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X, Y and Z are positive integers, and X+2Y+2Z=13. Z=?

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X, Y and Z are positive integers, and X+2Y+2Z=13. Z=? [#permalink] New post 15 May 2012, 21:26
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E

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48% (01:52) correct 52% (01:05) wrong based on 27 sessions
X, Y and Z are positive integers, and X+2Y+2Z=13. Z=?

(1) X>Y>Z
(2) None of them is equal to 4
[Reveal] Spoiler: OA
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Re: X, Y and Z are positive integers, and X+2Y+2Z=13. Z=? [#permalink] New post 15 May 2012, 22:36
Expert's post
X, Y and Z are positive integers, and X+2Y+2Z=13. Z=?

(1) X>Y>Z. If z=2 then the least values of y and x are 3 and 4 respectively, in this case x+2y+2z=14>13, so z must be less than 2 and since given that it's a positive integer then it can only be 1. Sufficient.

(2) None of them is equal to 4. Not sufficient, consider: x=3, y=2, z=3 and x=3, y=3, z=2.

Answer: A.

Hope it's clear.
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Re: X, Y and Z are positive integers, and X+2Y+2Z=13. Z=? [#permalink] New post 27 May 2012, 19:43
(1) X>Y>Z. If z=2 then the least values of y and x are 3 and 4 respectively, in this case x+2y+2z=14>13, so z must be less than 2 and since given that it's a positive integer then it can only be 1. Sufficient.

Bunuel, any reason why you did not consider Z=1 so in this case case y=2 and z=3 and then the solution is insufficient.
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Re: X, Y and Z are positive integers, and X+2Y+2Z=13. Z=? [#permalink] New post 28 May 2012, 02:35
Expert's post
rggoel9 wrote:
(1) X>Y>Z. If z=2 then the least values of y and x are 3 and 4 respectively, in this case x+2y+2z=14>13, so z must be less than 2 and since given that it's a positive integer then it can only be 1. Sufficient.

Bunuel, any reason why you did not consider Z=1 so in this case case y=2 and z=3 and then the solution is insufficient.


I guess you mean z=1, y=2 and x=3 (z<y<z). This values are not valid since they does not satisfy x+2y+2z=13.
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Re: X, Y and Z are positive integers, and X+2Y+2Z=13. Z=? [#permalink] New post 30 May 2012, 05:01
another way to look at the question is that the sum is 13... and it is x+2y+2z, which means that z has to be odd as 2z+2y will be even and hence z has to be 1, bcoz any other odd and the condition x>y>z does not give 13.

Second condition is clearly insufficient.
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Re: X, Y and Z are positive integers, and X+2Y+2Z=13. Z=? [#permalink] New post 30 May 2012, 08:40
pavanpuneet - Very good explanation. I liked it.
Re: X, Y and Z are positive integers, and X+2Y+2Z=13. Z=?   [#permalink] 30 May 2012, 08:40
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