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# Is 30 the factor of n? A. 30 is the factor of n^2 B. 30 is

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Director
Joined: 03 Jul 2003
Posts: 655
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Is 30 the factor of n? A. 30 is the factor of n^2 B. 30 is [#permalink]  18 Feb 2004, 21:28
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Is 30 the factor of n?

A. 30 is the factor of n^2
B. 30 is the factor of 2n
SVP
Joined: 30 Oct 2003
Posts: 1797
Location: NewJersey USA
Followers: 5

Kudos [?]: 41 [0], given: 0

I guess C is the answer.

A) if n = sqrt(30) n^2 = 30 divisible by 30 but n is not
if n = 30 then n^2 = 900 divisible by 30 and n is also divisible by 30
B) if n = 15 then 2n= 30 divisible by 30 but n is not
if n = 30 then 2n = 60 divisible by 30 and n is also divisible by 30

Combine these two

n^2 = x * 30
2n = y * 30

Since x and y are integers n has to be mutiple of 15 and 2

Last edited by anandnk on 19 Feb 2004, 12:42, edited 1 time in total.
Director
Joined: 03 Jul 2003
Posts: 655
Followers: 2

Kudos [?]: 22 [0], given: 0

Any one else want to take a look at this problem?
Director
Joined: 03 Jul 2003
Posts: 655
Followers: 2

Kudos [?]: 22 [0], given: 0

Here is our way(Anand + mine) to sove this problem.

From 1: n^2 = a * 30; where a = integer
"a" could be 1 or 30; so n could be fraciton sqrt(30) or 30; NOT SUFF

From 2: 2n = b * 30 ; ==> n = b* 15 ; where b is an integer
b could be 3 or 2 ; (assume)
If b=3 ; then n = 45 ; 30 is not a factor;
If b=2; then n = 30 ; then 30 is a factor;
NOT SUFF

From 1+2:

n^2 = a * 30 --- (1)
2n = b * 30
n = b * 15 ---- (2)

sub (2) in (1)

b^2 * 15^2 = a * 30
b^2 * 15 = a * 2 -----(3)

where both "a" and "b" are integers.
For egn (3) to be valid, 30 should be a factor of "a" and 4 should be
a factor of b^2 or 2 should be a factor of "b".

So; "a" could be any number multiple of 30
"b" could be any number multiple of 2.

a = y*30 and b = z * 2
putting these values back in (1) or (2) proves
that
30 is a factor of N.

If we assume that N is an integer than the answer is A.
But, that is not given in the question stem.
SVP
Joined: 30 Oct 2003
Posts: 1797
Location: NewJersey USA
Followers: 5

Kudos [?]: 41 [0], given: 0

Good explaination kpadma. Just the way we went over it.

Well there is not much time to do this on real GMAT. Some of the steps kpadma has written have to be done in the brain. You can tell just by few steps what will come next.
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