Hey guys....can anyone help me with this one...?

[litteraround]

here goes...

The total age of 22 Boys and 24 Girls is 160. What is the total age of 1 Boy and 1 Girl, if all the boys are the same age and all the girls are the same age (only full years are counted).

A. 5

B. 6

C. 7

D. 8

E. 9

[Ian Stewart]

The question only works because we know the ages must be positive integers.

From the question:
22b + 24g = 160

Might as well make the numbers smaller by dividing both sides by 2:

11b + 12g = 80
11b = 80 - 12g

Notice that the left side is divisible by 11. The right side must be as well. So we need to find a (small) positive integer value of g that makes 80 - 12g a positive multiple of 11, and the only value that works is g = 3. This gives b = 4, and g+b = 7. Luckily the numbers are small here- otherwise this question could take a while!

[litteraround]

That's awesome man, thanks. I tried it several times but never got it. I just wanted to know if there is a proper mathematical way without resorting to manpulation?

[beeparoo]

... I just wanted to know if there is a proper mathematical way without resorting to manpulation?

What do you mean manipulation vs. mathematical method? The question is rather ambiguous.

I second Ian's approach; it is the same one I took. But, instead of simplifying the equation to smaller numbers, I left the constants as-is and just fiddled with random plug-ins. Took me less than 1 minute.

I think Ian's approach is elegant and most direct.

[litteraround]

hey beeparoo,

I am not questioning Ian's method, infact its fast and does the trick. But, what I am saying is if it could be possible to do it without the hit and trial method as he did - plugging in 3 for 'g'. I just wanted to know if a derivation was possible without this hit and trial approach.

Hope, I made myself clear this time.

[beeparoo]

I see what you mean now.

Don't discredit the "plugging-in values" method! There are many official GMAT questions that can be solved in a fraction of the speed by doing this method than by solving algebraically.

Re: This question
There's no way to solve it algebraically because you have two variables and one equation. In order to solve two variables, you need TWO distinct equations.

Cheers,
Sandra

[Ian Stewart]

Yes, Sandra is correct that there is no 'pure' algebraic solution. We have a single equation with two unkowns, and the only reason we get one solution only here is because the variables need to be small positive integers. It's because the number of choices we need to test is small that we have some hope of finishing the question in 'GMAT time'- two minutes! With more choices, the question would become too time-consuming.

[litteraround]

i see.. thanks guys, exactly what i needed to know.

But, what if we don't start with two variables, what if we say that the only variable is 'x' i.e. the sum of ages of 1 boy and 1 girl. Is it possible somehow to solve it like that.


Otherwise, your solution is perfect.

[beeparoo]

But, what if we don't start with two variables, what if we say that the only variable is 'x' i.e. the sum of ages of 1 boy and 1 girl. Is it possible somehow to solve it like that.

Otherwise, your solution is perfect. Don't mess with perfection...!

It's tempting to regard one B + one G as one variable, say, x. But they are not proportional to each other.

You can tell just from this initial equation: 22b + 24g = 160, and the constants for b and g that they are unequal. There is no way to isolate B and g as one variable. You can try, but you will still be left with two variables in the end.

Try to solve it algebraically.. You'll see that no matter how you try to combine b and g, you will still be left with two unknown variables in that equation.

[litteraround]

thanks ian and thanks sandra.

Cheers.