Step 1: Analyse Question Stemq 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 / BCEStatement 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. _________________
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