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A and B are 2-digit numbers with non-zero digits. Both digit

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A and B are 2-digit numbers with non-zero digits. Both digit

by BTGmoderatorDC » Wed Jul 24, 2019 10:43 pm

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A and B are 2-digit numbers with non-zero digits. Both digits in A are distinct, and B is formed by reversing the digits of A. Which of the following is always a factor of A^2 - B^2?

A. 5
B. 15
C. 45
D. 75
E. 99

OA E

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A and B are 2-digit numbers with non-zero digits. Both digit

by Brent@GMATPrepNow » Thu Jul 25, 2019 5:17 am
BTGmoderatorDC wrote:A and B are 2-digit numbers with non-zero digits. Both digits in A are distinct, and B is formed by reversing the digits of A. Which of the following is always a factor of A^2 - B^2?

A. 5
B. 15
C. 45
D. 75
E. 99

OA E

Source: e-GMAT
A fast approach is to test some values of A and B

For example, it COULD be the case that A = 21 and B =12
In this case, A² - B² = 21² - 12²
= (21 + 12)(21 - 12) [aside: since 21² - 12² is a DIFFERENCE OF SQUARES, we can first factor it before evaluating it]
= (33)(9)
= (3)(11)(3)(3)

Since 5 is not a factor of (3)(11)(3)(3), we can eliminate answer choice A
Since 15 is not a factor of (3)(11)(3)(3), we can eliminate answer choice B
Since 45 is not a factor of (3)(11)(3)(3), we can eliminate answer choice C
Since 75 is not a factor of (3)(11)(3)(3), we can eliminate answer choice D
HOWEVER, 99 IS a factor of (3)(11)(3)(3). So, KEEP answer choice E

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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