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GRE Math Challenge #112If n = pqr, where p, q, and r [#permalink]
15 May 2015, 11:54
Question Stats:
58% (00:55) correct
41% (00:15) wrong based on 17 sessions
If n = pqr, where p, q, and r are three different positive prime numbers, how many different positive divisors does n have, including l and n? (A) 3 (B) 5 (C) 6 (D) 7 (E) 8
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Re: GRE Math Challenge #112 [#permalink]
27 Aug 2015, 18:31
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1 and n makes it 2 divisors p,q,r makes it another 3 n combinations of 2 from pqr  pq,qr,pr (gives it another 3) So, answer is 8 Posted from my mobile device



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Re: GRE Math Challenge #112If n = pqr, where p, q, and r [#permalink]
24 Jul 2020, 12:23
Another method of solving:
Total # of positive divisors of x^a * y^b * z^c, where x, y, and z are all prime is equal to (a+1) * (b+1) * (c+1)
So if n = p*q*r, and p, q, and r are all prime, then you can also write p*q*r as p^1 * q^1 * r^1. Therefore, the total # of positive divisors of n = (1+1) * (1+1) * (1+1) = 8
E is the answer



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Re: GRE Math Challenge #112If n = pqr, where p, q, and r [#permalink]
29 Jul 2020, 06:13
sandy wrote: If n = pqr, where p, q, and r are three different positive prime numbers, how many different positive divisors does n have, including l and n?
(A) 3 (B) 5 (C) 6 (D) 7 (E) 8 Another approach is to test some values that satisfy the given conditionsn = pqr, where p, q, and r are three different positive prime numbersLet p = 2 Let q = 3 Let r = 5 So, n = pqr = (2)(3)(5) = 30 How many different positive divisors does n have, including 1 and n?In other words, "How many different positive divisors does 30 have, including 1 and 30?" The positive divisors of 30 are: 1, 2, 3, 5, 6, 10, 15 and 30 There are 8 positive divisors Answer: E Cheers, Brent
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Re: GRE Math Challenge #112If n = pqr, where p, q, and r
[#permalink]
29 Jul 2020, 06:13





