We can also rearrange the equation algebraically. If x = y + z, then:
y = x - z
z = x - y

Compare these to our answer choices:

(A) (y - z)/x
We know that y + z = x, so (y + z)/x = 1. If all terms are non-zero, then there's no way that y + z = y - z, so (y - z)/x must not equal 1.

(B) (y - x)/z
y - x is what we'd get if we multiplied (x - y) by -1. So we could say:
x - y = z --> y - x = -z
So (y - x)/z = -1, not 1.

(C) (z - x)/y
Similarly, z - x is what we'd get if we multiplied (x - z) by -1. So we could say:
x - z = y --> z - x = -y
So (z - x)/y = -1, not 1.

(D) (z - y)/x
We know that z + y = x, so (z + y)/x = 1. If all terms are non-zero, then there's no way that z + y = z - y, so (z - y)/x must not equal 1.

(E) (x - z)/y
Since we derived that x - z = y, we can substitute:
(x - z)/y = y/y = 1.

The answer is E.

BTGmoderatorDC wrote:If x, y, and z are all nonzero numbers, and x = y + z, which of the following is equal to 1?

(A) (y - z)/x
(B) (y - x)/z
(C) (z - x)/y
(D) (z - y)/x
(E) (x - z)/y

NOTE: this is one of those questions that require us to check/test each answer choice. In these situations, always check the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top.

For more on this strategy, see my article: https://www.gmatprepnow.com/articles/han ... -questions

Given: x = y + z

E) (x - z)/y
Replace x with y + z to get: (y + z - z)/y
Simplify: y/y
This definitely equals 1.

Answer: E

Cheers,
Brent

BTGmoderatorDC wrote:If x, y, and z are all nonzero numbers, and x = y + z, which of the following is equal to 1?

(A) (y - z)/x
(B) (y - x)/z
(C) (z - x)/y
(D) (z - y)/x
(E) (x - z)/y

Since x - z = y, if we divide both sides by y we get: (x - z)/y = 1.

Answer: E