aaron1981 wrote:What is the remainder when 2n is divided by 8?

(1) n, when divided by 6, leaves remainder 5.
(2) 3n, when divided by 6, leaves remainder 3.

OA E

I wish to know if assuming a suitable value the best approach?

It depends how you approach a question. At times assuming a smart value can be an efficient approach; however, not in every case.

Statement 1: n, when divided by 6, leaves remainder 5.

n divided by 6, leaves remainder 5, and assuming the quotient to be a , we have:
n ƒ= 6a ‚+ 5 . . . (i)

If a ƒ= 0; n ƒ= 5:
Thus, 2n =ƒ 2 x 5 ƒ= 10: We have 2n =ƒ 10 divided by 8 gives '2' as remainder.

If a ƒ= 1; n ƒ= 11:
Thus, 2n ƒ= 2 x 11 ƒ= 22: We have 2n =ƒ 22 divided by 8 gives '6' as remainder.
No unique answer. Insufficient.

Statement 2: 3n, when divided by 6, leaves remainder 3.

3n divided by 6, leaves remainder 3, and assuming the quotient to be b , we have:
3n =ƒ 6a ‚+ 3 . . . (i)

If a =ƒ 0; n =ƒ 1:
Thus, 2n ƒ= 2 x 1 ƒ= 2: We have 2n =ƒ 2 divided by 8 gives '2' as remainder.

If a ƒ= 1; n ƒ= 3:
Thus, 2n ƒ= 2 x 3 =ƒ 6: We have 2n =ƒ 6 divided by 8 gives '6' as remainder.
No unique answer. Insufficient.

Since each statement returns the same two values of remainder '2' or '6', remainder
cannot be uniquely determined even after combining both the statements.

The correct answer: A

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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