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Algebra - Ages of Al and Bob

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Algebra - Ages of Al and Bob

by Brent@GMATPrepNow » Wed Jan 28, 2009 8:59 am
In three years, Bob will be three-fourths as old as Al. In 11 years, Bob will be five-sixths as old as Al. What is the sum of their current ages?
(A) 15
(B) 19
(C) 22
(D) 24
(E) 28
Please note that this is not an official GMAT question; it’s my attempt to create difficult (650+ level) GMAT-style questions for this forum.
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by dmateer25 » Wed Jan 28, 2009 9:12 am
A = al
B = Bob

3/4(a+3) = b +3
3a + 9 = 4b + 12
3a = 4b + 3
a = 4b+3/3


5/6(a+11)=b+11
5a + 55 = 6b + 66
5a = 6b + 11
a = (6b + 11)/5
(4b+3)/3 = (6b + 11)/5
20b + 15 = 18b + 33
2b = 18
b=9

substituting b back in

a = (4(9)+3)/3
a= 39/3
a = 13

13 + 9 = 22

I will go with C
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by Brent@GMATPrepNow » Wed Jan 28, 2009 9:22 am
Nice work, dmateer25. The answer is C.
I'm posting my solution as well, because it is slightly different.

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by mdavis » Wed Jan 28, 2009 11:58 am
Thanks for the explanation to this problem. I had a question regarding the explained answer though.

Why do you at the very end multiply Bob's age by 5/6 on only one side of the equation? I always thought that you have to do things to both sides?

Thanks!
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by Brent@GMATPrepNow » Wed Jan 28, 2009 12:32 pm
mdavis wrote:Thanks for the explanation to this problem. I had a question regarding the explained answer though.

Why do you at the very end multiply Bob's age by 5/6 on only one side of the equation? I always thought that you have to do things to both sides?

Thanks!
You're right that we must always perform the same operations to both sides of an equation. However, up until the point where we multiplied Al's age by 5/6, we didn't have an equation. We multiplied by 5/6 to create an equation.

For example, let's say that I'm twice as old as you. For the moment, we can't say that our two ages are equal (which means that we can't create an equation).
However, we could say that our ages are equal if we fiddled with one of our ages.
For example, if we doubled your age, then our ages would be equal. The equation would be: (my age) = 2(your age)

Another way to make our ages equal would be to halve my age. That would make us the same age. In this case, the equation would be: 1/2(my age) = (your age)

I hope that helps.
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