Quantitative Aptitude Mock Test 6 Practice

1. The unit digit of 3^26 is:

• A. 1
• B. 3
• C. 7
• D. 9 (Correct)

Explanation: Unit digit cycle of powers of 3 is 3, 9, 7, 1. Since 26 leaves remainder 2 on division by 4, the answer is the second term, 9.

2. Population grows by 8% each year for 2 years. Approx net growth =

• A. 15.5%
• B. 16%
• C. 16.64% (Correct)
• D. 17%

Explanation: 8 + 8 + (8 x 8)/100 = 16.64%.

3. A invests Rs 24,000 for 8 months and B invests Rs 18,000 for 12 months. If total profit is Rs 17,000, A's share is:

• A. Rs 8,000 (Correct)
• B. Rs 8,500
• C. Rs 9,000
• D. Rs 9,500

Explanation: Capital-months: A = $24000\times8=192000$, B = $18000\times12=216000$. Ratio = 8:9, so A's share $=\frac{8}{17}\times17000=8000$.

4. A boat covers 48 km downstream in 3 hours and the same distance upstream in 6 hours. What is the speed of the boat in still water?

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

Explanation: Downstream speed = 48/3 = 16 km/hr. Upstream speed = 48/6 = 8 km/hr. Still water speed $=(16+8)/2=12$ km/hr.

5. What is the degree of $7x^4 - 3x + 8$?

• A. 2
• B. 3
• C. 4 (Correct)
• D. 5

Explanation: The highest power of $x$ is 4, so the degree is 4.

6. How many committees of 3 can be formed from 8 students?

• A. 28
• B. 35
• C. 56 (Correct)
• D. 336

Explanation: Use combinations: $^8C_3 = 56$.

7. G is the centroid of triangle ABC. If median AD = 15 cm, find AG.

• A. 5 cm
• B. 10 cm (Correct)
• C. 12 cm
• D. 7.5 cm

Explanation: The centroid divides each median in the ratio 2:1 from the vertex. So AG = 2/3 of AD = 10 cm.

8. The CI on Rs 12,000 for 3 years at 5% annually is:

• A. Rs 1,791.50
• B. Rs 1,891.50 (Correct)
• C. Rs 1,990.50
• D. Rs 2,025

Explanation: $A=12000(1.05)^3=13891.50$. So $CI=1891.50$.

9. A store wants 25% gain after allowing 20% discount. The marked price should be what percent of cost price?

• A. 140%
• B. 150%
• C. 156.25% (Correct)
• D. 160%

Explanation: Take $CP=100$. Needed $SP=125$. $MP=\frac{125}{0.8}=156.25$.

10. What is the slope of the line joining (2,3) and (5,9)?

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

Explanation: $m=(9-3)/(5-2)=6/3=2$.

11. The unit digit of 7^103 is:

• A. 1
• B. 3 (Correct)
• C. 7
• D. 9

Explanation: Unit digit cycle of powers of 7 is 7, 9, 3, 1. Since 103 leaves remainder 3 on division by 4, the answer is the third term, 3.

12. Machine value falls by 20% and then by 25%. Net decrease =

• A. 40% (Correct)
• B. 42%
• C. 45%
• D. 50%

Explanation: -20 + -25 + ((-20) x (-25))/100 = -40%.

13. If 18 workers complete a job in 20 days, how many workers are needed to complete the same job in 12 days?

• A. 24
• B. 28
• C. 30 (Correct)
• D. 36

Explanation: Total work = $18\times20=360$ worker-days. Required workers $=360/12=30$.

14. Arjun can complete a wall in 20 days and Diya in 30 days. How long will they take together?

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

Explanation: Combined rate = 1/20 + 1/30 = 5/60 = 1/12. So together they take 12 days.

15. What is the degree of the term $6x^3y^2$?

• A. 3
• B. 4
• C. 5 (Correct)
• D. 6

Explanation: In a multivariable term, add exponents: $3 + 2 = 5$.

16. Find $^9C_7$ quickly.

• A. 28
• B. 36 (Correct)
• C. 45
• D. 72

Explanation: Use symmetry: $^9C_7 = ^9C_2 = \frac{9 \times 8}{2} = 36$.

17. A triangle has sides 5, 12, and 13. What type of triangle is it?

• A. Acute
• B. Right-angled (Correct)
• C. Obtuse
• D. Equilateral

Explanation: Since 5^2 + 12^2 = 13^2, the triangle satisfies Pythagoras and is right-angled.

18. A sum becomes Rs 13,225 in 2 years at 15% annually. Find the principal.

• A. Rs 9,500
• B. Rs 10,000 (Correct)
• C. Rs 10,200
• D. Rs 10,500

Explanation: $P=13225/(1.15)^2=10000$.

19. An item marked Rs 5,000 is available at successive discounts of 10%, 10%, and 20%. Customer pays:

• A. Rs 3,200
• B. Rs 3,240 (Correct)
• C. Rs 3,400
• D. Rs 3,600

Explanation: $SP=5000\times0.9\times0.9\times0.8=3240$.

20. What is the slope of a line perpendicular to a line with slope 3?

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

Explanation: For perpendicular lines, $m_1m_2=-1$. So the required slope is $-1/3$.

21. The unit digit of 9^48 is:

• A. 1 (Correct)
• B. 3
• C. 7
• D. 9

Explanation: Unit digit cycle of 9 is 9, 1. Cycle length = 2. Since 48 leaves remainder 0 on division by 2, take the last term of the cycle, 1.

22. After a 25% increase, a number becomes 375. What was the original number?

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

Explanation: After a 25% increase, new value = 125% of original. Original value $=375\times\frac{100}{125}=300$.

23. The average weight of 12 students is 48 kg. A teacher weighing 72 kg joins them. What is the new average?

• A. 49.5 kg
• B. 49.846 kg (Correct)
• C. 50.5 kg
• D. 51 kg

Explanation: Original total weight = $12\times48=576$ kg. New total = 576 + 72 = 648 kg. New average $=648/13=49.846$ kg.

24. Rohan is 3 times as efficient as Rahul. Together they finish a job in 9 days. How many days does Rohan alone take?

• A. 12 days (Correct)
• B. 13 days
• C. 15 days
• D. 18 days

Explanation: Let Rahul's rate be r. Then Rohan's rate is 3r, so together they work at 4r. Total work = 4r x 9 = 36r. Rohan alone takes 36r / 3r = 12 days.

25. If $2x + 3 = x + 11$, then $x =$

• A. 6
• B. 7
• C. 8 (Correct)
• D. 9

Explanation: Bring like terms together: $2x - x = 11 - 3$. So $x = 8$.

26. How many teams of 4 can be chosen from 6 boys and 5 girls if exactly 2 girls are required?

• A. 120
• B. 135
• C. 150 (Correct)
• D. 165

Explanation: Choose 2 girls and 2 boys: $^5C_2 \times ^6C_2 = 10 \times 15 = 150$.

27. In triangle ABC, M and N are midpoints of AB and AC. If BC = 20 cm, find MN.

• A. 5 cm
• B. 10 cm (Correct)
• C. 15 cm
• D. 8 cm

Explanation: The segment joining the midpoints of two sides is half the third side. So MN = 20/2 = 10 cm.

28. At what rate will Rs 25,000 amount to Rs 30,250 in 2 years at annual CI?

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

Explanation: $(1+r)^2=30250/25000=1.21$. So $r=10\%$.

29. A dealer marks goods 30% above cost price and gives 10% discount. His gain percentage is:

• A. 15%
• B. 17% (Correct)
• C. 17.5%
• D. 20%

Explanation: Net factor $=1.3\times0.9=1.17$, so gain is 17%.

30. In what ratio does the x-axis divide the segment joining (4,-6) and (1,3)?

• A. 2:1 (Correct)
• B. 1:2
• C. 1:4
• D. 4:1

Explanation: At the x-axis, $y=0$. Using section formula for y-coordinate: $(3k-6)/(k+1)=0$ gives $k=2$.

31. What is the smallest number that must be added to 278 to make it divisible by 6?

• A. 2
• B. 3
• C. 4 (Correct)
• D. 5

Explanation: $278 = 6 x 46 + 2$. The remainder is 2, so to reach the next multiple of 6, add $6 - 2 = 4$.

32. A price is increased by 20% and then reduced by 10%. The final price is what percent of the original?

• A. 106%
• B. 108% (Correct)
• C. 110%
• D. 112%

Explanation: Use multipliers: $1.20\times0.90=1.08$. So the final price is 108% of the original.

33. The average of 25 numbers is 36. Later, one value recorded as 64 is corrected to 39. What is the corrected average?

• A. 35 (Correct)
• B. 35.2
• C. 35.4
• D. 35.6

Explanation: Total decreases by $64-39=25$. Average decreases by $25/25=1$, so corrected average = 35.

34. A can do a work in 15 days and B in 20 days. They work together for 6 days, then A leaves. How many more days does B need?

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

Explanation: LCM of 15 and 20 is 60 units. A does 4 units/day, B does 3 units/day. In 6 days together, they do 42 units. Remaining work = 18 units. B alone takes 18/3 = 6 days.

35. Solve: $4x - 9 = 3$

• A. 2
• B. 3 (Correct)
• C. 4
• D. 5

Explanation: Add 9 to both sides: $4x = 12$. So $x = 3$.

36. From 5 boys and 4 girls, how many groups of 3 contain at least one girl?

• A. 64
• B. 70
• C. 74 (Correct)
• D. 84

Explanation: Total groups $= ^9C_3 = 84$. All-boy groups $= ^5C_3 = 10$. Required $= 84 - 10 = 74$.

37. In triangle ABC, AB = 6, AC = 8, and BC = 10. Find the median from A to BC.

• A. 5 cm (Correct)
• B. sqrt(41) cm
• C. sqrt(45) cm
• D. 6 cm

Explanation: Since BC = 10, its midpoint splits it into 5 and 5. By Apollonius, 6^2 + 8^2 = 2(AD^2 + 5^2), giving AD^2 = 25 and AD = 5 cm.

38. How many years will Rs 16,000 become Rs 19,360 at 10% annual CI?

• A. 1
• B. 2 (Correct)
• C. 3
• D. 4

Explanation: $16000(1.1)^2=19360$, so the time is 2 years.

39. If an article sold for Rs 2,280 at 5% discount still gives 20% profit, its cost price is:

• A. Rs 1,800
• B. Rs 1,850
• C. Rs 1,900 (Correct)
• D. Rs 1,950

Explanation: The actual selling price is Rs 2,280. $CP=2280\times\frac{100}{120}=1900$.

40. Find the centroid of the triangle with vertices (2,4), (6,2), and (4,6).

• A. (4,4) (Correct)
• B. (3,3)
• C. (6,6)
• D. (2,2)

Explanation: Centroid $=\left((2+6+4)/3,(4+2+6)/3\right)=(4,4)$.

41. What is the greatest number that must be subtracted from 278 to make it divisible by 6?

• A. 1
• B. 2 (Correct)
• C. 3
• D. 4

Explanation: $278 = 6 x 46 + 2$. The greatest number to subtract is the remainder itself, so subtract 2.

42. A class has 60% boys. If 12 boys leave, boys become 50% of the class. How many students were originally in the class?

• A. 48
• B. 60 (Correct)
• C. 72
• D. 84

Explanation: Let original total be $T$. Boys = $0.6T$. After 12 boys leave, $0.6T-12=0.5(T-12)$. Solving gives $0.1T=6$, so $T=60$.

43. Simplify the ratio 54:81.

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

Explanation: Divide both terms by their HCF, 27. So 54:81 = 2:3.

44. If 12 workers build a house in 20 days, how many workers are needed to build it in 15 days?

• A. 14
• B. 16 (Correct)
• C. 18
• D. 20

Explanation: Total work = 12 x 20 = 240 worker-days. Required workers = 240/15 = 16.

45. Which of the following is a polynomial in $x$?

• A. $x^{-1} + 2$
• B. $\sqrt{x} + 1$
• C. $3x^2 - 5x + 4$ (Correct)
• D. $\frac{1}{x} - 7$

Explanation: A polynomial has only non-negative integer powers of the variable. So $3x^2 - 5x + 4$ is the valid choice.

46. At a workshop, 9 participants each shake hands once with every other participant. Number of handshakes?

• A. 28
• B. 36 (Correct)
• C. 45
• D. 72

Explanation: Each handshake is an unordered pair, so count $= ^9C_2 = 36$.

47. Which of the following is NOT a valid congruency condition?

• A. SSS
• B. SAS
• C. SSA (Correct)
• D. AAS

Explanation: SSA is not a standard congruency rule because it can produce more than one triangle.

48. CI on Rs 20,000 at 12% for 1 year is:

• A. Rs 2,200
• B. Rs 2,300
• C. Rs 2,400 (Correct)
• D. Rs 2,500

Explanation: For one year, CI = SI. $20000\times12/100=2400$.

49. Which is better for a customer?

• A. 30% then 10%
• B. 35% then 5% (Correct)
• C. Both same
• D. Cannot compare

Explanation: Offer A gives 37% off and Offer B gives 38.25% off, so B is better.

50. Two vertices of a triangle are (-2,5) and (-4,4), and its centroid is at the origin. Find the third vertex.

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

Explanation: If the centroid is $(0,0)$, then the sum of x-coordinates and the sum of y-coordinates are both 0. So $x_3=6$ and $y_3=-9$.

51. Which of the following is a whole number but not a natural number?

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

Explanation: Natural numbers begin from 1, while whole numbers begin from 0. So 0 belongs to whole numbers, but it is not a natural number.

52. A student scores 72 marks out of 90. To make the percentage 85% after one more test of 60 marks, how many marks are needed in the next test?

• A. 51
• B. 52.5
• C. 54
• D. 55.5 (Correct)

Explanation: Total marks after two tests = 150. 85% of 150 = 127.5. Required marks in next test = $127.5-72=55.5$.

53. A sum of Rs 1260 is divided between Aarav and Meera in the ratio 2:5. Aarav gets:

• A. Rs 360 (Correct)
• B. Rs 900
• C. Rs 367
• D. Rs 353

Explanation: Total parts = 7. One part = 1260/7 = 180. Aarav gets 2 x 180 = Rs 360.

54. Priya can type 1200 words in 30 minutes. How many words can she type in 2.5 hours?

• A. 5000
• B. 5500
• C. 6000 (Correct)
• D. 6500

Explanation: Rate = 1200/30 = 40 words per minute. In 2.5 hours = 150 minutes, she types 40 x 150 = 6000 words.

55. If $7x + 4 = 46$, then $x =$

• A. 5
• B. 6 (Correct)
• C. 7
• D. 8

Explanation: Subtract 4: $7x = 42$. Therefore $x = 6$.

56. How many diagonals does a nonagon have?

• A. 18
• B. 24
• C. 27 (Correct)
• D. 36

Explanation: Total pairs of vertices $= ^9C_2 = 36$. Subtract 9 sides to get 27 diagonals.

57. Two triangles have angles 40deg, 60deg, 80deg and 40deg, 60deg, 80deg respectively. They are:

• A. Congruent
• B. Similar (Correct)
• C. Neither
• D. Both congruent and similar

Explanation: Equal angles guarantee AA similarity, but not necessarily congruency.

58. The amount after 3 years on Rs 5,000 at 20% annual CI is:

• A. Rs 8,540
• B. Rs 8,620
• C. Rs 8,640 (Correct)
• D. Rs 8,700

Explanation: $A=5000(1.2)^3=8640$.

59. The difference between a single 30% discount and successive 20% and 10% discounts on Rs 6,000 is:

• A. Rs 0
• B. Rs 60
• C. Rs 120 (Correct)
• D. Rs 180

Explanation: Single discount price $=4200$. Successive discount price $=4320$. Difference $=120$.

60. The points (2,-k), (0,-5), and (5/2,0) are collinear. Find k.

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

Explanation: Using the area-zero condition for collinear points gives $k=1$.