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find the sum of ages

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by ashish1354 » Thu Mar 05, 2009 1:14 am
22. The sum of the ages of 22 boys and 24 girls is 160.What is the sum of ages of one boy plus one girl, if all the boys are of the same age and all the girls are of the same age, and only full years are counted?

(a) 5.
(b) 6.
(c) 7.
(d) 8.
(e) 9.

Please suggest a fast way to calculate the answer
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by pakaskwa » Thu Mar 05, 2009 1:34 am
Here's how I did it. I'm not sure if it's the best way.

Boy's age is x, girl's age is y:
22x+24y=160 --> 11x+12y=80
x=(80-12y)/11, x is integer. So 80-12y must be divisible by 11.
So 80-12y=n11

y is integer, 12y must be even number. And value of (80-12y) must be an even number too. Then there are only 3 possible values for 80-12y: 22,44,66.

44 is the only option to make y an integer. So y=3, x=4.

Answer is 7.
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by kamu » Thu Mar 05, 2009 1:41 am
Fastest way I could think of..

22x+24y=160

11x+12y=80

plug values such that the add up to give units as zero.

x=2,y=4, but this does not satisfy.
x=4,y=3, this does. 4+3 =7 . Done.!
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