If x and y are positive integers, and 4x is the least

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If x and y are positive integers, and 4x is the least common multiple of x and y, which of the following MUST be true?

i) x is the greatest common divisor of x and y
ii) x = y/4
iii) x is a multiple of 4

A) i only
B) ii only
C) iii only
D) ii and iii only
E) none

Answer: E
Difficulty level: 500 - 550
Source: www.gmatprepnow.com
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GMAT/MBA Expert

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by Brent@GMATPrepNow » Wed May 23, 2018 6:56 am
Brent@GMATPrepNow wrote:If x and y are positive integers, and 4x is the least common multiple of x and y, which of the following MUST be true?

i) x is the greatest common divisor of x and y
ii) x = y/4
iii) x is a multiple of 4

A) i only
B) ii only
C) iii only
D) ii and iii only
E) none

Answer: E
Difficulty level: 500 - 550
Source: www.gmatprepnow.com
Let's find some values for x and y that satisfy the given information and see what happens....

If x = 3 and y = 4, then the least common multiple of x and y is 12.
Notice that 12 = 4x, so x = 3 and y = 4 work perfectly.

Now let's plug x = 3 and y = 4 into the statements...
i) 3 is the greatest common divisor of 3 and 4
NOT TRUE. 1 is the greatest common divisor of 3 and 4

ii) 3 = 4/4
NOT TRUE

iii) 3 is a multiple of 4
NOT TRUE

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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