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If n is a positive integer less than 50, what is the value 05 Nov 2006, 15:06
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If n is a positive integer less than 50, what is the value of n?

(1) n is a multiple of the square of the sum of two distinct factors of n.
(2) n is a perfect square with 9 factors.



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If n is a positive integer less than 50, what is the value 05 Nov 2006, 15:55
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But it's a multiple of the square of the SUM of two distinct factors..
(1) is insufficient because, for example, (1+2)^2 = 9 so 18 and 36 work.
(2) hmm, 1 (no), 4 (no), 9 (no), 16 (no), 25 (no), 36 (yes), 49 (no) so sufficient. (1,2,3,4,6,9,12,18, 36 are factors of 36).
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If n is a positive integer less than 50, what is the value 07 Nov 2006, 06:04
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joeydvivre
But it's a multiple of the square of the SUM of two distinct factors..
(1) is insufficient because, for example, (1+2)^2 = 9 so 18 and 36 work.
(2) hmm, 1 (no), 4 (no), 9 (no), 16 (no), 25 (no), 36 (yes), 49 (no) so sufficient. (1,2,3,4,6,9,12,18, 36 are factors of 36).
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For the same reason B.

I am still a bit apprehensive about choosing B. Can a number be more than 50, perfect square, and has 9 factors? remote chance.
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If n is a positive integer less than 50, what is the value 07 Nov 2006, 06:33
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ak_idc
joeydvivre
But it's a multiple of the square of the SUM of two distinct factors..
(1) is insufficient because, for example, (1+2)^2 = 9 so 18 and 36 work.
(2) hmm, 1 (no), 4 (no), 9 (no), 16 (no), 25 (no), 36 (yes), 49 (no) so sufficient. (1,2,3,4,6,9,12,18, 36 are factors of 36).

For the same reason B.

I am still a bit apprehensive about choosing B. Can a number be more than 50, perfect square, and has 9 factors? remote chance.
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Remote chance? There are an infinite number of them.
In fact, if n = p1*p2 where p1 and p2 are prime numbers, then n^2 has 9 factors. The factors are {1, p1, p2, p1^2, p1*p2, p2^2, p1*p2^2, p2*p1^2, n^2}. Examples of such numbers are
100 = {1, 2, 4, 5, 10, 20, 25, 50, 100}
225 = {1, 3, 5, 9, 15, 25, 45, 75, 225}
....
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ak_idc
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If n is a positive integer less than 50, what is the value 08 Nov 2006, 05:50
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joeydvivre
ak_idc
joeydvivre
But it's a multiple of the square of the SUM of two distinct factors..
(1) is insufficient because, for example, (1+2)^2 = 9 so 18 and 36 work.
(2) hmm, 1 (no), 4 (no), 9 (no), 16 (no), 25 (no), 36 (yes), 49 (no) so sufficient. (1,2,3,4,6,9,12,18, 36 are factors of 36).

For the same reason B.

I am still a bit apprehensive about choosing B. Can a number be more than 50, perfect square, and has 9 factors? remote chance.

Remote chance? There are an infinite number of them.
In fact, if n = p1*p2 where p1 and p2 are prime numbers, then n^2 has 9 factors. The factors are {1, p1, p2, p1^2, p1*p2, p2^2, p1*p2^2, p2*p1^2, n^2}. Examples of such numbers are
100 = {1, 2, 4, 5, 10, 20, 25, 50, 100}
225 = {1, 3, 5, 9, 15, 25, 45, 75, 225}
....
Show more


Kevin, is the answer E? :shock:



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Hi there,
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Thank you for understanding, and happy exploring!
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