## At a picnic there were 3 times as many adults GMAT SOLUTION

This question is more complicated than it needs to be, but it is simply an issue of careful substitution. Look at it this way: we need the number of men in terms of *x, *which would imply that we get all of the other information in terms of *m. *

At a picnic there were 3 times as many adults as children and twice as many women as men. If there was a total of x men, women, and children at the picnic, how many men were there, in terms of x?

A. x/2

B. x/3

C. x/4

D. x/5

E. x/6

The first thing to do is to register the number of Adults and the number of Children as variables. The easiest thing to do, then, would be to say something like this:

Adults: a

Children: c

## Then, if we have *three times as many adults as children, *this would read *a = 3c.*

Now, we can presume (by GMAT standards, at any rate), that adults is the total of the Men and Women.

Let’s call…

Men: m

Women: w

## **At a picnic, there were 3 times as many adults as children…**

This would imply that Adults = Men + Women, or…

*a *= *m + w*

Next, we are told that the total number of Men, Women, and Children at the picnic is *x. *

That is, *m + w + c = x*

We are also told that the number of Women is twice the number of Men, or…

*w = 2m*

## Remember that *a = 3c *from above, but the number of Adults will just be the number of Women plus the number of Men.

*a = 3c ⇒ m + w = 3c *

…and if we substitute the value *2m *for *w, *we see this:

*m + 2m = 3c ⇒ 3m = 3c ⇒ m = c*

Now we can take the statement *m + w + c = x *and sub in all of our values in terms of *m. *Remember that Men are *m, *Women are *2m, *and Children are *m. *

That is: *m + w + c = m + 2m + m = 4m = x*

So if *4m = x, *we see that *m = x/4. *