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# In the expression 3x − 2y < z, is y positive?

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Math Expert
Joined: 02 Sep 2009
Posts: 59622
In the expression 3x − 2y < z, is y positive?  [#permalink]

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31 Jan 2016, 07:37
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Difficulty:

35% (medium)

Question Stats:

63% (01:41) correct 37% (01:38) wrong based on 43 sessions

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In the expression 3x − 2y < z, is y positive?

(1) x = 3
(2) z = 17

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Re: In the expression 3x − 2y < z, is y positive?  [#permalink]

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01 Feb 2016, 05:45
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.

In the expression 3x − 2y < z, is y positive?

(1) x = 3
(2) z = 17

In the original condition, there are 3 variables(x,y,z) and 1 equation(3x-2y<z), which should match with the number of equations. So you need 2 more equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer.
When 1) & 2), 3*3-2y<17, 9-17<2y, -8<2y, -4<y에서 y=2 -> yes, y=-2 -> no, which is not sufficient. Therefore, the answer is E.

-> For cases where we need 2 more equations, such as original conditions with “2 variables”, or“3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% 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 C 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, D or E.
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Re: In the expression 3x − 2y < z, is y positive?  [#permalink]

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01 Feb 2016, 07:15
Bunuel wrote:
In the expression 3x − 2y < z, is y positive?

(1) x = 3
(2) z = 17

3x − 2y < z
i.e. y > (3x-z)/2

Question: Is y > 0?

Statement 1: x = 3
We don't have any information about z to answer the question. Hence
NOT SUFFICIENT

Statement 1: z = 17
We don't have any information about x to answer the question. Hence
NOT SUFFICIENT

Combining the two statements
y > (3x-z)/2
i.e. y > (9-17)/2
i.e. y > -4
i.e. y may be Negative or may be positive as well. Hence
NOT SUFFICIENT

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Re: In the expression 3x − 2y < z, is y positive?  [#permalink]

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25 Nov 2019, 22:45
From 1, 9-2y<z , y & z not known. INSUFFICIENT
From 2, 3x-2y<17, x & y not known. INSUFFICIENT

1+2, 17>9-2y =>y>-4

We dont know y is -3,-2,-1 or any positive. INSUFFICIENT. So Answer E
Re: In the expression 3x − 2y < z, is y positive?   [#permalink] 25 Nov 2019, 22:45
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