Quantitative aptitude
- What is the largest four-digit number exactly divisible by 88? Answer: C. 9944 Answer: (C) 9944 9999 ÷ 88 leaves remainder 55. Largest = 9999 − 55 = 9944. Note: 9856 is divisible by 88 but is not the lar... 1
- What is the remainder when \(17^{23}\) is divided by 16? Answer: A. 1 Answer: (A) 1 17 = 16 + 1, so 17²³ leaves the same remainder as 1²³ = 1. 1
- What is the unit digit of \(2137^{754}\)? Answer: C. 9 Answer: (C) 9 Only the unit digit 7 matters. Cycle of 7: 7, 9, 3, 1. 754 ÷ 4 leaves remainder 2, so the unit digit is 9. 1
- How many zeros are there at the end of 100! (100 factorial)? Answer: C. 24 Answer: (C) 24 Count the factors of 5: ⌊100/5⌋ + ⌊100/25⌋ = 20 + 4 = 24. Trap: 20 forgets the extra 5s in 25, 50, 75 and 100. 1
- What is the sum of all the factors of 72? Answer: A. 195 Answer: (A) 195 72 = 2³ × 3² . Sum of factors = (1 + 2 + 4 + 8)(1 + 3 + 9) = 15 × 13 = 195. 1
- The sum of the squares of three consecutive natural numbers is 2030. What is the middle number? Answer: D. 26 Answer: (D) 26 Let the numbers be n − 1, n, n + 1. Sum of squares = 3n² + 2 = 2030, so n² = 676. n = 26. Check: 25² + 26² + 27... 1
- \(49^{15} - 1\) is exactly divisible by which of the following? Answer: D. 48 Answer: (D) 48 aⁿ - bⁿ is always divisible by a - b . So 49¹⁵ - 1¹⁵ is divisible by 49 − 1 = 48. 50 = 49 + 1 divides it only w... 1
- A number leaves a remainder of 3 when divided by 6. What is the remainder when the square of the number is divided by 6? Answer: A. 3 Answer: (A) 3 Write the number as 6k + 3. Its square leaves the same remainder as 3² = 9, and 9 ÷ 6 leaves 3. 1
- Which fraction is equal to \(0.\overline{36}\)? Answer: A. 4/11 Answer: (A) 4/11 For a pure recurring decimal, write the repeating block over as many 9s: 36/99 = 4/11 . Trap: 9/25 = 0.36 (... 1
- Which fraction is equal to \(0.2\overline{3}\)? Answer: D. 7/30 Answer: (D) 7/30 Mixed recurring: (all digits − non-recurring part) over 9 for each recurring digit and 0 for each non-recur... 1
- Which of the following is the largest? Answer: D. sqrt[4]5 Answer: (D) sqrt[4]5 Raise all to the 12th power (LCM of 2, 3, 4, 6): √(2) → 2⁶ = 64 , sqrt[3]3 → 3⁴ = 81 , sqrt[4]5 → 5... 1
- What is the remainder when \(3^{100}\) is divided by 7? Answer: A. 4 Answer: (A) 4 3⁶ = 729 leaves remainder 1 on division by 7. 100 = 6 × 16 + 4, so 3¹⁰⁰ leaves the same remainder as 3⁴ = 81 . 81... 1
- What is the remainder when 1! + 2! + 3! + … + 100! is divided by 12? Answer: B. 9 Answer: (B) 9 From 4! onwards every factorial is divisible by 12 (4! = 24). So the remainder comes from 1! + 2! + 3! = 1 + 2 +... 1
- How many factors of 3600 are perfect squares? Answer: A. 12 Answer: (A) 12 3600 = 2⁴ × 3² × 5² . A square factor uses even powers only. Choices: power of 2 from 0, 2, 4 (3 ways), of 3 fr... 1
- What is the remainder when \(5^{90}\) is divided by 124? Answer: C. 1 Answer: (C) 1 Notice 124 = 125 − 1 = 5³ - 1 , so 5³ leaves remainder 1. 5⁹⁰ = (5³)³⁰ leaves remainder 1³⁰ = 1. 1
- The area of a square is 196 m². What is its perimeter? Answer: C. 56 m Answer: (C) 56 m Side = √196 = 14 m. Perimeter = 4 × 14 = 56 m. 1
- What is the area of a circle of radius 14 cm? Take \(\pi = \frac{22}{7}\). Answer: C. 616 cm² Answer: (C) 616 cm² Area = πr² = 22/7 × 14 × 14 = 616 cm². Trap: 88 cm is the circumference. 1
- What is the area of a triangle with base 18 cm and height 12 cm? Answer: C. 108 cm² Answer: (C) 108 cm² Area = 1/2 × 18 × 12 = 108 cm². 1
- What is the volume of a cube of edge 6 cm? Answer: D. 216 cm³ Answer: (D) 216 cm³ Volume = a³ = 6 × 6 × 6 = 216 cm³. 1
- The circumference of a circle is 44 cm. What is its radius? Take \(\pi = \frac{22}{7}\). Answer: A. 7 cm Answer: (A) 7 cm 2πr = 44, so r = 44 × 7/2 × 22 = 7 cm. Trap: 14 cm is the diameter. 1
- What is the total surface area of a cuboid measuring 12 cm × 8 cm × 5 cm? Answer: B. 392 cm² Answer: (B) 392 cm² TSA = 2(lb + bh + hl) = 2(96 + 40 + 60) = 2 × 196 = 392 cm². Trap: 480 is the volume. 1
- The diagonal of a square is \(10\sqrt{2}\) cm. What is its area? Answer: B. 100 cm² Answer: (B) 100 cm² Area of a square = d²/2 = 200/2 = 100 cm². (Side = 10 cm.) 1
- The perimeter of a rectangle is 46 cm and its area is 120 cm². What is the length of its diagonal? Answer: C. 17 cm Answer: (C) 17 cm l + b = 23 and lb = 120, so l = 15, b = 8. Diagonal = √(15² + 8²) = √289 = 17 cm. Shortcut: d² = (l + b)²... 1
- What is the volume of a cylinder with radius 7 cm and height 10 cm? Take \(\pi = \frac{22}{7}\). Answer: D. 1540 cm³ Answer: (D) 1540 cm³ V = πr²h = 22/7 × 49 × 10 = 1540 cm³. 1