Quantitative aptitude
- A number is increased by 10% and the result is then increased by 20%. What is the net percentage increase? Answer: A. 32% Answer: (A) 32% Shortcut (successive change): a + b + ab/100 = 10 + 20 + 200/100 = 32% . Plain: 100 → 110 → 132, a net rise o... 1
- The population of a town is 50,000. It grows by 10% every year. What will it be after 2 years? Answer: A. 60,500 Answer: (A) 60,500 Shortcut: 10% twice = 21% net (10 + 10 + 1). 21% of 50,000 = 10,500, so population = 60,500. Plain: 50,... 1
- In an election between two candidates, the winner got 58% of the valid votes and won by 4,800 votes. How many valid votes were cast? Answer: D. 30,000 Answer: (D) 30,000 Shortcut: winning margin = 58% − 42% = 16% of valid votes. 16% = 4,800, so 100% = 4,800 × 100 ÷ 16 = 30... 1
- In an election, 50,000 votes were cast and 10% of them were invalid. The winning candidate got 60% of the valid votes. How many votes did the losing candidate (the only other candidate) get? Answer: A. 18,000 Answer: (A) 18,000 Valid votes = 90% of 50,000 = 45,000. Loser's share = 100% − 60% = 40% of valid votes = 0.4 × 45,000 =... 1
- A student needs 40% marks to pass. He gets 178 marks and fails by 22 marks. What are the maximum marks? Answer: B. 500 Answer: (B) 500 Shortcut: pass mark = 178 + 22 = 200 = 40% of maximum. Maximum = 200 × 100/40 = 500. Trap: 178/0.4 = 445 igno... 1
- A is 20% less than B and C is 25% more than B. A is what percent of C? Answer: D. 64% Answer: (D) 64% Shortcut: take B = 100. Then A = 80 and C = 125. 80/125 × 100 = 64% . 1
- The length of a rectangle is increased by 20% and its breadth is decreased by 20%. What happens to its area? Answer: A. It decreases by 4% Answer: (A) It decreases by 4% Shortcut (successive change): a + b + ab/100 = 20 - 20 + 20 × (-20)/100 = -4% .... 1
- What is 20% of 30% of 40% of 5000? Answer: B. 120 Answer: (B) 120 Shortcut: 40% of 5000 = 2000; 30% of 2000 = 600; 20% of 600 = 120. Or multiply: 0.2 × 0.3 × 0.4 = 0.024, and... 1
- The price of petrol rises by 25%. By what percent must a car owner cut his consumption so that his spending on petrol rises by only 10%? Answer: A. 12% Answer: (A) 12% Shortcut: spending = price × consumption. New consumption factor = 1.10/1.25 = 0.88 , so the cut is 12%. Plai... 1
- Ravi spends 75% of his income. His income rises by 20% and his expenditure rises by 10%. By what percent do his savings increase? Answer: B. 50% Answer: (B) 50% Take income = 100: expenditure = 75, savings = 25. New income = 120, new expenditure = 75 × 1.1 = 82.5, new s... 1
- Two numbers are 30% and 40% less than a third number. By what percent is the first number more than the second? Answer: D. 162/3 % Answer: (D) 162/3 % Shortcut: third = 100, first = 70, second = 60. First is more by 10 on a base of 60 = 162/3% . Trap:... 1
- A 60-litre mixture of milk and water contains 20% water. How many litres of water must be added so that water becomes 25% of the new mixture? Answer: D. 4 litres Answer: (D) 4 litres Shortcut: milk stays fixed. Milk = 80% of 60 = 48 L. In the new mixture milk is 75%, so new total =... 1
- The population of a village fell by 10% in the first year and rose by 20% in the second year. It is now 54,000. What was it at the start? Answer: A. 50,000 Answer: (A) 50,000 Shortcut: net factor = 0.9 × 1.2 = 1.08. Start = 54,000 ÷ 1.08 = 50,000. Check: 50,000 → 45,000 → 54,00... 1
- 40% of a number is 54 more than 25% of the same number. What is the number? Answer: B. 360 Answer: (B) 360 Shortcut: 40% − 25% = 15% of the number = 54. Number = 54 × 100 ÷ 15 = 360. 1
- Because of a 20% fall in the price of rice, a man can buy 5 kg more rice for ₹800. What was the original price per kg? Answer: C. ₹40 Answer: (C) ₹40 Shortcut: the 20% saved on ₹800 = ₹160 buys the extra 5 kg, so the new price = 160 ÷ 5 = ₹32 per kg. Original... 1
- How many numbers from 1 to 500 are divisible by 3 or 7? Answer: D. 214 Answer: (D) 214 Divisible by 3: ⌊500/3⌋ = 166. By 7: ⌊500/7⌋ = 71. By both (21): ⌊500/21⌋ = 23. By 3 or 7 = 166 + 71 − 23 = 2... 1
- Which of the following numbers is divisible by 11? Answer: C. 4832718 Answer: (C) 4832718 Rule: a number is divisible by 11 if the difference between the sums of its alternate digits is 0 or... 1
- What is the unit digit of \(7^{95}\)? Answer: B. 3 Answer: (B) 3 Unit digits of powers of 7 repeat in a cycle of 4: 7, 9, 3, 1. 95 ÷ 4 leaves remainder 3, so the unit digit is th... 1
- How many prime numbers are there from 1 to 50? Answer: C. 15 Answer: (C) 15 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47: 15 primes. Remember: 25 primes up to 100, 15 of them up... 1
- What is the smallest number that must be added to 2500 to make it exactly divisible by 23? Answer: D. 7 Answer: (D) 7 2500 ÷ 23 leaves remainder 16 (23 × 108 = 2484). Number to add = 23 − 16 = 7. Trap: 16 is the number to subtract,... 1
- What is the sum of the first 30 natural numbers? Answer: B. 465 Answer: (B) 465 n(n+1)/2 = 30 × 31/2 = 465 . 1
- If the four-digit number 54x6 is divisible by 9, what is the digit x? Answer: B. 3 Answer: (B) 3 Digit sum = 5 + 4 + x + 6 = 15 + x must be a multiple of 9. So 15 + x = 18 and x = 3. 1
- A number when divided by 56 leaves a remainder of 29. What will be the remainder when the same number is divided by 8? Answer: B. 5 Answer: (B) 5 Shortcut: 8 divides 56, so the remainder is just 29 ÷ 8 → remainder 5. 1
- How many factors (divisors) does 360 have? Answer: B. 24 Answer: (B) 24 360 = 2³ × 3² × 5¹ . Number of factors = (3 + 1)(2 + 1)(1 + 1) = 24. 1