CAPF AC 2020 Q112: General Mental Ability – Quantitative Aptitude

CAPF AC 2020, Paper I (General Ability and Intelligence) · General Mental Ability

1. (a) 12
2. (b) 24
3. (c) 48
4. (d) 64

Answer: (c) 48

Explanation

Product of three consecutive even numbers

How to think: try the smallest case first.

The smallest three consecutive even numbers are 2, 4 and 6.

Their product is 48, so the greatest number that divides every such product exactly cannot be more than 48.

Why it always works: write the numbers as 2n, 2n + 2 and 2n + 4.

The product is 8 × n × (n + 1) × (n + 2).

The product of three consecutive numbers n, n + 1, n + 2 is always divisible by 6.

So the whole product is always divisible by 8 × 6 = 48.

The options checked:

Answer: (c) 48.

Why each option is right or wrong

• (a) Incorrect. 12 divides every such product, but 48 is greater and also divides.
• (b) Incorrect. 24 divides every such product, but it is not the greatest.
• (c) CORRECT. The product is 8 × n(n + 1)(n + 2), always divisible by 8 × 6 = 48.
• (d) Incorrect. 64 does not divide 2 × 4 × 6 = 48.

Key point

Product of three consecutive even numbers = 8 × n(n + 1)(n + 2), always divisible by 48. Product of three consecutive numbers is always divisible by 6.

Remember

Three consecutive even numbers: product is always divisible by 48.

Common mistakes

• Stopping at 24 without testing 48.
• Choosing 64 because it is the largest option.
• Forgetting that the product of three consecutive numbers is always divisible by 6.

Exam tip

Educated guess: test the smallest case, 2 × 4 × 6 = 48. The answer cannot exceed 48, so 64 is out and 48 itself is worth checking first.

Sources

• NCERT Class VI Mathematics — Playing with Numbers (divisibility)
• NCERT Class X Mathematics — Real Numbers

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