Data Sufficiency

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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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.

We need to determine the remainder when 2n is divided by 8.

Statement One Alone:

n, when divided by 6, leaves remainder 5.

Thus, we see n can be a number such as 5, 11, 16, 21, 26, 31, 35, etc.

When 2(5) = 10 is divided by 8, the remainder is 2.

When 2(11) = 22 is divided by 8, the remainder is 6.

Statement one alone is not sufficient to answer the question.

Statement Two Alone:

3n, when divided by 6, leaves remainder 3.

Thus, we see that 3n can be a number such as 3, 9, 15, 21, 28, etc.

When 3n is 3, n is 1; when 3n is 9, n is 3; when 3n is 15, n is 5; etc.

In other words n will always be an odd number: 1, 3, 5, 7, ...

When 2(1) = 2 is divided by 8, the remainder is 2.

When 2(3) = 6 is divided by 8, the remainder is 6.

Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using our two statements, we see the first value for n that satisfies both statements is 5. We also see that in statement two, n can be any odd number. So, another number that would match is n = 11.

When 2(5) = 10 is divided by 8, the remainder is 2.

When 2(11) = 22 is divided by 8, the remainder is 6.

We see that the statements together are still not sufficient to answer the question.

Answer: E