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The positive two-digit integers x and y have the same digits

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by BTGmoderatorDC » Sun Mar 03, 2019 5:08 am

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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?

(A) 6
(B) 9
(C) 10
(D) 11
(E) 14

OA D

Source: Official Guide
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by Ian Stewart » Sun Mar 03, 2019 6:00 am
If AB is a two digit number, where A is the tens digit and B the units digit, then the number is equal to 10A + B.

Here we are adding AB and BA, which is the same as adding 10A+B and 10B + A. Adding those we get 11A + 11B, which clearly has 11 as a factor.
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by Brent@GMATPrepNow » Sun Mar 03, 2019 10:27 am
BTGmoderatorDC wrote: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?

(A) 6
(B) 9
(C) 10
(D) 11
(E) 14
Another approach is to test some values for x and y that satisfy the given information.

Positive two-digit integers x and y have the same digits, but in reverse order
So, it COULD be the case that x = 12 and y = 21

Which of the following must be a factor of x + y?
x + y = 12 + 21 = 33

Now check the answer choices...
(A) 6 is NOT a factor of 33. ELIMINATE
(B) 9 is NOT a factor of 33. ELIMINATE
(C) 10 is NOT a factor of 33. ELIMINATE
(D) 11 is a factor of 33. KEEP
(E) 14 is NOT a factor of 33. ELIMINATE

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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