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Question: If x^2 +y^2 = 100, what is the value of (x - y)^2?
- x = 48/y
- x^2 - y^2 = -28
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statements ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Explanation:
Approach Solution (1)
We know that: x^2 + y^2 = 100
Using the identity: (x - y)^2 = x^2 + y^2 - 2xy
S1: x = 48/y
This can be written as: xy = 48
We can easily calculate the value of (x - y)^2.
So, S1 is sufficient
S2: x^2 - y^2 = -28
From the question, we get: x^2 +y^2 = 100
Solving these equations, we get: x^2 = 36, y^2 = 64
So, x = +6 or -6 and y = +8 or -8
This means that we can have different values for (x-y) and hence different values for (x - y)^2.
Statement 2 alone is insufficient.
Using the identity: (x - y)^2 = x^2 + y^2 - 2xy
S1: x = 48/y
This can be written as: xy = 48
We can easily calculate the value of (x - y)^2.
So, S1 is sufficient
S2: x^2 - y^2 = -28
From the question, we get: x^2 +y^2 = 100
Solving these equations, we get: x^2 = 36, y^2 = 64
So, x = +6 or -6 and y = +8 or -8
This means that we can have different values for (x-y) and hence different values for (x - y)^2.
Statement 2 alone is insufficient.
Correct option: A
Approach Solution (2)
1. x = 48/y
xy = 48
(x - y)^2 = x^2 + y^2 - 2xy
(x - y)^2 = 100 - 2(48) = 100 - 96 = 4
(x - y)^2 = 4
Hence, sufficient
2. x^2 - y^2 = -28
x^2 +y^2 = 100
Solving these equations, we get: x^2 = 36, y^2 = 64
So, x = +6 or -6 and y = +8 or -8
This means that we can have different values for (x-y) and hence different values for (x - y)^2.
Hence, insufficient
xy = 48
(x - y)^2 = x^2 + y^2 - 2xy
(x - y)^2 = 100 - 2(48) = 100 - 96 = 4
(x - y)^2 = 4
Hence, sufficient
2. x^2 - y^2 = -28
x^2 +y^2 = 100
Solving these equations, we get: x^2 = 36, y^2 = 64
So, x = +6 or -6 and y = +8 or -8
This means that we can have different values for (x-y) and hence different values for (x - y)^2.
Hence, insufficient
Correct option: A
“If x^2 +y^2 = 100, what is the value of (x - y)^2?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.
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