miscellaneous Quant
Quantitative Aptitude – Mixed Practice Questions for Placements
Quantitative aptitude rounds in placement tests rarely stick to one topic. You might get a number system question followed by a Venn diagram, then a logarithm, then a train problem. That's exactly what this article prepares you for — a mixed set covering 8 topic areas with MCQ-style questions, solving hints, and answers.
Work through each section seriously. The variety is intentional.
1. Number System and Factorials
Q1. Find the number of zeroes at the end of 250!
Hint: Count how many times 5 divides into 250!. Use Legendre's formula: ⌊250/5⌋ + ⌊250/25⌋ + ⌊250/125⌋.
✅ (c) 62
Q2. What is the remainder when 5⁹⁹ is divided by 13?
Hint: Find the pattern of remainders when powers of 5 are divided by 13. The cycle repeats — find the cycle length and use 99 mod cycle.
✅ (a) 8
Q3. Find the unit digit of 194¹⁰² + 294¹⁰³.
Hint: Unit digit of any power depends only on the unit digit of the base. Find unit digit cycles for 4¹⁰² and 4¹⁰³ separately, then add.
✅ (c) 0
Q4. Find the highest power of 6 that divides 50! completely.
Hint: 6 = 2 × 3. The limiting factor is the power of 3 in 50! (since 3 appears less than 2). Use Legendre's formula for 3.
✅ (d) 23
Q5. Find the number of even factors of 2⁷ × 3⁴ × 7³.
Hint: Total factors = (7+1)(4+1)(3+1). For even factors, the power of 2 must be at least 1, so use (7)(5)(4).
✅ (b) 140
Q6. Find the sum of all factors of 270.
Hint: Factorize 270 = 2¹ × 3³ × 5¹. Sum of factors = (1+2)(1+3+9+27)(1+5).
✅ (b) 720
2. Set Theory and Venn Diagrams
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
Hint for all parts: Use the inclusion-exclusion formula. Draw a Venn diagram and fill in each region starting from the center (all three = 20), then work outward.
Q7(i). How many speak only Hindi?
✅ (a) 50
Q7(ii). How many speak both Hindi and Telugu but not English?
✅ (a) 30
Q7(iii). How many speak exactly one language?
✅ (a) 120
Q7(iv). How many speak neither English nor Hindi?
✅ (b) 60
Q7(v). How many speak either English or Telugu?
✅ (d) 190
3. Boats, Trains and Time-Speed-Distance
Q8. A motorboat travels at 10 km/h in still water. It goes 91 km downstream and returns in 20 hours. Find the rate of flow of the river.
Hint: Time downstream = 91/(10+r), time upstream = 91/(10−r). Their sum = 20. Solve for r.
✅ (b) 3 km/h
Q9. A train 800 m long runs at 78 km/h and crosses a tunnel in 1 minute. Find the length of the tunnel.
Hint: Convert 78 km/h to m/s. Distance in 60 seconds = speed × 60 = train length + tunnel length.
✅ (c) 500 m
Q10. A train travels 30 km/h for 12 minutes and 45 km/h for 8 minutes. Find its average speed.
Hint: Average speed = total distance ÷ total time. Calculate each distance separately.
✅ (a) 36 km/h
Q11. A train 150 m long crosses a 500 m bridge in 30 seconds. How long to cross a 370 m platform?
Hint: Find speed from first scenario. Time = (150 + 370) ÷ speed.
✅ (b) 24 seconds
Q12. A person travels equal distances at 3 km/h, 4 km/h, and 5 km/h. Total time = 47 minutes. Find total distance.
Hint: Let each distance = d km. Total time = d/3 + d/4 + d/5 = 47/60. Solve for d, then multiply by 3.
✅ (b) 3 km
Q13. A and B travel from Delhi to Meerut (60 km). A is 4 km/h slower than B. B reaches Meerut, returns, and meets A who is 12 km from Meerut. Find A's speed.
Hint: When they meet, A has covered 48 km. B has covered 60 + 12 = 72 km. Ratio of distances = ratio of speeds. B's speed = A's speed + 4.
✅ (b) 4 km/h
4. Percentages, Profit and Loss, Discounts
Q14. A vendor sells 36 oranges and incurs a loss equal to the selling price of 4 oranges. What is the loss percent?
Hint: Loss = SP of 4 oranges. Total SP = SP of 36 oranges. Loss% = Loss ÷ CP × 100. CP = SP of 40 oranges (since CP = SP + Loss).
✅ (c) 10%
Q15. A vendor buys bananas at 6 for ₹10 and sells at 4 for ₹6. What is the profit or loss percentage?
Hint: Find CP per banana and SP per banana. Compare to get profit/loss%.
✅ (a) 10% loss
Q16. Sheila sold a mobile for ₹1,950 at a 25% loss. At what price must she sell it for a 30% profit?
Hint: Find CP from the loss scenario first. Then apply 30% profit to that CP.
✅ (b) ₹3,120
Q17. Find the equivalent single discount for successive discounts of 10% and 20%.
Hint: Apply on ₹100. After 10% → ₹90. After 20% on ₹90 → ₹72. Discount = 100 − 72.
✅ (b) 28%
5. Time and Work, Speed Ratio
Q18. Walking at 3/4 of his usual speed, a man reaches his office 20 minutes late. What is his usual time?
Hint: At 3/4 speed, time becomes 4/3 of usual. Extra time = t/3 = 20 minutes.
✅ (a) 60 minutes
6. Logarithms and Exponents
Q19. If log 2 = 0.301 and log 3 = 0.4771, find log 45.
Hint: log 45 = log(9 × 5) = log 9 + log 5 = 2 log 3 + log(10/2) = 2 log 3 + 1 − log 2.
✅ (b) 1.6532
Q20. Evaluate: 25^(−1/4 × log₅ 25)
Hint: log₅ 25 = 2. So the exponent = −1/4 × 2 = −1/2. Expression = 25^(−1/2) = 1/√25.
✅ (b) 1/5
Q21. If log 2 = 0.3010, how many digits are there in 2⁶⁴?
Hint: Number of digits = ⌊log₁₀(2⁶⁴)⌋ + 1 = ⌊64 × 0.3010⌋ + 1.
✅ (c) 20
Q22. Evaluate: log(3/14) + log(5/11) − log(15/22)
Hint: Combine using log rules: log A + log B − log C = log(AB/C). Simplify the resulting fraction.
✅ (c) 0
7. Algebra and Polynomials
Q23. The polynomial 4x² − kx + 7 leaves a remainder of −2 when divided by (x − 3). Find k.
Hint: By the remainder theorem, substitute x = 3 into the polynomial and set it equal to −2. Solve for k.
✅ (c) 13
8. Miscellaneous Word Problems
In a class: 72 students drink only tea, 50% drink coffee, 25% drink both tea and coffee, 5% drink neither.
Hint for all parts: Let total = N. Students who drink only tea = N × (tea%) − N × (both%) = 72. Use this to find N first.
Q24(i). What is the total number of students?
✅ (b) 160
Q24(ii). How many drink only tea or only coffee?
✅ (c) 112
Q24(iii). How many drink neither tea nor coffee?
✅ (c) 8
Q24(iv). How many drink only coffee?
✅ (d) 40
Q24(v). How many drink at least one of the two?
✅ (a) 152
Q25. Find the HCF of 2/3, 8/9, 64/81, 10/27.
Hint: HCF of fractions = HCF of numerators ÷ LCM of denominators. HCF of (2, 8, 64, 10) = 2. LCM of (3, 9, 81, 27) = 81.
✅ (a) 2/81
Wrap Up
Mixed aptitude sets like this one are the closest thing to what you'll actually face in a placement test. The questions jump topics, the options are designed to catch common errors, and there's no time to re-derive formulas from scratch. That's why practicing topic-by-topic first and then doing mixed sets is the right approach — you build the instincts, then you test them under pressure.
For more reasoning practice, check out these also
For a structured placement prep roadmap explore,