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# M03-33

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Math Expert
Joined: 02 Sep 2009
Posts: 45422

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16 Sep 2014, 00:21
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Difficulty:

25% (medium)

Question Stats:

67% (03:10) correct 33% (00:39) wrong based on 162 sessions

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Are integers $$x$$, $$y$$, and $$z$$ consecutive?

(1) The average (arithmetic mean) of $$x$$ and $$z$$ equals to $$y$$

(2) $$x = -z$$

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Math Expert
Joined: 02 Sep 2009
Posts: 45422

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16 Sep 2014, 00:21
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Official Solution:

(1) The average (arithmetic mean) of $$x$$ and $$z$$ equals to $$y$$. This statement tells that $$y=\frac{x+z}{2}$$: if $$x=y=z=0$$ then the answer is NO but if $$x=-1$$, $$y=0$$ and $$z=1$$ then the answer is YES. Not sufficient.

(2) $$x = -z$$. Not sufficient since no info about $$y$$.

(1)+(2) Examples discussed for statement (1) are still valid, so we can have both NO ($$x=y=z=0$$) and YES ($$x=-1$$, $$y=0$$ and $$z=1$$) answers. Not sufficient.

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Joined: 04 Sep 2014
Posts: 49
Schools: CBS '18 (D)

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24 Jun 2015, 23:21
I think a set of 3 equally spaced numbers would also show that statement 1 is insufficient because of the property that mean = median.
Current Student
Joined: 12 Aug 2015
Posts: 291
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
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WE: Management Consulting (Consulting)

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12 Feb 2016, 01:11
I think this is a high-quality question and I agree with explanation. i think it s 700 lv q
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Senior Manager
Joined: 31 Mar 2016
Posts: 402
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)

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30 Aug 2016, 05:07
I think this is a high-quality question and I agree with explanation.
Intern
Joined: 08 Oct 2014
Posts: 4

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09 Nov 2017, 13:43
If x,y,z are consecutive then
why can't we take x,x+1,x+2? this satisfies st.1

Math Expert
Joined: 02 Sep 2009
Posts: 45422

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09 Nov 2017, 21:14
Life! wrote:
If x,y,z are consecutive then
why can't we take x,x+1,x+2? this satisfies st.1

We don't know whether x, y, and z are consecutive integers. The question asks: ARE integers x, y, and z are consecutive?
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Joined: 22 Jun 2017
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20 May 2018, 09:04
I think this is a high-quality question and I agree with explanation.
Re M03-33   [#permalink] 20 May 2018, 09:04
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# M03-33

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