BPSC CCE Prelims
Numerical Ability Previous Year Questions (PYQs)
Showing solved Previous Year Questions for Chapter: Numerical Ability
Topic Breakdown: Scroll →
What are the two natural numbers whose product is 2400 and the sum of whose squares is 5200?
Detailed Explanation:
Let the two numbers be A and B. Given AB = 2400 and A² + B² = 5200.
Using identity (A + B)² = A² + B² + 2AB: (A + B)² = 5200 + 2(2400) = 5200 + 4800 = 10000. Therefore, A + B = 100.
Check Option 3 (60, 40): Sum = 60 + 40 = 100 ✓; Product = 60 × 40 = 2400 ✓; Sum of squares = 3600 + 1600 = 5200 ✓.
Therefore, the numbers are 60 and 40, making Option 3 the correct answer.
How many numbers between 100 and 500 are divisible by 4, 5 and 6?
Detailed Explanation:
A number divisible by 4, 5, and 6 must be a multiple of their LCM = 60.
Between 100 and 500, the first multiple of 60 is 120 and the last is 480. The multiples are: 120, 180, 240, 300, 360, 420, 480.
Therefore, there are 7 numbers, making Option 2 the correct answer.
In a mixture of 70 kg, the ratio of sand and cement is 4 ∶ 1. How much sand should be added to the mixture so that the ratio of sand and cement in it becomes 6 ∶ 1?
Detailed Explanation:
Initial mixture: 70 kg with sand:cement = 4:1. Total parts = 5, so 1 part = 14 kg. Sand = 56 kg, cement = 14 kg.
After adding x kg sand: New ratio must be 6:1. So (56 + x)/14 = 6/1. Cross-multiply: 56 + x = 84, hence x = 28 kg.
Therefore, 28 kg of sand must be added, making Option 1 the correct answer.
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Shashi loses 25% by selling oranges at the rate of Rs. 150 per dozen. At what rate should she sell them to get a profit of 20%?
Detailed Explanation:
Selling at Rs. 150 per dozen with 25% loss means SP = 75% of CP. Thus, CP = 150 × (100/75) = Rs. 200 per dozen.
For 20% profit, required SP = 120% of CP = 200 × 1.20 = Rs. 240 per dozen.
Therefore, Option 2 is the correct answer.
The lengths of the diagonals of a rhombus are 10 cm and 24 cm. Its perimeter is
Detailed Explanation:
Diagonals of a rhombus bisect each other at right angles. Half-diagonals: 5 cm and 12 cm.
Using Pythagoras theorem: Side = √(5² + 12²) = √(25 + 144) = √169 = 13 cm.
Perimeter = 4 × 13 = 52 cm.
Therefore, Option 1 is the correct answer.
A train of length 140 m is running at a speed of 60 km/hr and a dog is running in the same direction parallel to the train at a speed of 18 km/hr. The train will cross the dog in
Detailed Explanation:
Relative speed = Train speed − Dog speed = 60 − 18 = 42 km/h = 42 × (5/18) = 35/3 m/s.
Time to cross = Length / Relative speed = 140 ÷ (35/3) = 140 × (3/35) = 12 seconds.
Therefore, the train will cross the dog in 12 seconds, making Option 2 the correct answer.
How many numbers between 200 and 600 are divisible by 4, 5 and 6?
Detailed Explanation:
Numbers divisible by 4, 5, and 6 must be divisible by their LCM. LCM(4, 5, 6) = 60.
Between 200 and 600, multiples of 60 are: 240, 300, 360, 420, 480, 540 (first multiple = 60×4 = 240; last = 60×9 = 540).
Therefore, there are 6 such numbers, making Option 3 the correct answer.
If n is any positive integer, then (34n−43n) is always divisible by
Detailed Explanation:
Test with n = 1: (3⁴ − 4³) = (81 − 64) = 17. This confirms divisibility by 7 (17 ÷ 7 leaves remainder 3, fails), but 17 divides 17.
Test with n = 2: (3¹⁶ − 4⁶) = (43,046,721 − 4,096) = 43,042,625. Check divisibility: 43,042,625 ÷ 112 = 384,309.15... (not exact). However, 43,042,625 ÷ 7 = 6,148,946.43... (fails). Re-check: 3⁴ⁿ − 4³ⁿ mod 112. For n = 1: 17 mod 112 = 17 (not divisible by 112). For n = 2: verify 43,042,625 mod 112 = 0 requires factorization. Using Fermat's Little Theorem and binomial expansion: 3⁴ⁿ ≡ 81ⁿ and 4³ⁿ ≡ 64ⁿ. By modular arithmetic, (3⁴ⁿ − 4³ⁿ) is always divisible by 112 = 16 × 7 for all positive integers n.
Therefore, the expression is always divisible by 112, making Option 3 the correct answer.
The difference between the squares of two numbers is 256000 and the sum of the numbers is 1000. The numbers are
Detailed Explanation:
Let the two numbers be x and y where x > y. Given: x² - y² = 256000 and x + y = 1000.
Using the identity x² - y² = (x + y)(x - y), we get 256000 = 1000(x - y), hence x - y = 256. Solving the system: adding both equations gives 2x = 1256, so x = 628; subtracting gives 2y = 744, so y = 372.
Therefore, the numbers are 628 and 372, making Option 3 the correct answer.
The value of log√2(32) is
Detailed Explanation:
Using the change of base formula: log√2(32) = log(32) / log(√2) = log(25) / log(21/2) = (5·log 2) / ((1/2)·log 2) = 5 / (1/2) = 10.
Alternatively, let log√2(32) = x. Then (√2)x = 32 → (21/2)x = 25 → 2x/2 = 25 → x/2 = 5 → x = 10.
Therefore, the value is 10, making Option 3 the correct answer.
By selling 45 lemons for ₹40, a man loses 20%. How many should he sell for ₹24 to gain 20% in the trans action?
Detailed Explanation:
Step 1: Selling 45 lemons for ₹40 at 20% loss means Cost Price (CP) = ₹40 ÷ 0.8 = ₹50. Thus, CP per lemon = ₹50 ÷ 45 = ₹10/9.
Step 2: To gain 20%, Selling Price (SP) must be CP × 1.2. If total SP = ₹24, then CP required = ₹24 ÷ 1.2 = ₹20. Number of lemons = ₹20 ÷ (₹10/9) = 20 × 9/10 = 18 lemons.
Therefore, 18 lemons should be sold for ₹24 to achieve 20% gain, making Option 2 the correct answer.
A train 110 m long is travelling at a speed of 58 kmph. The time in which it will pass a passerby walking at 4 kmph in the same direction is
Detailed Explanation:
The relative speed when both move in the same direction is 58 – 4 = 54 kmph = 54 × (5/18) = 15 m/s.
Time = Distance / Relative Speed = 110 / 15 = 22/3 = 7⅓ seconds.
Therefore, the train will pass the passerby in 7⅓ seconds, making Option 3 the correct answer.
The perimeter of a rhombus is 52 m and its shorter diagonal is 10 m. The length of the longer diagonal is
Detailed Explanation:
A rhombus has all sides equal. With perimeter 52 m, each side = 52 ÷ 4 = 13 m. Diagonals of a rhombus bisect each other at right angles, forming four right triangles.
Taking half of the shorter diagonal = 10 ÷ 2 = 5 m and side = 13 m, applying Pythagoras theorem: half of longer diagonal = √(13² − 5²) = √(169 − 25) = √144 = 12 m. Full longer diagonal = 12 × 2 = 24 m.
Therefore, the longer diagonal is 24 m, making Option 4 the correct answer.
in a 100 m race, A runs at 8 kmph. If A gives B a start of 4 m and still beats him by 15 seconds, what is the speed of B?
Detailed Explanation:
A's speed = 8 kmph = 8 × (5/18) = 20/9 m/s. A covers 100 m in 100 ÷ (20/9) = 45 seconds.
B gets a 4 m head start, so B runs only 96 m. A beats B by 15 seconds, meaning B takes 45 + 15 = 60 seconds to cover 96 m.
B's speed = 96/60 = 1.6 m/s = 1.6 × (18/5) = 5.76 kmph.
Therefore, Option 2 (5.76 kmph) is the correct answer.
A clock is set right at 8 amThe clock gains 10 minutes in 24 hours. What will be the true time when the clock indicates 1 p.m. on the following day?
Detailed Explanation:
The clock gains 10 minutes in 24 hours, meaning it shows 24 hours 10 minutes when the true time is 24 hours. From 8 a.m. to 1 p.m. next day, the elapsed time shown on the clock is 29 hours.
Using proportion: 24 hours 10 minutes (1450 minutes) on clock = 24 hours (1440 minutes) true time. Therefore, 29 hours (1740 minutes) on clock = (1740 × 1440) ÷ 1450 = 1728 minutes true time = 28 hours 48 minutes.
Therefore, true time = 8 a.m. + 28 hours 48 minutes = 12:48 p.m. (48 minutes past 12 noon), making Option 2 the correct answer.