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For positive integer a, is the product (a)(a + 1)(a + 2) div

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For positive integer a, is the product (a)(a + 1)(a + 2) div

by GMATinsight » Thu Oct 08, 2015 10:08 am
For positive integer a, is the product (a)(a + 1)(a + 2) divisible by 48?

(1) a is even.
(2) 4a is divisible by 32.

Answer: option B
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by GMATinsight » Thu Oct 08, 2015 10:08 am
GMATinsight wrote:For positive integer a, is the product (a)(a + 1)(a + 2) divisible by 48?

(1) a is even.
(2) 4a is divisible by 32.

Answer: option B
Question : is the product (a)(a + 1)(a + 2) divisible by 48?

Inference : (a)(a + 1)(a + 2) is a product of three consecutive Positive Integer
48 = 2*3*8
Product of 3 consecutive Integers always include a multiple of 3 so all we have to find is whether product of these three consecutive Integers is divisible by 16 or not

Question REPHRASED : is the product (a)(a + 1)(a + 2) divisible by 16?

Statement 1: a is even.
@a=2, (a)(a + 1)(a + 2) = 24 i.e. NOT divisible by 16 or 48
@a=6, (a)(a + 1)(a + 2) = 6*7*8 i.e. Divisible by 16 and 48
NOT SUFFICIENT

Statement 2: 4a is divisible by 32.
i.e. a is divisible by 8
i.e. (a)(a + 1)(a + 2) will have two even integers a and (a+2) and one is multiple of 8 and other is definitely a multiple of 2
i.e. (a)(a + 1)(a + 2) will be divisible by 8*2*3=16 *3 = 48
SUFFICIENT

Answer: option B
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