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555-605 (Medium)|   Algebra|      
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Bunuel
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What is the value of x + y? (1) 7x + 3y + 6z = 16 (2) 3x + 5y = 3z + 5 10 Feb 2017, 09:50
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

74% (01:21) correct 26% (01:22) wrong based on 376 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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C
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BrentGMATPrepNow
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What is the value of x + y? (1) 7x + 3y + 6z = 16 (2) 3x + 5y = 3z + 5 10 Feb 2017, 11:28
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Bunuel
What is the value of x + y?

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

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

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

Answer: C

Cheers,
Brent
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rohit8865
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What is the value of x + y? (1) 7x + 3y + 6z = 16 (2) 3x + 5y = 3z + 5 10 Feb 2017, 10:21
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Bunuel
What is the value of x + y?

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

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


(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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What is the value of x + y? (1) 7x + 3y + 6z = 16 (2) 3x + 5y = 3z + 5 22 May 2017, 13:13
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Bunuel
What is the value of x + y?

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

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

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

Adding we get:

13x + 13y = 26

x+y = 2

Answer is - C
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What is the value of x + y? (1) 7x + 3y + 6z = 16 (2) 3x + 5y = 3z + 5 12 Apr 2018, 12:23
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Bunuel
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

Answer: C

Cheers,
Brent
Show more

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?
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What is the value of x + y? (1) 7x + 3y + 6z = 16 (2) 3x + 5y = 3z + 5 24 Jul 2019, 11:13
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lostnumber
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Bunuel
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

Answer: C

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?
Show more

It needs to be mathematically determined in each case. Here's a simple example:

What is the value of x + y?

(1) x + y + z = 3
(2) 3x + 2y + z = 6

In this case, you can't solve for the value of x + y exactly, even if you have both equations. The correct answer would be E.

To prove that's the case, note that x = 0, y = 3, and z = 0 fit both equations, and x + y = 0 + 3 = 3.

Also, x = 1, y = 1, and z = 1 fit both equations, and x + y = 1 + 1 = 2.

So, the question can have at least two different answers, 2 or 3, so the statements are insufficient together.

The reason this happens is because in my example problem here, when you cancel out z, you end up with different coefficients for x and for y. Therefore, you can't simplify the resulting equation to x + y = something. Instead, you get something like 2x + y = something, which doesn't help you find the value of x + y.
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What is the value of x + y? (1) 7x + 3y + 6z = 16 (2) 3x + 5y = 3z + 5 24 Jul 2019, 12:56
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x+y = ?

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

On combining,

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

On Adding we get:

13x + 13y = 26

x+y = 2

Hence
IMO - C

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What is the value of x + y? (1) 7x + 3y + 6z = 16 (2) 3x + 5y = 3z + 5 05 Dec 2022, 19:25
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