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[quote="hariharakarthi"]If n=6p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n? A.2 B.3 C.4 D.6 E.8

any prime>2 is odd

all devis = (1,2,3,6,p,2p,3p,6p ) however (1,3,p,3p are odd) thus answer is 4..C

If n=6p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n? A.2 B.3 C.4 D.6 E.8

Please explain the ans in detail.

Is that really the question, or does it say that p is greater than 3? If p > 3, then 6p = 2*3*p, which has 8 divisors, half of which are even: 2, 2*3, 2*p and 2*3*p. If p = 3, however, then 6p = 2*3^2, which has only six divisors, three of which are even: 2, 2*3 and 2*3^2. As written, the question has two possible correct answers, three or four, depending on the value of p.
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But, the actual question stated as given in the problem. I too had the same doubt. Hence I posted the question to find out if I miss anything.

I have a quick qn here, can you let me know how find out 8 divisors for 6p, where as I could find only the following, 1,2,3,p,2p,3p,2*3*p out of which 2,2p,2*3*p only are even divisors. what I am missing here? can you kindly explain.

But, the actual question stated as given in the problem. I too had the same doubt. Hence I posted the question to find out if I miss anything.

I have a quick qn here, can you let me know how find out 8 divisors for 6p, where as I could find only the following, 1,2,3,p,2p,3p,2*3*p out of which 2,2p,2*3*p only are even divisors. what I am missing here? can you kindly explain.

regards, hhk

If the original question is phrased as in the original post, there's a problem with the question. Where is it from?

If p is a prime greater than 3, the divisors of 6p = 2*3*p are:

1, 2, 3, p, 2*3, 2p, 3p, 2*3*p

(you're missing 2*3 = 6 in your list).
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If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

will substition work in all questions like these??

personally , i wont generalize any approach in GMAT, that said and after a while of practice you will develope an eye for different problems that will guide you to the most suitable approach. regards

n = 6p and 2 < p. possible divisors are: 2, 6, 6p, n. so, a total of 4 divisors.

ans: c

As noted above the question has TWO possible correct answers 4 in case p>3, for example if p=5, 6p=30 and 30 has 4 positive even divisors: 2, 6, 10, and 30; 3 in case p=3. In this case 6p=18 and 18 has 3 positive even divisors: 2, 6 and 18.

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