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Math Expert V
Joined: 02 Sep 2009
Posts: 58381
What is the value of y? (1) 2 x + 2 y = 14 (2) 2 y + 2 z = 14  [#permalink]

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Difficulty:   5% (low)

Question Stats: 91% (00:50) correct 9% (00:56) wrong based on 222 sessions

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What is the value of y?

(1) 2 x + 2 y = 14

(2) 2 y + 2 z = 14

_________________
Intern  B
Joined: 13 Apr 2015
Posts: 30
Re: What is the value of y? (1) 2 x + 2 y = 14 (2) 2 y + 2 z = 14  [#permalink]

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Is the answer E ? As we do not have any further information between x and z.We have two eq and 3 variables
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4006
What is the value of y? (1) 2 x + 2 y = 14 (2) 2 y + 2 z = 14  [#permalink]

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Bunuel wrote:
What is the value of y?

(1) 2x + 2y = 14
(2) 2y + 2z = 14

Target question: What is the value of y?

Statement 1: 2x + 2y = 14
Simplify by dividing both sides by 2 to get: x + y = 7
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 0 and y = 7. Here, y = 7
Case b: x = 1 and y = 6. Here, y = 6
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: http://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: 2y + 2z = 14
Simplify by dividing both sides by 2 to get: y + z = 7
There are several values of y and z that satisfy statement 1. Here are two:
Case a: y = 7 and z = 0. Here, y = 7
Case b: y = 6 and z = 1. Here, y = 6
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x + y = 7
Statement 2 tells us that z + y = 7
If we subtract the bottom equation from the top, we get x - z = 0
This means that x = z. That's ALL we can conclude when we COMBINE the statements.
As such, there's no way to determine the value of y.
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Aside: If we want to be 100% sure of our answer consider these values of x, y and z that satisfy BOTH equations:
Case a: x = 0, y = 7 and z = 0. Here, y = 7
Case b: x = 1, y = 6 and z = 1. Here, y = 6

Cheers,
Brent
_________________

Originally posted by GMATPrepNow on 21 Mar 2016, 15:58.
Last edited by GMATPrepNow on 07 Aug 2016, 13:33, edited 1 time in total.
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8011
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: What is the value of y? (1) 2 x + 2 y = 14 (2) 2 y + 2 z = 14  [#permalink]

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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.

What is the value of y?

(1) 2 x + 2 y = 14

(2) 2 y + 2 z = 14

In the original condition, there are 3 variables(x,y,z), which should match with the number of equations. So you need 3 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer. When 1) & 2), the value of y is not unique, which is not sufficient.
Therefore, the answer is E.

 For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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Schools: Yale '18
GMAT 1: 650 Q43 V37 GRE 1: Q157 V158 GPA: 2.66
Re: What is the value of y? (1) 2 x + 2 y = 14 (2) 2 y + 2 z = 14  [#permalink]

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1
Bunuel wrote:
What is the value of y?

(1) 2 x + 2 y = 14

(2) 2 y + 2 z = 14

This question plays a very subtle trick

x + y = 7

z + y= 7

therefore

x=z

HOWEVER

Just x=z that doesn't necessarily mean that the value of Y can be identified as Y can be several things.

E
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Re: What is the value of y? (1) 2 x + 2 y = 14 (2) 2 y + 2 z = 14  [#permalink]

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_________________ Re: What is the value of y? (1) 2 x + 2 y = 14 (2) 2 y + 2 z = 14   [#permalink] 19 Jan 2019, 08:34
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