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Problem Solving - Numbers properties

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by Max@Math Revolution » Tue Aug 25, 2015 4:43 am
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.


If n=8p, 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


since p is a prime number greater than 2, it's always an odd number. since there are 6 even divisors (2,4,8,2p,4p,8p) the answer is D.



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by maxmayr93 » Sun Dec 10, 2017 11:53 am
GMATGuruNY wrote:
koby_gen wrote:If n=8p, 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
We can plug in a value for p.
Let p = 3.
Then n = 8*3 = 24.
Even factors of 24 are 2, 4, 6, 8, 12, 24 = 6 even factors.

The correct answer is D.

can somebody explain to me why everybody is always only considering the first prime number bigger than two which indeed is 3 so the result would be 24.

But when I add the next prime numbers greater than 2 I get the following number line:

8*3 = 24
8*5 = 40
8*7 = 56
8*11 = 88
8* 13 = 104

Assuming that this line is representative for all the higher prime numbers to come I want to find out the common positive factors of 24, 40, 56, 88 and 104 which actually are 4 in total (factor 2, 4, 8 and n itself).

Can somebody explain why this approach is incorrect?

Best regards,
Max
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by [email protected] » Sun Dec 10, 2017 12:38 pm
Hi Max,

When dealing with GMAT questions, it's important to make sure that you answer the specific question that is ASKED. This question asks for the total number of EVEN DIVISORS of N (NOT the number of common even divisors of all possible values of N). Since the answer choices are numbers, one of them MUST be the answer (regardless of the prime number value you choose for P). This is why most Test Takers simply choose P=3 (since that's the "easiest" value that fits what we're told). If you wanted to choose P=5 or P=7, then that would be fine... but the correct answer would still be the same.

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by Scott@TargetTestPrep » Fri Sep 27, 2019 7:36 am
koby_gen wrote:If n=8p, 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
Since p must be odd and 8 = 2^3, the even divisors of 8p are 2, 4, 8, 2p, 4p and 8p.

Answer: D

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