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x + y a multiple of 11

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x + y a multiple of 11

by sanju09 » Sat Apr 04, 2009 5:53 am
If both x and y are positive integers less than 100 and greater than 10, is the sum x + y a multiple of 11?

(1) x - y is a multiple of 22

(2) The tens digit and the units digit of x are the same; the tens digit and the units digit of y are the same
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by karmayogi » Sat Apr 04, 2009 10:42 am
#1

x - y = 22n

where n = 1, 2,3, an 4

x = 37, y = 15
x-y = 22 and x + y = 52 (not divisible by 11)

x = 99, y = 11
x - y = 88, x + y = 110 (divisible by 11)

Not sufficient.

#2
x = XX and y = YY
x = 11 * X and y = 11 * Y
x+y = 11 * X + 11 * YY = 11 (X + Y) (divisible by 11)

Sufficient

IMO B.
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