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# If 10x + 10y + 16x^2 + 25y^2 = 10 + Z, what is the value of x + y?

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If 10x + 10y + 16x^2 + 25y^2 = 10 + Z, what is the value of x + y? [#permalink]
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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 + 25y²
Take the given info (10x + 10y + 16x² + 25y² = 10 + z) and replace z with 16x² + 25y²
We get: 10x + 10y + 16x² + 25y² = 10 + 16x² + 25y²
Subtract 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 = 1
Since 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 1
We 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

Originally posted by BrentGMATPrepNow on 07 Aug 2016, 14:19.
Last edited by BrentGMATPrepNow on 01 Jun 2020, 09:32, edited 1 time in total.
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Re: If 10x + 10y + 16x^2 + 25y^2 = 10 + Z, what is the value of x + y? [#permalink]
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Re: If 10x + 10y + 16x^2 + 25y^2 = 10 + Z, what is the value of x + y? [#permalink]
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