gracie wrote:
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
We use the concept that the number 46, for example, can be expressed as (4)(10) + (6)(1) = 46. Thus, we see that the number “xy” = (10)(x) + (y)(1) = 10x + y.
Since the number “xy” = 10x + y, then its reverse “yx” = 10y + x.
Since “yx” is x less than twice “xy”:
2(10x + y) - x = 10y + x
20x + 2y - x = 10y + x
19x + 2y = 10y + x
18x - 8y = 0
9x - 4y = 0
Since x and y are single digits, the only way 9x - 4y = 0 is if x = 4 and y = 9. Thus, x + y = 4 + 9 = 13.
Answer: E
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