Carcass 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 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