The positive two-digit integers x and y

The positive two-digit integers x and y have the same digits, but in reverse order. Which of the following must be a factor of x + y?

1 Explanation

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Jeffrey Braganza

choosing numbers:
17+71 = 77 (7 & 11 are factors but only 11 is in the answer choice)
29+92 = 121 (11 is a factor)
26+62 = 88 (11 & 8 are factors, but only 11 is in the answer choice)

Say the 2 digit number X is composed of nm
and Y is mn

X + Y = nm + mn = (10.n + m) + (10.m + n) = 11n + 11m = 11(n+m)

Dec 31, 2015 • Comment

Cydney Seigerman, Magoosh Tutor

Good job! Yes, we can show that 11 is a factor of the sum. Thus, the answer is 132 (choice C), which is the only choice that has 11 as a factor.

Dec 31, 2015 • Reply

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