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Factors of 24

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Factors of 24

by jainpiyushjain » Thu Mar 07, 2013 3:20 am
Came across this question in Kaplan. What is the best way to attack this particular question

If x and y are distinct factors of 24, then which of the following CANNOT be a factor of 24?

I. (x+y)2
II. x2−y2
III. xy+y2

A. I only
B. I and II only
C. II and III only
D. II only
E. III only

OA A

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by Anurag@Gurome » Thu Mar 07, 2013 3:30 am
jainpiyushjain wrote:If x and y are distinct factors of 24, then which of the following CANNOT be a factor of 24?

I. (x+y)²
II. x²−y²
III. xy+y²
The possible values of x and y are : 1, 2, 3, 4, 6, 8, 12, and 24 also x ≠ y

Option I
This is a perfect square.
The only factors of 24 that are perfect squares are 1 and 4.
If (x + y)² is equal to 1 or 4, then (x + y) = 1 or (x + y) = 2
There is no way, x and y can have values from the above list such that x ≠ y but (x + y) is equal to either 1 or 4.

Hence, I CANNOT be a factor of 24.

Option II
Take x = 2 and y = 1 ---> (x² − y²) = (4 - 1) = 3 ---> A factor of 24

Hence, II CAN be a factor of 24.

Option III
Take x = 2 and y = 1 ---> (xy − y²) = (2 - 1) = 1 ---> A factor of 24

Hence, III CAN be a factor of 24.

The correct answer is A.
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by GMATGuruNY » Thu Mar 07, 2013 6:52 am
jainpiyushjain wrote: If x and y are distinct factors of 24, then which of the following CANNOT be a factor of 24?

I. (x+y)2
II. x2−y2
III. xy+y2

A. I only
B. I and II only
C. II and III only
D. II only
E. III only

OA A
Try to DISPROVE I, II and III by showing that each CAN be a factor of 24.
Plug in the smallest possible values for x and y, since small values are more likely to divide into 24.
If we plug x=2 and y=1 into I, II and III, we get:

I: (2+1)² = 9, which is not a factor of 24.
Hold onto I.

II: 2² - 1² = 3, which is a factor of 24.
Eliminate B, C and D, each of which includes II.

III: 2*1 + 1² = 3, which is a factor of 24.
Eliminate E, which includes III.

The correct answer is A.

No need to worry about why answer choice I cannot be a factor of 24, since A is the only remaining answer choice.
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