### Monthly GMAT Challenge Problem Showdown: January 13, 2013

We invite you to test your GMAT knowledge for a chance to win! The second week of every month, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that month’s drawing for free Manhattan GMAT prep materials. Tell your friends to get out their scrap paper and start solving!

Here is this month’s problem:

If

p,q, andrare different positive integers such thatp+q+r= 6, what is the value ofx?(1) The average of

xand^{p}xis^{q}x.^{r}(2) The average of

xand^{p}xis not^{r}x.^{q}

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The answer is E

There can be 3 possible equations based on the values of p,q and r. They fall in the set (1, 2, 3).

Accordingly using statement 1,

value of x can be -1/2 or 1 based on 1 equation.

1 based on second equation

-2 or 1 based on another equation

Even if wetake statement2, we can eliminate any 1 of the above 3 equations which leaves us with at least 2 different values of ‘x’ in each case.

Hence even by combining both statements, we cannot solve the value of ‘x’.

So answer is E

A

E.

I do not think option B helps in anyways because it is said that x, y and z are different integers. But it is true that X is 1. But since the X=1 does not suffice the statement, the answer should be c.

Please correct me if wrong

A