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If a and b are positive even integers, and the least common [#permalink]
11 Oct 2005, 17:32

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This post was BOOKMARKED

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A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

47% (02:25) correct
53% (01:25) wrong based on 116 sessions

If a and b are positive even integers, and the least common multiple of a and b is expressed as a*b/n, which of the following statements could be false?

A. n is a factor of both a and b B. (a*b)/n < ab C. ab is multiple of 2. D. (a*b)/n is a multiple of 2. E. n is a multiple of 4.

If 'a' and 'b' are positive even integers, and the least common multiple of 'a' and 'b' is expressed as ab/n, which of the following could be false? A) n is a factor of both a and b B) ab/n < ab C) ab is a multiple of 2 D) ab/n is a multiple of 2 E) n is a multiple of 4

This question is easier if you know that, for any positive integers a and b:

LCM(a,b) * GCD(a,b) = a*b

So LCM(a,b) = ab/GCD(a,b)

In this question, n is just the GCD of a and b. So we know automatically that n is a factor of a and b... A) must be true. If a and b are both even, they are both divisible by 2, so the smallest possible value for their GCD is 2. That is, n >= 2, so B) must be true If a and b are even, ab is clearly even, and so is the LCM of a and b, so C) and D) must be true. E) is the only one that might be false; E will only be true if both a and b are divisible by 4.

hence E

_________________

When you want to succeed as bad as you want to breathe ...then you will be successfull....

If 'a' and 'b' are positive even integers, and the least common multiple of 'a' and 'b' is expressed as ab/n, which of the following could be false? A) n is a factor of both a and b B) ab/n < ab C) ab is a multiple of 2 D) ab/n is a multiple of 2 E) n is a multiple of 4

E) is the only one that might be false; E will only be true if both a and b are divisible by 4.

hence E

Any information is provided such that a and b cannot be a multiple of 4 ( 'a' and 'b' are positive even integers - a can be 4 and b can be 16 or 8) ? I don't think it is valid question.

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gmatclubot

Re: This one from Kaplan.... If 'a' and 'b' are positive even
[#permalink]
19 Jan 2014, 06:40