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# What is the value of x + y? (1) 7x + 3y + 6z = 16 (2) 3x + 5y = 3z + 5

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Joined: 02 Sep 2009
Posts: 52278
What is the value of x + y? (1) 7x + 3y + 6z = 16 (2) 3x + 5y = 3z + 5  [#permalink]

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10 Feb 2017, 08:50
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Difficulty:

25% (medium)

Question Stats:

70% (01:27) correct 30% (01:17) wrong based on 166 sessions

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What is the value of x + y?

(1) 7x + 3y + 6z = 16

(2) 3x + 5y = 3z + 5

_________________
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Joined: 05 Mar 2015
Posts: 1003
Re: What is the value of x + y? (1) 7x + 3y + 6z = 16 (2) 3x + 5y = 3z + 5  [#permalink]

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10 Feb 2017, 09:21
Bunuel wrote:
What is the value of x + y?

(1) 7x + 3y + 6z = 16

(2) 3x + 5y = 3z + 5

(1) no info on z
insuff.
(2) similar reason as (1)
insuff

combining
substituting the value of z from (1) as 3z=8-3.5x-1.5y+5 to equation (2)
we get x+y=2
suff

Ans C
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Joined: 11 Sep 2015
Posts: 3331
Re: What is the value of x + y? (1) 7x + 3y + 6z = 16 (2) 3x + 5y = 3z + 5  [#permalink]

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10 Feb 2017, 10:28
2
Top Contributor
1
Bunuel wrote:
What is the value of x + y?

(1) 7x + 3y + 6z = 16

(2) 3x + 5y = 3z + 5

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

Cheers,
Brent
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Re: What is the value of x + y? (1) 7x + 3y + 6z = 16 (2) 3x + 5y = 3z + 5  [#permalink]

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22 May 2017, 12:13
Bunuel wrote:
What is the value of x + y?

(1) 7x + 3y + 6z = 16

(2) 3x + 5y = 3z + 5

x+y = ?

(1) We don't know Z, So - Not Sufficient
(2) We don't know Z, So - Not Sufficient

Combine

When we see the equation we see that 3Z & 6Z can be cancelled if we multiply equation (2) by 2

13x + 13y = 26

x+y = 2

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Joined: 28 Mar 2018
Posts: 46
Re: What is the value of x + y? (1) 7x + 3y + 6z = 16 (2) 3x + 5y = 3z + 5  [#permalink]

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12 Apr 2018, 11:23
GMATPrepNow wrote:
Bunuel wrote:
What is the value of x + y?

(1) 7x + 3y + 6z = 16

(2) 3x + 5y = 3z + 5

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

Cheers,
Brent

I made the highlighted mistake. Is it universally true that in this type of scenario, we can solve for X+Y with two equations, or does it need to be mathematically determined in each case?
Re: What is the value of x + y? (1) 7x + 3y + 6z = 16 (2) 3x + 5y = 3z + 5 &nbs [#permalink] 12 Apr 2018, 11:23
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# What is the value of x + y? (1) 7x + 3y + 6z = 16 (2) 3x + 5y = 3z + 5

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