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VivianKerr wrote:Hey Mallika,
This is in the wrong forum. You'll want to post Data Sufficiency questions here: https://www.beatthegmat.com/data-sufficiency-f7.html
To answer your question, let's first look at the construction:
Let b and x be positive integers. If b is the greatest divisor of x that is less than x, is the sum of the divisors of x, which are less than x itself and greater than one, greater than 2b?
I find this problem overly wordy and a bit too intentionally confusing than most GMAT DS, so I definitely wouldn't fault you for some confusion! To break this thing down, let's examine the givens and the simple question:
GIVENS:
-b and x are positive integers
-b is the greatest divisor of x
-b < x
-divisors of x = between 1 and x
QUESTION:
Is the SUM of the divisors of x (between 1 and x) LARGER than 2b?
This is a "YES/NO" question, so a statement is sufficient if it allows us to answer the question 100% YES or 100% NO.
As written, we definitely need more information about x and b. What are the possible values for these two variables? A sufficient statement should limit the values of x and b such that it allows the question to only be answered one way. Ask yourself: does this statement limit x and b ENOUGH?
Let's tackle the statements!
(1) b^2 = x
Picking number is a good strategy here, since we do not know what x and b are. Let's say b = 2 and x = 4. The only divisors of 4 between 1 and 4 is 2, so the sum is 2. In this case, the sum is NOT larger than 2b, or 2(2) = 4. The answer to the question is NO.
Let's choose a larger number for b and see if we get a different result. Let's say b = 4, and x = 16. Already this option doesn't work, because it contradicts the givens. 4 is NOT the largest divisor of 16 that is less than 16, so this isn't a possible set. REMEMBER THAT YOUR PICKED NUMBERS MUST ABIDE BY THE GIVENS!
What about b = 3 and x = 9. That would work, since 3 is the largest divisor of 9 that is less than 9. We get the same result as when we chose b = 2 and x = 4. The sum of the divisors of 9 between 1 and 9 is 3. 3 is NOT less than 2b (2*3) = 6. The answer is always NO.
It's not the "PRIME"-ness that matters in this question, it's that it just so happens that the numbers that work with the givens are prime: 2, 3, etc.
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