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# M03-33

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:21
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25% (medium)

Question Stats:

66% (02:58) correct 34% (00:39) wrong based on 180 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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16 Sep 2014, 00:21
1
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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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.
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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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30 Aug 2016, 05:07
I think this is a high-quality question and I agree with explanation.
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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

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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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20 May 2018, 09:04
I think this is a high-quality question and I agree with explanation.
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26 Jun 2018, 09:47
Hi Bunuel,

For a problem like this, when it asks are x,y,z consecutive, does that mean that they have to be consecutive in that order?

For example, I tested x=3,z-1,y=2. It satisfies S1, but they are not consecutive in the order that is listed on the question. So I am not sure if my test case is allowed or not. Wouldn't the question need to use the word "respectively" to convey that the order matters?
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26 Jun 2018, 10:03
1
norovers wrote:
Hi Bunuel,

For a problem like this, when it asks are x,y,z consecutive, does that mean that they have to be consecutive in that order?

For example, I tested x=3,z-1,y=2. It satisfies S1, but they are not consecutive in the order that is listed on the question. So I am not sure if my test case is allowed or not. Wouldn't the question need to use the word "respectively" to convey that the order matters?

It's not necessary x, y, and z to be consecutive in that order. They would be considered consecutive if say z=1, x=2 and y=3.
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04 Jan 2019, 00:32
Statement 2 here says x=-z < the only number equal to it's opposite is 0. Therefore x and z are zero. Hence x,y,z can never be consecutive integer . Bunuel can you please explain what am i missing here?
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04 Jan 2019, 00:49
Abhi077 wrote:
Statement 2 here says x=-z < the only number equal to it's opposite is 0. Therefore x and z are zero. Hence x,y,z can never be consecutive integer . Bunuel can you please explain what am i missing here?

The above is not correct. x = -z can be true for infinitely many numbers:

x = 1 and z = -1 --> x = -z.
x = 2 and z = -2 --> x = -z.
x = 3 and z = -3 --> x = -z.
...
x = -1 and z = 1 --> x = -z.
...
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Re: M03-33   [#permalink] 04 Jan 2019, 00:49
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# M03-33

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