If 2x(5n) = t, what is t?

[kobel51]

If 2x(5n) = t, what is the value of t?

1) x = n+3

2) 2x = 32

[Mike@Magoosh]

If 2x(5n) = t, what is the value of t?

1) x = n+3

2) 2x = 32

Dear kobel51,
I'm happy to help.

Basically, we can rearrange multiplication in any order, so

(2x)*(5n) = 2*5*x*n = 10*xn = t

We need to know the product of xn to find t.

Statement #1: x = n+3
This is equivalent to x - n = 3. In other words, we know the difference between the two variables. Either a sum or a difference of two variables is not enough to give us a product. This statement, alone and by itself, is insufficient.

Statement #2: 2x = 32
In other words, x = 16. We know the value of x and have no clue about n, so this statement, alone and by itself, is insufficient.

Combined: From #2, we get the value of x, and then plugging that into #1, we get the value of n and can solve. Combined, the statements are sufficient.

Does this make sense?
Mike

[Patrick_GMATFix]

The initial equation corresponds to t = 10xn. To find t, we need xn.

Rephrase: what is xn?. Neither statement alone allows us to find this but what about the statements together? Well together the provide two independent linear equations; we can find x from statement (2), then plug that into (1) to get n. Once we know both x and n, we can answer the question.

The answer is C. I go through the question in detail in the full solution below (taken from the GMATFix App).



-Patrick