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If n = 2pq, where p and q are distinct prime numbers

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by GMATGuruNY » Sat Nov 18, 2017 5:50 am
lheiannie07 wrote:If n = 2pq, where p and q are distinct prime numbers greater than 2, how many different positive even divisors does n have, including n ?

(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight
Let p=3 and q=5, with the result that n = 2*3*5 = 30.
Factors pairs of 30:
1*30
2*15
3*10
5*6.

As illustrated by the blue values above, the number of even factors = 4.

The correct answer is C.
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by Brent@GMATPrepNow » Sat Nov 18, 2017 7:45 am
lheiannie07 wrote:If n = 2pq, where p and q are distinct prime numbers greater than 2, how many different positive even divisors does n have, including n ?

(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight
Mitch's approach is definitely the best.
However, if you didn't come up with that approach, here's another.

If p and q are distinct prime numbers greater than 2, then p and q are each odd
So, if n = 2pq, then the positive EVEN divisors of n are: 2, 2p, 2q and 2pq (4 in total)
Answer: C

Cheers,
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by Scott@TargetTestPrep » Wed Dec 13, 2017 12:22 pm
lheiannie07 wrote:If n = 2pq, where p and q are distinct prime numbers greater than 2, how many different positive even divisors does n have, including n ?

(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight
We can let p = 3 and q = 5. Thus, the product of 2pq is 2 x 3 x 5 = 30. The factors of 30 are:

1, 30, 2, 15, 3, 10, 5, 6

Since 30 has 4 even factors, n has 4 even factors.

Alternatively, we can solve the problem algebraically. Keep in mind that p and q will be odd primes since they are greater than 2.

The factors of n are:

1, 2pq, 2, pq, p, 2q, q, 2p

We see that the even factors of n are 2pq, 2, 2q, and 2p, so there are 4 even factors.

Answer: C

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by BTGmoderatorDC » Wed Jan 10, 2018 9:44 pm
Brent@GMATPrepNow wrote:
lheiannie07 wrote:If n = 2pq, where p and q are distinct prime numbers greater than 2, how many different positive even divisors does n have, including n ?

(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight
Mitch's approach is definitely the best.
However, if you didn't come up with that approach, here's another.

If p and q are distinct prime numbers greater than 2, then p and q are each odd
So, if n = 2pq, then the positive EVEN divisors of n are: 2, 2p, 2q and 2pq (4 in total)
Answer: C

Cheers,
Brent
Thanks a lot!
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by BTGmoderatorDC » Wed Jan 10, 2018 9:45 pm
Scott@TargetTestPrep wrote:
lheiannie07 wrote:If n = 2pq, where p and q are distinct prime numbers greater than 2, how many different positive even divisors does n have, including n ?

(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight
We can let p = 3 and q = 5. Thus, the product of 2pq is 2 x 3 x 5 = 30. The factors of 30 are:

1, 30, 2, 15, 3, 10, 5, 6

Since 30 has 4 even factors, n has 4 even factors.

Alternatively, we can solve the problem algebraically. Keep in mind that p and q will be odd primes since they are greater than 2.

The factors of n are:

1, 2pq, 2, pq, p, 2q, q, 2p

We see that the even factors of n are 2pq, 2, 2q, and 2p, so there are 4 even factors.

Answer: C
Thanks a lot!
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