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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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Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

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).
_________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

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.