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What is the value of y? (1) 2 x + 2 y = 14 (2) 2 y + 2 z = 14

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

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New post 21 Mar 2016, 07:17
1
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A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

88% (00:38) correct 12% (00:40) wrong based on 137 sessions

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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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New post 21 Mar 2016, 11:00
Is the answer E ? As we do not have any further information between x and z.We have two eq and 3 variables
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What is the value of y? (1) 2 x + 2 y = 14 (2) 2 y + 2 z = 14 [#permalink]

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New post Updated on: 07 Aug 2016, 13:33
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
Answer =

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
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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.
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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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New post 21 Mar 2016, 18:36
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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Re: What is the value of y? (1) 2 x + 2 y = 14 (2) 2 y + 2 z = 14 [#permalink]

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New post 10 Sep 2017, 12:58
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
Re: What is the value of y? (1) 2 x + 2 y = 14 (2) 2 y + 2 z = 14   [#permalink] 10 Sep 2017, 12:58
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