What is the value of x + y?
(1) x^2 + y^2 = 5
(2) xy = 2
The OA is the option E.
Can I use that (x+y)^2=x^2+2xy+y^2 and get that (x+y)=3. Why are both statements not sufficient? Experts, may you help me here? Please.
What is the value of x + y?
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- elias.latour.apex
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When doing data sufficiency, it is best to start out by asking ourselves: What do I need? In this case, we need a single equation or system of equations that gives us one discreet value for x and y or some equation that gives us x+y when we cancel the rest of it out.
Statement 1: Since this contains squares, it does not provide a single value for x and y. Even if we assume that y=2, x could be 1 or -1.
Statement 2: Since this equation contains two variables, there are an infinite number of solutions. We could say x=1, y=2 or x=4, y=0.5
Together: Even together, we do not get a single value for x and y. We could say that x=1 and y=2 so x+y=3 OR we could say that x=-1 and y=-2 so x+y=-3.
(E)
Statement 1: Since this contains squares, it does not provide a single value for x and y. Even if we assume that y=2, x could be 1 or -1.
Statement 2: Since this equation contains two variables, there are an infinite number of solutions. We could say x=1, y=2 or x=4, y=0.5
Together: Even together, we do not get a single value for x and y. We could say that x=1 and y=2 so x+y=3 OR we could say that x=-1 and y=-2 so x+y=-3.
(E)
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- Brent@GMATPrepNow
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Target question: What is the value of x + y?Vincen wrote:What is the value of x + y?
(1) x² + y² = 5
(2) xy = 2
Statement 1: x² + y² = 5
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 2 and y = 1 (notice that x² + y² = 2² + 1² = 5). In this case, the answer to the target question is x + y = 2 + 1 = 3
Case b: x = -2 and y = 1 (notice that x² + y² = (-2)² + 1² = 5). In this case, the answer to the target question is x + y = -2 + 1 = -1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: xy = 2
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 2 and y = 1 (notice that xy = (2)(1) = 2). In this case, the answer to the target question is x + y = 2 + 1 = 3
Case b: x = -2 and y = -1 (notice that xy = (-2)(-1) = 2). In this case, the answer to the target question is x + y = (-2) + (-1) = -3
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that x² + y² = 5
Statement 2 tells us that xy = 2
ASIDE: When you see the terms x², y² and xy, you should be thinking SPECIAL PRODUCTS
(x + y)² = (x + y)(x + y) = x² + 2xy + y²
(x - y)² = (x - y)(x - y) = x² - 2xy + y²
If xy = 2, then 2xy = 4
So, x² + 2xy + y² = 5 + 4 = 9
In other words, (x + y)² = 9, which means x + y = 3
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent