miscellaneous Quant

Quantitative Aptitude – Objective Questions

1. Number System and Factorials

1. Find the number of zeroes at the end of 250!
   (a) 35 (b) 22 (c) 62 (d) 24

2. What is the remainder when $5^{99}/13$?
   (a) 8 (b) 12 (c) 6 (d) 7

3. Find the unit digit of: $194^{102}+294^{103}$
   (a) 6 (b) 5 (c) 0 (d) 2

4. Find the highest power of 6 that divides 50! completely.
   (a) 21 (b) 32 (c) 22 (d) 23

5. Find the number of even factors of: $2^7\times 3^4\times 7^3$
   (a) 130 (b) 140 (c) 124 (d) 181

6. Find the sum of all factors of 270.
   (a) 360 (b) 720 (c) 710 (d) 700

2. Set Theory (Venn Diagram)

7. In a group of 240 students:
   - 100 speak English
   - 110 speak Hindi
   - 140 speak Telugu
   - 30 speak both English and Hindi
   - 50 speak both Hindi and Telugu
   - 50 speak both Telugu and English
   - 20 speak all three languages

(i) How many speak only Hindi?
(a) 30 (b) 150 (c) 20 (d) 80

(ii) How many speak both Hindi and Telugu but not English?
(a) 30 (b) 20 (c) 150 (d) 50

(iii) How many speak exactly one language?
(a) 120 (b) 180 (c) 30 (d) 240

(iv) How many speak neither English nor Hindi?
(a) 40 (b) 60 (c) 50 (d) 20

(v) How many speak either English or Telugu?
(a) 180 (b) 120 (c) 160 (d) 190

3. Boats, Trains & Time-Speed-Distance

8. A motorboat travels at 10 km/hr in still water. It goes 91 km downstream and returns in a total of 20 hours. Find the rate of flow of the river.
   (a) 2 (b) 5 (c) 6 (d) 8

9. A train 800 m long is running at a speed of 78 km/h. If it crosses a tunnel in 1 minute, find the length of the tunnel.
   (a) 260 (b) 500 (c) 400 (d) 300

10. A train travels 30 km/h for 12 minutes and 45 km/h for 8 minutes. Find its average speed.
    (a) 35 (b) 22 (c) 48 (d) 24

11. A train 150 m long crosses a bridge 500 m long in 30 seconds. How much time will it take to cross a platform 370 m long?
    (a) 18 (b) 24 (c) 30 (d) 36

12. A person travels equal distances at speeds of 3 km/h, 4 km/h, and 5 km/h. Total time taken is 47 minutes. Find the total distance (in km).
    (a) 1.8 (b) 1.2 (c) 3.6 (d) 1.2

13. Two boys A and B start from Delhi to Meerut (60 km apart). A travels 4 km/h slower than B. B reaches Meerut and returns, meeting A 12 km from Meerut. Find A’s speed.
    (a) 7 (b) 5 (c) 6 (d) 8

4. Percentages, Profit & Loss, Discounts

14. A vendor sells 36 oranges and incurs a loss equal to the selling price of 4 oranges. What is the loss percent?
    (a) 13% (b) 15% (c) 10% (d) 18%

15. A vendor buys bananas at 6 for ₹10 and sells them at 4 for ₹6. What is the profit/loss percentage?
    (a) 10% (b) 15% (c) 16% (d) 18%

16. Sheila sold a mobile phone for ₹1950 at a 25% loss. At what price must she sell it to make a 30% profit?
    (a) 3580 (b) 3380 (c) 6280 (d) 2480

17. What is the equivalent single discount for successive discounts of 10% and 20%?
    (a) 30% (b) 28% (c) 60% (d) 38%

5. Time & Work, Speed Ratio

18. By walking at 3/4 of his usual speed, a man reaches his office 20 minutes late. What is his usual time to reach?
    (a) 60 min (b) 50 min (c) 66 min (d) 80 min

6. Logarithms and Exponents

19. If ${\log }_2=0.301$ and ${\log }_3=0.4771$, find the value of $\log 45$.
    (a) 1.5532 (b) 1.6532 (c) 1.6542 (d) 1.6954

20. Evaluate: $25^{(-1/4{\log }_{5}25)}$
    (a) 25 (b) 1/5 (c) 1/25 (d) -1/25

21. If ${\log }_2=0.3013$, how many digits are there in $2^{64}$?
    (a) 22 (b) 21 (c) 20 (d) 19

22. Evaluate: $\log \frac{14}{3}+\log \frac{11}{5}–\log \frac{22}{15}$
    (a) 1 (b) 1 (c) 0 (d) log 7

7. Algebra & Polynomials

23. The polynomial 4x² - kx + 7 leaves a remainder of -2 when divided by (x – 3). Find the value of k.
    (a) 15 (b) 12 (c) 13 (d) 16

8. Miscellaneous Word Problems

24. In a class, 72 students drink only tea. 50% drink coffee, 25% drink both tea and coffee, and 5% drink neither.
    (i) What is the total number of students?
    (a) 160 (b) 180 (c) 140 (d) 120
    (ii) How many drink only tea or only coffee?
    (a) 113 (b) 112 (c) 114 (d) 128
    (iii) How many drink neither tea nor coffee?
    (a) 7 (b) 5 (c) 8 (d) 12
    (iv) How many drink only coffee?
    (a) 29 (b) 38 (c) 49 (d) 40
    (v) How many drink at least one of the two?
    (a) 152 (b) 144 (c) 128 (d) 152

25. Find the HCF of: 2/3, 8/9, 64/81, 10/27
    (a) 2/81 (b) 2/3 (c) 160/3 (d) 160/81