If x, y, and z are all nonzero numbers, and x = y + z, which

[BTGmoderatorDC]

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

OA E

Source: Veritas Prep

[GMATGuruNY]

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

x = y + z is valid if x=2, y=1 and z=1.
The correct answer must yield a value of 1 when x=2, y=1 and z=1.
Only E works:
(x-z)/y = (2-1)/1 = 1.

The correct answer is E.

[ceilidh.erickson]

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.

[fskilnik@GMATH]

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
Source: Veritas Prep

Perfect opportunity to give emphasis to the connection of the first leg (FOCUS) and the third leg (ALTERNATIVE CHOICES) of our WINNING TRIAD!

An additional glance at the relationship between x, y and z (DATA, the second leg) shows us we must...

Consider the difference among two of the three letters in a specific order:

(x-y) over z (not available)
OR
(x-z) over y (the correct answer E).

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

[Brent@GMATPrepNow]

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

[Scott@TargetTestPrep]

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