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Age problem

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by oks » Wed May 13, 2009 5:09 pm
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 explain. Thanks

OA: C
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Source: — Data Sufficiency |
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by DeepakR » Wed May 13, 2009 5:30 pm
Given that, 22B + 24G = 160 --- (1)
We need to find B+G= ?

I used the back solving by plugging the answer choices:

If B+G=7 --- (2)
(2) * 22 -- 22B+22G=154 --- (3)

Solving 1 and 3 we get, G=3 and B=4 and it satisfies the given equation 1 and 2. However if you plug in B+G=5

22B + 22G=110 so solving with 1 we get, G= 25 since B+5=5 G cannot be 25 or B cannot be -ve. so 8 is ruled out and only 7 works.

C.)

-Deepak
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by aj5105 » Wed May 13, 2009 10:38 pm
Plug in the answer choices. Split 7 into 4 and 3.

(C)
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by PAB2706 » Fri May 15, 2009 8:46 am
plugging seems to be the best choice here..


i used a crude way to solve...

let x be age of all boys and y be age of all girls

then

taking ratio we get

x/y = 11/12

x+y
----- = 23 / 12
y

160
----- = 23/ 12
y

y = 83

now i have to find a number closest to 83 that is divisible by 24 i get 24*3=72

and 160-72= 88 which is 22*4

thus we get the age of individual boy nd girl

so 3+4=7

hope this helps

cheers.
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