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Math Expert V
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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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If $$10x + 10y + 16x^2 + 25y^2 = 10 + z$$, what is the value of x + y?

(1) $$z = (4x)^2 + (5y)^2$$
(2) $$x = 1$$

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Marshall & McDonough Moderator D
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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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St1: z = $$16x^2 + 25y^2$$ --> 10(x + y) = 10 --> x + y = 1. Sufficient

St2: Clearly insufficient as we do not know the value of y and z

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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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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1
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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

When you modify the original condition and the question, x+y=(10+z-16x^2-25y^2)/10 is derived. For 1), x+y=1 is derived from z=16x^2+25y^2, which is sufficient. The answer is A.

 Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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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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Top Contributor
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

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If you enjoy my solutions, you'll love my GMAT prep course. Originally posted by BrentGMATPrepNow on 07 Aug 2016, 13:19.
Last edited by BrentGMATPrepNow on 01 Jun 2020, 08:32, 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] 03 Nov 2019, 23:33

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