What is the value of xy?

[BTGmoderatorDC]

What is the value of xy?

(1) y = x + 1

(2) y = x^2 + 1

OA E

Source: Official Guide

[ceilidh.erickson]

Question: What is the value of xy?
To answer this question, we need either values for x and y individually, or simply a value for the product xy.

(1) y = x + 1
This gives us y in terms of x, but cannot give us the value of xy. Insufficient.

(2) y = x^2 + 1
This gives us y in terms of x^2, but cannot give us the value of xy. Insufficient.

(1) and (2) together
We know the rule that we need 2 equations to solve for the values of 2 variables... but be careful! Even exponents can give us multiple possible values. Let's see what happens when we try to solve:
y = x + 1
y = x^2 + 1
x + 1 = x^2 + 1
x = x^2
x = either 1 or 0
Thus, y = either 2 or 1

Since we have 2 possible sets of values that would give us different values for xy, this is insufficient to answer the question.

The answer is E.

[ceilidh.erickson]

For more on how the GMAT subverts our expectations of the 2 equations / 2 variables rule, see:
https://www.manhattanprep.com/gmat/blog ... ons-rules/