If q is a positive integer less than 17 and r is the remainder when 17

Question

If q is a positive integer less than 17 and r is the remainder when 17 is divided by q, what is the value of r?

(1) q > 10
(2) q = 2^k, where k is a positive integer

Bunuel · Accepted Answer

Red part is not correct.

For (2):
17 divide by 2 yields remainder of 1;
17 divide by 4 yields remainder of 1;
17 divide by 8 yields remainder of 1;
17 divide by 16 yields remainder of 1;

So when q=2^k then the remainder upon division 17 by q is always 1.

Answer: B.

Hope it helps.

rraggio · Answer

(1) q>10
This means q can be any integer between 11 and 16. So the remainder can be any integer from 6 to 1.
Statement (1) is not sufficient. So it's B or C or E.

(2) q=2^k
This means q can be one of these values: 2, 4, 8, 16. So the remainder can be respectively 15, 13, 9, 1.
Statement (2) is not sufficient. So it's C or E.

(1) and (2)
This means q must be 16, so the remainder is 1.
Right answer is C.

I don't know why the official answer is B.
Did I miss anything?

Thanks!

GMATWhizTeam · Answer

Step 1: Analyse Question Stem

q is a positive integer less than 17; therefore, q can take any integer value from 1 to 16, inclusive.

When 17 is divided by q, the remainder is r.

We need to find the value of r, for which we need the value of q.

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1:  q > 10

If q = 11, the remainder when 17 is divided by 11, is 6; therefore, r = 6.

But, if q = 16, the remainder when 17 is divided by 16, is 1; therefore, r = 1.

The data in statement 1 is insufficient to find a definite value for r.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.

Statement 2:  q =  2^k , where k is a positive integer

As per this constraint, q can be  2^1  or  2^2  or  2^3  or  2^4 , since q is a positive integer lesser than 17. 
This means the possible values of q are 2 or 4 or 8 or 16.

At this stage, test takers who are not careful will end up concluding that this information is not sufficient, since there are multiple values of q.

However, when 17 is multiplied by each of these values of q, the remainder is 1 in all cases. Therefore, we have a definite value for r i.e. r = 1.

Multiple cases do not always mean that there will be multiple answers, you will fall for this trap if you do not hold on to the question you are trying to answer – remember, the question was about r, not about q.

The data in statement 2 is sufficient to find a definite value for r.
Statement 2 alone is sufficient. Answer options C and E can be eliminated.

The correct answer option is B.

bumpbot · Answer

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If q is a positive integer less than 17 and r is the remainder when 17

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