Bunuel wrote:
If \(10x + 10y + 16x^2 + 25y^2 = 10 + z\), what is the value of x + y?
(1) z = (4x)² + (5y)²
(2) x = 1
Target question: What is the value of x + y? Given: 10x + 10y + 16x² + 25y² = 10 + z Statement 1: z = (4x)² + (5y)² In other words,
z = 16x² + 25y²Take the given info (10x + 10y + 16x² + 25y² = 10 +
z) and replace
z with
16x² + 25y²We get: 10x + 10y + 16x² + 25y² = 10 +
16x² + 25y²Subtract 16x² from both sides to get: 10x + 10y + 25y² = 10 + 25y²
Subtract 25y² from both sides to get: 10x + 10y = 10
Factor the left side: 10(x + y) = 10
Divide both sides by 10 to get:
x + y = 1Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: x = 1 Take the given info (10x + 10y + 16x² + 25y² = 10 + z) and replace x with
1We get: 10(
1) + 10y + 16(
1²) + 25y² = 10 + z
As you can see, two variables remain, which means y and z can have any number of values.
This means
the sum x + y can have any number of values.
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
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