Data Sufficiency (GMAT)

Question

If wxyz ≠ 0, does wxyz = 1?

Statement (1): w = 1/x, y = z

Statement (2): wx² = 1/xyz

CHOICES:

A - Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient.

B - Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient

C - BOTH Statement 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient

D - EACH statement ALONE is sufficient to answer the question

E - STATEMENT 1 and 2 TOGETHER are not sufficient to answer the questions

Answer 1

For data sufficiency problems, we first want to evaluate each statement separately.

If it is the case that at least 1 or both of the statements are sufficient individually, we are done.

If it is the case that both statements are insufficient, we can evaluate using the two statements together.

Let's evaluate both statements individually for our problem.

Statement (1): w = 1/x, y = z

1. Does wxyz = 1?

We can replace variables in the expression wxyz to simply.

Since w = 1/x,

1. wxyz = (1/x * x) * yz
2. Since (1/x * x) = 1
3. wxyz = 1 * yz

Now, since y = z,

1. yz = y^2 or z^2

We now know that wxyz evaluates to y^2 or z^2, but we have no idea about the values of y or z.

Therefore, Statement 1 is NOT independently sufficient.

Statement (2): wx² = 1/xyz

1. Does wxyz = 1?

We can multiply both sides of wx² = 1/xyz by xyz:

1. w(x^3)yz = 1

If we factor out an x^2, we have

1. wxyz * x^2 = 1
2. wxyz = y^2 = z^2

Since we do not know the value of x^2, statement 2 is NOT independently sufficient.

Evaluating both statements together

We now know that

1. wxyz * x^2 = 1
2. wxyz = y^2 = z^2
3. w = 1/x

With this information, we can see that the expression can evaluate to 1 if x = -1 or x = 1.

The truth of the statements depends entirely on the value of x.

However, neither statement 1 nor 2 gives any requirements for the value of x.

Therefore, both statements together are insufficient to answer the question.