Bunuel wrote:
pretzel wrote:
IMO D is the answer.
For second statement, if K + 1/3 or (K+1)/3, K is even. And so, in (K + 2) (K^2 + 4K + 3) = (K+2)(K+3)(K+1) = even x odd x odd
Am I correct?
No, the correct answer is A.
For positive integer k, is the expression (k + 2)(k^2 + 4k + 3) divisible by 4?\((k + 2)(k^2 + 4k + 3)=(k+1)(k+2)(k+3)\), so the expression is the product of three consecutive integers.
(1) k is divisible by 8 --> \(k=8n=even\) --> \((k+1)(k+2)(k+3)=odd*even*odd\). Now, \(k+2=8n+2\), though even, is not a multiple of 4 (it's 2 greater than a multiple of 8), therefore the expression is not divisible by 4. Sufficient.
(2) (k + 1)/3 is an odd integer --> \(k+1=3*odd=odd\) --> \(k=even\) --> \((k+1)(k+2)(k+3)=odd*even*odd\). Now, \(k+2=even\) may or may not be divisible by 8, therefore the expression may or may not be divisible by 8. For example, consider \(k=2\) and \(k=6\). Not sufficient.
Answer: A.
Hope it's clear.
After admiring Bunuel's answers to many tricky quant problems, I realized lots of times, it takes tremendous pattern recognition to even realize you need to make certain moves in various situations. Here he factored out the quadratic in this case, coming to the realization that it's multiplying 3 consecutive integers.
Bunuel, would you say the famous 10,000-hour rule applies to acing GMAT quant?
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