xy is a 2 digit integer whose reverse. . .

[Vincen]

xy is a 2 digit integer whose reverse, yx, is x less than twice xy. What is the sum of x and y?

A) 8
B) 9
C) 11
D) 12
E) 13

The OA is E.

What formula solves this PS question? I couldn't establish it.

[Jay@ManhattanReview]

xy is a 2 digit integer whose reverse, yx, is x less than twice xy. What is the sum of x and y?

A) 8
B) 9
C) 11
D) 12
E) 13

The OA is E.

What formula solves this PS question? I couldn't establish it.

The 2-digit number [xy] can be represented as 10x + y, thus, its reverse [yx] = 10y + x

We are given that [yx] = 2*[xy] - x

10y + x = 2(10x + y) - x

4y = 9x

Since 4 and 9 are co-prime, and x and y are single-digit numbers, only possible values of x = 4 and y = 9.

Thus, the sum of the digits = 4 + 9 = 13.

The correct answer: E

Hope this helps!

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-Jay
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