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Math SAT Practice Problem

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Don’t fall for the SAT tricks and traps. Here is a Math problem that is not as complicated as it looks:

13. If x2 +y2 = 87 and xy = 38, what is the value of (x + y)2?

A) 87

B) 125

C) 163

D) 250

E) 361

Identify: Let’s identify the problem type. There are variables in an equation, and it looks like I will need to manipulate those variables somehow. This must be an ALGEBRA problem.

Set Up: Write down what you know, even if you have to rewrite the question in a different way.

x2 + y2 = 87

xy =38

Is there any way to substitute xy into the first equation? It looks like I can’t because the variables in the first equation are squared. Maybe they are related somehow? Let’s see what the problem is asking because that can give us a clue as to how to manipulate these equations.

(x + y)2?

Hey, I know, this expression can be expanded:

(x + y)2 = x2 + 2xy + y2

Make Sure: Make sure you are answering the right question and you haven’t missed a step. Regroup the terms.

 (x + y)2 =( x2 + y2)+ 2xy

Execute: Now, just substitute the given equations:

(x + y)2 =87 + 2(38)

Solve arithmetic with a calculator.

(x + y)2 =163

 

Answer: C

[Reference: Test 6G, Section 7, Problem 13]


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