chetan2u wrote:

What is the value of \(32xy^2+16x^2y\)?

(1) \((x+2y)^2=64\)

(2) x=2y

Great question!

Target question: What is the value of 32xy² + 16x²y?After scanning the two statements, I see that we might benefit from

rephrasing the target question.

32xy² + 16x²y = 16xy(2y + x)So.....

REPHRASED target question: What is the value of 16xy(2y + x)? Statement 1: (x+2y)² = 64This tells us 2 things: EITHER x+2y = 8 OR x+2y = -8

There are several values of x and y that satisfy statement 1. Here are two:

Case a: x = 0 and y = 8, in which case

16xy(2y + x) = 0Case b: x = 1 and y = 7, in which case

16xy(2y + x) = some value other than 0Since we cannot answer the

REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x = 2y There are several values of x and y that satisfy statement 2. Here are two:

Case a: x = 0 and y = 0, in which case

16xy(2y + x) = 0Case b: x = 2 and y = 1, in which case

16xy(2y + x) = some value other than 0Since we cannot answer the

REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined Statement 1 tells us that EITHER x+2y = 8 OR x+2y = -8

Statement 2 tells us that x = 2y

So, we have two possible systems of equations:

x+2y = 8

x = 2yAND

x+2y = -8

x = 2yIf we solve the

first system, we get: x = 4 and y = 2, in which case

16xy(2y + x) = 16(4)(2)[2(2) + (4)] = some POSITIVE numberIf we solve the

second system, we get: x = -4 and y = -2, in which case

16xy(2y + x) = 16(-4)(-2)[2(-2) + (-4)] = some NEGATIVE numberSince we cannot answer the

REPHRASED target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

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