days
• B. 20 days (Correct)
• C. 22 days
• D. 24 days

Explanation: Total work = 20 x 18 = 360 man-days. Work done in 6 days = 120 man-days. Remaining = 240 man-days. Remaining men = 12. Days needed = 240/12 = 20 days.

25. If $2x + y = 11$ and $x + y = 7$, find $x$.

• A. 2
• B. 3
• C. 4 (Correct)
• D. 5

Explanation: Subtract the second equation from the first: $x = 4$.

26. How many ways can 6 people sit around a round table?

• A. 24
• B. 60
• C. 120 (Correct)
• D. 720

Explanation: Circular permutations of 6 distinct people are $(6-1)! = 120$.

27. The diagonal of a rectangle is 13 cm and one side is 5 cm. Find its area.

• A. 60 cm^2 (Correct)
• B. 65 cm^2
• C. 52 cm^2
• D. 78 cm^2

Explanation: Use Pythagoras to get the other side: sqrt(13^2 - 5^2) = 12 cm. Area = 5 x 12 = 60 cm^2.

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

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

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

29. A merchant buys 40 kg sugar at Rs 36/kg and 60 kg sugar at Rs 44/kg. At what price per kg should he sell the mixture to gain 20%?

• A. Rs 45.60
• B. Rs 46.80
• C. Rs 48.00 (Correct)
• D. Rs 49.20

Explanation: Average CP $=40$. For 20% gain, $SP=48$.

30. A point (x,y) is equidistant from (a+b, b-a) and (a-b, a+b). Which relation follows?

• A. ax = by
• B. bx = ay (Correct)
• C. x = y
• D. a = b

Explanation: Equating squared distances and simplifying gives $bx = ay$.

31. Which of the following is the greatest?

• A. -9
• B. -3 (Correct)
• C. -11
• D. -6

Explanation: Among negative numbers, the number closer to 0 is greater. So among -9, -3, -11 and -6, the greatest is -3.

32. 12.5% as a fraction is:

• A. 1/4
• B. 1/6
• C. 1/8 (Correct)
• D. 1/10

Explanation: 12.5% = 12.5/100 = 1/8.

33. 16 workers can finish a job in 18 days. In how many days will 24 workers finish it?

• A. 12 days (Correct)
• B. 13 days
• C. 11 days
• D. 15 days

Explanation: Workers and days are inversely proportional. 16 x 18 = 24 x d, so d = 12 days.

34. Kiran can do 2/3 of a task in 16 days. In how many days will she complete the full task?

• A. 20 days
• B. 22 days
• C. 24 days (Correct)
• D. 26 days

Explanation: If 2/3 of the task takes 16 days, then the full task takes 16 x 3/2 = 24 days.

35. Find the roots of $x^2 - 5x + 6 = 0$.

• A. 1 and 6
• B. 2 and 3 (Correct)
• C. -2 and -3
• D. 3 and 4

Explanation: Factorize: $x^2 - 5x + 6 = (x-2)(x-3)$. So the roots are 2 and 3.

36. A fair die is rolled. Probability of getting an even number?

• A. $1/3$
• B. $1/2$ (Correct)
• C. $2/3$
• D. $5/6$

Explanation: Even outcomes are 2, 4, and 6. So probability $= \frac{3}{6} = \frac{1}{2}$.

37. A trapezium has parallel sides 10 m and 14 m, and height 8 m. Find its area.

• A. 96 m^2 (Correct)
• B. 112 m^2
• C. 88 m^2
• D. 120 m^2

Explanation: Area of trapezium = 1/2 x (sum of parallel sides) x height. So area = 1/2 x 24 x 8 = 96 m^2.

38. CI on Rs 25,000 for 6 months at 8% p.a. compounded half-yearly is:

• A. Rs 800
• B. Rs 1,000 (Correct)
• C. Rs 1,200
• D. Rs 1,400

Explanation: One half-year period at 4% gives CI = 25000 x 4 / 100 = 1000.

39. A stock is sold: 40% at 20% gain and the rest at 10% loss. Overall result is:

• A. 2% loss
• B. 2% gain (Correct)
• C. 4% loss
• D. 4% gain

Explanation: Overall\% $=0.4\times20+0.6\times(-10)=2\%$ gain.

40. If the slope of one line is 1, then the slope of a perpendicular line is:

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

Explanation: For perpendicular lines, product of slopes is -1. So the perpendicular slope to 1 is -1.

41. Which of the following is a rational number?

• A. pi
• B. sqrt(3)
• C. 0.375 (Correct)
• D. sqrt(11)

Explanation: 0.375 is a terminating decimal, so it can be written as a fraction: $0.375 = 375/1000 = 3/8$. Hence it is rational.

42. 60% of 500 is:

• A. 250
• B. 280
• C. 300 (Correct)
• D. 320

Explanation: 0.60 x 500 = 300.

43. The fraction 63/84 expressed as a ratio in simplest form is:

• A. 3:4 (Correct)
• B. 4:3
• C. 4:4
• D. 3:5

Explanation: 63:84 reduces by 21 to 3:4.

44. Pipe A fills a tank in 10 hours and Pipe B fills it in 15 hours. If both are opened together, how long will the tank take to fill?

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

Explanation: Combined rate = 1/10 + 1/15 = 5/30 = 1/6. So the tank fills in 6 hours.

45. For $x^2 - 7x + 10 = 0$, the sum of roots is:

• A. 7 (Correct)
• B. 10
• C. -7
• D. -10

Explanation: For $ax^2+bx+c=0$, sum of roots $= -b/a$. Here it is $-(-7)/1 = 7$.

46. A card is drawn from a standard deck. Probability that it is not a heart?

• A. $1/4$
• B. $1/2$
• C. $3/4$ (Correct)
• D. $13/52$

Explanation: Probability of a heart is $\frac{13}{52} = \frac14$, so probability of not a heart is $1 - \frac14 = \frac34$.

47. An equilateral triangle has side 12 cm. Find its area.

• A. 36sqrt(3) cm^2 (Correct)
• B. 72sqrt(3) cm^2
• C. 18sqrt(3) cm^2
• D. 24sqrt(3) cm^2

Explanation: Area of an equilateral triangle = (sqrt(3)/4)a^2. With a = 12, the area is 36sqrt(3) cm^2.

48. The difference between CI and SI on Rs 18,000 for 2 years at 10% is:

• A. Rs 160
• B. Rs 180 (Correct)
• C. Rs 200
• D. Rs 220

Explanation: For 2 years, difference = $P(R/100)^2$. = 18000 x 0.01 = 180.

49. A trader buys an article for Rs 2,400, spends Rs 180 on repair, then sells it for Rs 2,898. Gain percentage is:

• A. 10%
• B. 12%
• C. 12.33% (Correct)
• D. 15%

Explanation: Total CP $=2580$ and gain $=318$. Gain\% $=\frac{318}{2580}\times100=12.33\%$.

50. Two non-vertical parallel lines have slopes:

• A. Equal (Correct)
• B. Reciprocals
• C. Negative reciprocals
• D. Always zero

Explanation: Parallel lines run in the same direction, so their slopes are equal.

51. If n is an odd integer, then n^2 is:

• A. Always even
• B. Always odd (Correct)
• C. Sometimes even
• D. Always prime

Explanation: Let $n = 2k+1$. Then $(2k+1)^2 = 4k^2 + 4k + 1 = 2(2k^2+2k)+1$, which is of the form $2m+1$. So it is always odd.

52. 20% of 15% equals:

• A. 2%
• B. 3% (Correct)
• C. 4%
• D. 5%

Explanation: (20/100) x (15/100) = 3/100 = 3%.

53. A sum of Rs 1710 is divided between Aarav and Meera in the ratio 7:2. Aarav gets:

• A. Rs 1330 (Correct)
• B. Rs 380
• C. Rs 1339
• D. Rs 1321

Explanation: Total parts = 9. One part = 1710/9 = 190. Aarav gets 7 x 190 = Rs 1330.

54. A pipe fills a tank in 6 hours, but due to a leak it takes 8 hours. In how many hours can the leak empty the full tank?

• A. 20 hours
• B. 22 hours
• C. 24 hours (Correct)
• D. 26 hours

Explanation: Leak rate = 1/6 - 1/8 = 1/24 of the tank per hour. So the leak alone empties the tank in 24 hours.

55. For $2x^2 - 9x + 4 = 0$, the product of roots is:

• A. 1
• B. 2 (Correct)
• C. 3
• D. 4

Explanation: Product of roots is $c/a = 4/2 = 2$.

56. Two fair coins are tossed. Probability of exactly one head?

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

Explanation: Favourable outcomes are HT and TH, so probability $= \frac{2}{4} = \frac12$.

57. The area of a circle is 616 cm^2. Find its circumference. Use pi = 22/7.

• A. 88 cm (Correct)
• B. 44 cm
• C. 176 cm
• D. 132 cm

Explanation: From pi r^2 = 616, we get r^2 = 196 and r = 14. Circumference = 2pi r = 88 cm.

58. On what sum will the difference between CI and SI for 2 years at 5% be Rs 25?

• A. Rs 8,000
• B. Rs 9,000
• C. Rs 10,000 (Correct)
• D. Rs 12,000

Explanation: At 5%, difference for 2 years = $P\times25/10000=P/400$. So $P/400=25$ gives $P=10000$.

59. Out of total stock, one-third is sold at 10% loss. At what profit percent should the remaining stock be sold to gain 20% overall?

• A. 30%
• B. 35% (Correct)
• C. 40%
• D. 45%

Explanation: $\frac{1}{3}(-10)+\frac{2}{3}x=20$ gives $x=35\%$.

60. What is the distance of the point (6,8) from the origin?

• A. 8
• B. 10 (Correct)
• C. 12
• D. 14

Explanation: Distance from origin $=\sqrt{6^2+8^2}=\sqrt{100}=10$.