Quantitative Aptitude Mock Test 5 Practice

1. The product of two consecutive integers is 156. The integers are:

• A. 11 and 12
• B. 12 and 13 (Correct)
• C. 13 and 14
• D. 14 and 15

Explanation: Since $\sqrt{156}$ is close to 12.5, try 12 and 13. Indeed, $12 x 13 = 156$.

2. A value rises by 10% and then by 20%. Net increase =

• A. 28%
• B. 30%
• C. 32% (Correct)
• D. 34%

Explanation: 10 + 20 + (10 x 20)/100 = 32%.

3. A class has 20 boys with average score 64 and 30 girls with average score 70. The class average is:

• A. 67.6 (Correct)
• B. 68.6
• C. 66.6
• D. 67

Explanation: Weighted average = (20 x 64 + 30 x 70) / 50 = 67.6.

4. Arjun and Diya run on a 500 m circular track at 8 m/s and 2 m/s in the same direction. In how many seconds does Arjun lap Diya for the 5th time?

• A. 350 sec
• B. 400 sec
• C. 416.7 sec (Correct)
• D. 450 sec

Explanation: Relative speed = 8 - 2 = 6 m/s. One lap gain takes 500/6 = 83.33 sec. For the 5th lap gain, time = 5 x 83.33 = 416.7 sec.

5. If $\frac{2x-3}{5}=7$, then $x =$

• A. 17
• B. 18
• C. 19 (Correct)
• D. 20

Explanation: Multiply by 5: $2x-3=35$. So $2x=38$ and $x=19$.

6. How many 3-digit numbers with distinct digits can be formed from 0 to 9?

• A. 576
• B. 648 (Correct)
• C. 720
• D. 900

Explanation: Hundreds place has 9 choices, tens has 9, and units has 8. Total $= 9 \times 9 \times 8 = 648$.

7. The ratio of an interior angle to an exterior angle of a regular polygon is 5:1. Find the number of sides.

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

Explanation: If interior : exterior = 5 : 1, let exterior = x and interior = 5x. Then 6x = 180deg, so x = 30deg. Number of sides = 360deg / 30deg = 12.

8. A sum doubles under SI in 12 years. It will become 1.5 times in:

• A. 4 years
• B. 5 years
• C. 6 years (Correct)
• D. 8 years

Explanation: If a sum doubles, interest = P in 12 years. For 1.5 times, interest needed = 0.5P, so the time is half of 12 years.

9. A trader buys 100 pens for Rs 900 and sells all for Rs 1,080. His net gain is:

• A. 15%
• B. 18%
• C. 20% (Correct)
• D. 22%

Explanation: Gain $=180$ and gain\% $=\frac{180}{900}\times100=20\%$.

10. A tree breaks and its top touches the ground making a 30deg angle at a point 50 m from the foot. Find the original height.

• A. 50sqrt(3) m
• B. 100/sqrt(3) m
• C. 150/sqrt(3) m (Correct)
• D. 200/sqrt(3) m

Explanation: Remaining vertical part $=50/\sqrt{3}$ and broken part $=100/\sqrt{3}$. Total original height $=150/\sqrt{3}$ m.

11. Seat numbers from 1 to 120 are printed in a hall in Mumbai. How many of them are divisible by both 3 and 5?

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

Explanation: A number divisible by both 3 and 5 must be divisible by 15. $\lfloor 120/15 \rfloor = 8$.

12. A value decreases by 10% and then by 10%. Net decrease =

• A. 18%
• B. 19% (Correct)
• C. 20%
• D. 21%

Explanation: -10 + -10 + ((-10) x (-10))/100 = -19%.

13. Find the average of 12, 16, 20, 24, 28, 32.

• A. 22 (Correct)
• B. 23
• C. 21
• D. 132

Explanation: Average = (12 + 16 + 20 + 24 + 28 + 32) / 6 = 132/6 = 22.

14. The speed of a boat in still water is 10 km/hr. It goes 91 km downstream and returns in 20 hours. The speed of the stream is:

• A. 3 km/hr (Correct)
• B. 4 km/hr
• C. 5 km/hr
• D. 6 km/hr

Explanation: Let stream speed be v. Then 91/(10+v) + 91/(10-v) = 20. Solving gives v = 3 km/hr.

15. If one root of $x^2-kx+24=0$ is 6, then the other root is:

• A. 3
• B. 4 (Correct)
• C. 5
• D. 6

Explanation: Product of roots = 24. If one root is 6, the other root is $24/6=4$.

16. How many arrangements of BOOK are possible?

• A. 6
• B. 12 (Correct)
• C. 18
• D. 24

Explanation: BOOK has 4 letters with O repeated twice, so arrangements $= \frac{4!}{2!} = 12$.

17. The angles of a triangle are xdeg, (x + 20)deg, and (x + 40)deg. Find the largest angle.

• A. 60deg
• B. 80deg (Correct)
• C. 70deg
• D. 90deg

Explanation: x + (x + 20) + (x + 40) = 180 gives 3x = 120, so x = 40. The largest angle is x + 40 = 80deg.

18. A loan of Rs 30,000 is taken for 9 months at 16% SI. Find the interest.

• A. Rs 3,200
• B. Rs 3,400
• C. Rs 3,600 (Correct)
• D. Rs 4,000

Explanation: Time = 9/12 = 0.75 year. $SI=30000\times16\times0.75/100=3600$.

19. A shirt is sold for Rs 1,530 after a profit of 20%. Its cost price is:

• A. Rs 1,225
• B. Rs 1,250
• C. Rs 1,275 (Correct)
• D. Rs 1,300

Explanation: $CP=1530\times\frac{100}{120}=1275$.

20. From two points 2 km apart on the same straight line, the angles of elevation of an aeroplane are 45deg and 60deg. Find the height of the aeroplane above the ground.

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

Explanation: Let the nearer distance be $x$ km. Then $h=x\sqrt{3}$ and also $h=x+2$. Solving gives $x=\sqrt{3}+1$ and $h=x\sqrt{3}=3+\sqrt{3}$ km.

21. What is the remainder when 53 is divided by 7?

• A. 2
• B. 3
• C. 4 (Correct)
• D. 5

Explanation: $53 = 7 x 7 + 4$. So the remainder is 4.

22. Length increases by 25% and breadth decreases by 20%. Area change =

• A. No change (Correct)
• B. 5% increase
• C. 5% decrease
• D. 10% decrease

Explanation: 25 + (-20) + (25 x -20)/100 = 0%. So there is no change.

23. The average of 8 numbers is 33. If the sum of 7 of them is 231, the missing number is:

• A. 33 (Correct)
• B. 35
• C. 31
• D. 36

Explanation: Total sum = 33 x 8 = 264. Missing number = 264 - 231 = 33.

24. Three athletes run a 1200 m circular track in 80, 100, and 120 seconds. They first all meet at the starting point after:

• A. 400 sec
• B. 500 sec
• C. 600 sec (Correct)
• D. 700 sec

Explanation: The time when all return to start together is LCM(80, 100, 120) = 600 seconds.

25. How many integer solutions satisfy $|x-2|<4$?

• A. 5
• B. 6
• C. 7 (Correct)
• D. 8

Explanation: $|x-2| So $-2

26. How many ways can 5 students sit around a circular table?

• A. 12
• B. 20
• C. 24 (Correct)
• D. 120

Explanation: Circular arrangement of 5 distinct people is $(5-1)! = 24$.

27. The base angles of an isosceles triangle are each 40deg. Find the vertex angle.

• A. 80deg
• B. 100deg (Correct)
• C. 120deg
• D. 140deg

Explanation: Sum of angles in a triangle is 180deg. The vertex angle is 180deg - 40deg - 40deg = 100deg.

28. A sum becomes Rs 28,600 in 2 years at 5% SI. Find the principal.

• A. Rs 24,000
• B. Rs 25,000
• C. Rs 26,000 (Correct)
• D. Rs 27,000

Explanation: $A=P(1+RT/100)=1.1P$. So $P=28600/1.1=26000$.

29. A merchant loses 12.5% by selling a fan for Rs 1,050. The cost price is:

• A. Rs 1,150
• B. Rs 1,180
• C. Rs 1,200 (Correct)
• D. Rs 1,220

Explanation: 12.5% loss means $SP=\frac{7}{8}$ of CP, so $CP=1050\times\frac{8}{7}=1200$.

30. From a cliff 100 m high, the angles of depression of the top and bottom of a tower are 30deg and 60deg. Find the height of the tower.

• A. 100/3 m
• B. 200/3 m (Correct)
• C. 50 m
• D. 300/3 m

Explanation: If horizontal distance is $d$, then $\tan 60^\circ = 100/d$ so $d = 100/\sqrt{3}$. Also $\tan 30^\circ = (100-h)/d$. So $(100-h)=100/3$, which gives $h=200/3$ m.

31. What is the remainder when 248 is divided by 9?

• A. 4
• B. 5 (Correct)
• C. 6
• D. 7

Explanation: Since $10 \equiv 1 \pmod 9$, we can add digits. $2 + 4 + 8 = 14$, and $14 \equiv 5 \pmod 9$.

32. Side of a square increases by 10%. Area increases by:

• A. 10%
• B. 20%
• C. 21% (Correct)
• D. 22%

Explanation: Area change = 10 + 10 + (10 x 10)/100 = 21%.

33. The average marks of 18 students is 47, and of another 22 students is 59. The combined average is:

• A. 53.6 (Correct)
• B. 54.6
• C. 52.6
• D. 53

Explanation: Combined average = (18 x 47 + 22 x 59) / 40 = 53.6.

34. A can finish a job in 18 days. B is 50% more efficient than A. Working together, they finish the job in:

• A. 6 days
• B. 7.2 days (Correct)
• C. 8 days
• D. 9 days

Explanation: If A's rate is 1 unit, B's rate is 1.5 units. A alone takes 18 days, so total work = 18 rate-units. Together rate = 2.5 units/day. Time $=18/2.5=7.2$ days.

35. In an A.P., the 5th term is 18 and the 11th term is 42. What is the common difference?

• A. 3
• B. 4 (Correct)
• C. 5
• D. 6

Explanation: $a+4d=18$ and $a+10d=42$. Subtracting gives $6d=24$, so $d=4$.

36. From 6 players, how many ways can captain and vice-captain be chosen?

• A. 15
• B. 20
• C. 30 (Correct)
• D. 36

Explanation: Order matters, so use permutation: $^6P_2 = 6 \times 5 = 30$.

37. If two lines are perpendicular to the same line, then the two lines are:

• A. Intersecting
• B. Perpendicular to each other
• C. Parallel (Correct)
• D. Coincident

Explanation: Two lines that each make a right angle with the same line must run in the same direction, so they are parallel.

38. The SI on Rs 18,000 at 7.5% for 2 years is:

• A. Rs 2,600
• B. Rs 2,700 (Correct)
• C. Rs 2,800
• D. Rs 2,900

Explanation: $SI=\frac{18000\times7.5\times2}{100}=2700$.

39. A dress marked Rs 2,400 is sold at 15% discount. Find the selling price.

• A. Rs 2,000
• B. Rs 2,020
• C. Rs 2,040 (Correct)
• D. Rs 2,100

Explanation: $SP=2400\times0.85=2040$.

40. The shadow of a tree at 45deg sun elevation is 20 m longer than its shadow at 60deg. Find the height of the tree.

• A. 20(sqrt(3)+1) m
• B. 10sqrt(3)(sqrt(3)+1) m
• C. 47.32 m (Correct)
• D. 40 m

Explanation: Let height be $h$. Then shadows are $h$ and $h/\sqrt{3}$. So $h-h/\sqrt{3}=20$, giving $h=10\sqrt{3}(\sqrt{3}+1)\approx47.32$ m.

41. The remainder when 38 x 27 is divided by 5 is:

• A. 0
• B. 1 (Correct)
• C. 2
• D. 3

Explanation: $38 \equiv 3 \pmod 5$ and $27 \equiv 2 \pmod 5$. So $(38 x 27) \equiv 3 x 2 = 6 \equiv 1 \pmod 5$.

42. Side of a square decreases by 20%. Area decreases by:

• A. 32%
• B. 34%
• C. 36% (Correct)
• D. 40%

Explanation: Area change = -20 + -20 + ((-20) x (-20))/100 = -36%.

43. The average of 50 numbers was calculated as 44, but one number was taken as 39 instead of 19. The correct average is:

• A. 43.6 (Correct)
• B. 44.6
• C. 42.6
• D. 44

Explanation: Correction in total = 19 - 39 = -20. So average changes by -20/50 = -0.4. Correct average = 43.6.

44. Two inlet pipes fill a tank in 12 hours and 18 hours. An outlet empties it in 24 hours. If all are opened together, the tank fills in:

• A. 8 hours
• B. 9 hours
• C. 10.29 hours (Correct)
• D. 12 hours

Explanation: Net rate $=1/12+1/18-1/24$. Using LCM 72, rate $=(6+4-3)/72=7/72$ tank/hour. Time $=72/7=10.29$ hours.

45. If $\log_2 x=6$, then $x =$

• A. 16
• B. 32
• C. 48
• D. 64 (Correct)

Explanation: $\log_2 x=6$ means $x=2^6=64$.

46. How many 3-letter codes can be made from A, B, C, D, E without repetition?

• A. 10
• B. 15
• C. 40
• D. 60 (Correct)

Explanation: Ordered selection gives $^5P_3 = 5 \times 4 \times 3 = 60$.

47. Two similar triangles have perimeters 30 cm and 45 cm. If a side of the smaller triangle is 8 cm, find the corresponding side of the larger triangle.

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

Explanation: For similar triangles, the ratio of corresponding sides equals the ratio of perimeters. So side ratio = 30:45 = 2:3, and the larger side is 8 x 3/2 = 12 cm.

48. A sum triples in 16 years at SI. What is the rate?

• A. 10%
• B. 11.5%
• C. 12.5% (Correct)
• D. 15%

Explanation: Tripling means interest = 2P. So $RT=200$. With $T=16$, $R=12.5\%$.

49. An article is sold for Rs 1,710 after a 10% discount. Its marked price is:

• A. Rs 1,800
• B. Rs 1,850
• C. Rs 1,900 (Correct)
• D. Rs 2,000

Explanation: $MP=1710\times\frac{100}{90}=1900$.

50. The angle of elevation of a tower from 60 m away is 30deg. From 20 m away, what is the angle of elevation?

• A. 45deg
• B. 60deg (Correct)
• C. tan^-1(3)
• D. tan^-1(sqrt(3)/2)

Explanation: Height of the tower = $60\tan 30^\circ = 20\sqrt{3}$. At 20 m, $\tan\theta = 20\sqrt{3}/20 = \sqrt{3}$, so $\theta=60^\circ$.