If x ≠ y, what is the value of x + y?
(1) x - y = 1
(2) x^2- y^2 = x - y
Correct Answer is "B - Statement (2) ALONE is sufficient, but statement (1) is NOT sufficient"
But I believe it should be "D - EACH statement ALONE is sufficient". Why because:
Consider (2) \(X2- y 2 = x - y\) => \((x+y)(x-y) = (x-y)\) => \(x+y = 1\) by cancelling \(x-y\) on both sides
SufficientNow, consider (1) \(x - y = 1\).Adding \(2y\) on both sides,
\(x+y = 1 + 2y.\)
I agree, this does not give a concrete answer like case 2 (which gave x+y = 1). But this expression "\(x+y = 1 + 2y\)" will help me find the answer for x+y provided I know the value of y. Isn't it?
The guide says,
Quote:
The key to Data Sufficiency is to remember that it does not require you to answer the question asked in the question stem. Instead, you need to decide whether the statements provide enough information to answer the question.
Thus, I say I can find the value of x+y either with 1st 2nd statement alone (i.e., EACH statement ALONE is sufficient).
I am not saying I am correct. I know I am wrong because my answer is not matching with the correct answer. Its just that I do not seem to understand. Can someone correct me, please?
(1) x - y = 1. If x=1 and y=0, then x+y=1 but if x=2 and y=1, then x+y=3. We have two different answers thus the statement is not sufficient.
(2) x^2- y^2 = x - y --> (x-y)(x+y)=x-y. Now, since we are given that x-y≠0, then we can safely reduce by it and we get: x+y=1. Sufficient.
Answer: B.
As for your doubt. There are two kinds of data sufficient questions: YES/NO DS questions and DS questions which ask to find a value.
Now, our original question is asking about the value of x+y, thus the statement is sufficient ONLY if you can get the
of this expression.
Hope it's clear.
P.S. Please read carefully and follow:
Pay attention to the rules 2, 3, and 10. Thank you.