BTGmoderatorLU wrote:Source: e-GMAT
The number \(A\) can be expressed as \(p*q\) where \(p\) and \(q\) are positive integers. Is \(A\) divisible by 16?
1. \(p=8*k\), where \(k\) is an odd number.
2. \(q^2-8q+15=0.\)
The OA is C
We have A = pq.
We need to determine whether A is divisible by 16; for it to happen pq must be divisible by 16.
Let's take each statement one by one.
1. \(p=8*k\), where \(k\) is an odd number.
pq = 8kq
If q is even, the answer is yes; however, if q is odd, the answer is no. Insufficient.
2. \(q^2-8q+15=0.\)
q^2 - 3q - 5q + 15 = 0
q(q - 3) - 5(q - 3) = 0
q = 3 or 5, odd numbers
If p itself is divisible by 16, the answer is yes; however, if it is not, the answer is no. Insufficient.
(1) and (2) together
So, from (1) and (2), we have
pq = 8*k*3 = 24k; where k is odd => we see that pq is not divisible by 16. The answer is no.
OR
pq = 8*k*5 = 40k; where k is odd => we see that pq is not divisible by 16. The answer is still no.
Sufficient
The correct answer:
C
Hope this helps!
-Jay
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