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Manhattan CAT PS - 700-800

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Manhattan CAT PS - 700-800

by gbb » Wed Mar 18, 2009 5:39 pm
The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210?

A 3
B 14
C 30
D 42
E 70

answer D.

help!!!
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by cramya » Wed Mar 18, 2009 6:54 pm
16 = 2*2*2*2
n = 2*2 *..... (we dont know)


45 = 3*3*5
n = 3*......(we dont know) (definitely does not have a 5)


From the above 2 we know n must be atleast 2*2*3

210 = 2*5*3*7

GCF(210,n) = 2 * 3 * (something else)


Look at the answer choices

Eliminate 3 since we have 3*2(6) already
Eliminate 30 and 70 since there is not a 5 in n so cant be in GCD or GCF

6* (some integer) can never be 14


Choose 42(D) since n could have a 7 and 210 also has a 7
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