## What is the value of x + y?

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### What is the value of x + y?

by BTGmoderatorLU » Thu Sep 02, 2021 8:39 am

00:00

A

B

C

D

E

## Global Stats

Source: Veritas Prep

What is the value of x + y?

1) 7x + 3y + 6z = 16
2) 3x + 5y = 3z + 5

The OA is C

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### Re: What is the value of x + y?

by [email protected] » Thu Sep 02, 2021 2:38 pm

00:00

A

B

C

D

E

## Global Stats

BTGmoderatorLU wrote:
Thu Sep 02, 2021 8:39 am
Source: Veritas Prep

What is the value of x + y?

1) 7x + 3y + 6z = 16
2) 3x + 5y = 3z + 5

The OA is C
Great question!

Target question: What is the value of x + y?

Statement 1: 7x + 3y + 6z = 16
Notice that, since we have the 3rd variable, z, we can assign ANY values to x and y and then simply make the z-value such that the equation holds true.
For example, if we let x = 0 and y = 0, then we get 0 + 0 + 6z = 16. So, z = 16/6. In this case, x + y = 0 + 0 = 0
Similarly, if we let x = 1 and y = 1, then we get 7 + 3 + 6z = 16. So, z = 6/6. In this case, x + y = 1 + 1 = 2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 3x + 5y = 3z + 5
We can apply the same logic that we used for statement 1 to show that statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that 7x + 3y + 6z = 16
Statement 2 tells us that 3x + 5y = 3z + 5

IMPORTANT: Many students will assume that, since we have a system of 3 equations with 2 variables, then we cannot answer the target question.
This would be a correct assumption IF the target question asked for the individual values of x and y.
HOWEVER, notice that the target question only asks for the sum of x and y.
This we might be able to find.

First, take 3x + 5y = 3z + 5 and subtract 3z from from both sides to get: 3x + 5y - 3z = 5
Then multiply both sides by 2 to get: 6x + 10y - 6z = 10

We now have:
7x + 3y + 6z = 16
6x + 10y - 6z = 10

ADD the equations to get: 13x + 13y = 26
Divide both sides by 13 to get: x + y = 2
Since we can answer the target question with certainty, the combined statements are SUFFICIENT