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# If x, y and z are different integers, what is the value of y?

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Math Revolution GMAT Instructor
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If x, y and z are different integers, what is the value of y? [#permalink]

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Updated on: 09 Aug 2017, 09:17
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If x, y and z are different integers, what is the value of y?

1) The average (arithmetic mean) of x, y and z is 2
2) x<y<z

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Originally posted by MathRevolution on 21 Dec 2016, 01:47.
Last edited by chetan2u on 09 Aug 2017, 09:17, edited 1 time in total.
updated the OA
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Re: If x, y and z are different integers, what is the value of y? [#permalink]

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21 Dec 2016, 02:46
2
1) Signifies that Sum of the 3 Integers is 6 (Sum/3=2... Thus Sum= 6). (0,1,5) (1,2,3) (0,2,4) various combinations are Possible. Thus it's insufficient.

2) Clearly Insufficient

Combining 1+ 2

Y can either be 1 or 2 as per combinations mentioned in (1). Thus clearly insufficient.

P.S Request to poster to clarify how to tackle such question vis a vis inclusion of negative integers in such questions.

Omkar Kamat
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Re: If x, y and z are different integers, what is the value of y? [#permalink]

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21 Dec 2016, 03:06
1
I just came to the same conclusion. If the question would say "positive integers" it would be different. But with all integers, we can take (-5, 5, 6) for example and get the same mean of 2.

With only positive integers we can combine the two statements and see that it is (1, 2, 3) with one answer for y =2.
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Re: If x, y and z are different integers, what is the value of y? [#permalink]

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21 Dec 2016, 03:10
GMATforSeaCliff wrote:
I just came to the same conclusion. If the question would say "positive integers" it would be different. But with all integers, we can take (-5, 5, 6) for example and get the same mean of 2.

With only positive integers we can combine the two statements and see that it is (1, 2, 3) with one answer for y =2.

(0,1,5) is also possible. 0 is also an integer. Hence you can be either 1 or 2.

Omkar Kamat
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Re: If x, y and z are different integers, what is the value of y? [#permalink]

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21 Dec 2016, 03:11
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Omkar.kamat wrote:
GMATforSeaCliff wrote:
I just came to the same conclusion. If the question would say "positive integers" it would be different. But with all integers, we can take (-5, 5, 6) for example and get the same mean of 2.

With only positive integers we can combine the two statements and see that it is (1, 2, 3) with one answer for y =2.

(0,1,5) is also possible. 0 is also an integer. Hence you can be either 1 or 2.

Omkar Kamat
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Sorry, u r right... If it says POSITIVE INTEGERS, 0 WILL NOT BE INCLUDED.

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Re: If x, y and z are different integers, what is the value of y? [#permalink]

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21 Dec 2016, 03:17
Exactly, that's want I meant. You just received a Kudo
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Re: If x, y and z are different integers, what is the value of y? [#permalink]

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21 Dec 2016, 03:52
Hi guys, I'm rely confused here. Why exactly can it be answer c? I think with three integers and a sum of 6 it can also be 2 2 2, or 1 1 4 ? Don't get it sorry
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Re: If x, y and z are different integers, what is the value of y? [#permalink]

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21 Dec 2016, 03:58
Hi, don't worry. Happened to me quite often as well (unfortunately it still does)! You have to be very careful when reading the question. It says "three differen integers ..." . I really had to slow down mself. Although time-restricted the GMAT is a test of accuracy rather than speed. Just rushing through won't help you. I realised I overread crucial information aspecially in rather eas to medium questions, trying to solve it as fast as poosible = not a good idea Keep working on it
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Re: If x, y and z are different integers, what is the value of y? [#permalink]

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21 Dec 2016, 14:53
2
Right now the answer is E.
The set could have abundant combinations.
(-1,1,6) (-3,2,7) (1,2,3) etc.
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If x, y and z are different integers, what is the value of y? [#permalink]

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Updated on: 13 Sep 2017, 12:12
We have two examples as follows.

x = 1, y = 2, z = 3
x = 0, y = 1, z = 5

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Originally posted by MathRevolution on 23 Dec 2016, 02:27.
Last edited by MathRevolution on 13 Sep 2017, 12:12, edited 1 time in total.
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Re: If x, y and z are different integers, what is the value of y? [#permalink]

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23 Dec 2016, 02:32
MathRevolution wrote:
==> In the original condition, there are 3 variables (x, y, z), and in order to match the number of variables to the number of equations, there must be 3 equations, and therefore E is most likely to be the answer. By solving con 1) & con 2), you get (x+y+z)/3=2. Since it is x<y<z, you always get median=average=y=2. Hence it is unique and sufficient.

For median=mean the terms have to be in arithmetic progression. Unless and until it's clarified that this set is a set of POSITIVE integers myriad of options open up.

Kindly clarify

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Re: If x, y and z are different integers, what is the value of y? [#permalink]

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23 Dec 2016, 02:34
I#m sorry but the values (-5, 5, 6) or (0, 1, 5) for (x, y, z) satisfy both statements and we have different values for y. So the answer is (E), since both are insufficient.
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Re: If x, y and z are different integers, what is the value of y? [#permalink]

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24 Dec 2016, 22:23
Ex - (-1,1,6) or (1,2,3) satisfies both the equations. We are getting two different values for y.
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Re: If x, y and z are different integers, what is the value of y? [#permalink]

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27 Dec 2016, 05:45
MathRevolution wrote:
If x, y and z are different integers, what is the value of y?

1) The average (arithmetic mean) of x, y and z is 2
2) x<y<z

Bunuel

(1) is not sufficient to give the value of y since many sets of (x,y,z) are possible.
(2) clearly does not provide any unique value of y.

(1) and (2) combined
eg 1,2,3 y=2
-3,-1,10 y=-1

therefore both (1) and (2) together are not sufficient.
Please correct if I am wrong
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Re: If x, y and z are different integers, what is the value of y? [#permalink]

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10 Jan 2017, 23:15
MonkeyBrain12 wrote:
Hi guys, I'm rely confused here. Why exactly can it be answer c? I think with three integers and a sum of 6 it can also be 2 2 2, or 1 1 4 ? Don't get it sorry

Hi MonkeyBrain12,

It is clear that each condition alone is not sufficient.

Even though we consider both conditions together, we have many cases of (x,y,z) such as (0,1,5), ( -1,1,6).
Thus y is not unique.
Therefore, the correct answer is E.

Happy Studying!
Math Revolution
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Re: If x, y and z are different integers, what is the value of y? [#permalink]

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07 Jun 2017, 11:14
If x, y and z are different integers, what is the value of y?

1) The average (arithmetic mean) of x, y and z is 2
2) x<y<z

In this case C is only true if x,y,z are positive integers . Which is not stated in the question so it can not be presumed , in case of x,y,z being -ve integers more than one option are holding true , Hence E must be the OA
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Re: If x, y and z are different integers, what is the value of y? [#permalink]

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07 Jun 2017, 11:24
This is stupid. There's no condition of positive integers. The answer is E

Even putting them together: -1,3,4 = 2

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Re: If x, y and z are different integers, what is the value of y? [#permalink]

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07 Jun 2017, 19:41
Hi Bunuel please have a look at this question!

I doubt that the OA is wrong. Many thanks!
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Re: If x, y and z are different integers, what is the value of y? [#permalink]

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09 Aug 2017, 09:16
MathRevolution wrote:
If x, y and z are different integers, what is the value of y?

1) The average (arithmetic mean) of x, y and z is 2
2) x<y<z

Hi...
Responding to a PM...

The way Q is written, ans is E and the OA is being edited.
However just for info, what INSTEAD of ' different INTEGERS ' would make the answer C..
1) 3 consecutive integers
2) 3 different POSITIVE integers
3) 3 integers in arithmetic progression
4) 3 CONSECUTIVE even integers....

Ofcourse 1 and 4 are also in AP
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Re: If x, y and z are different integers, what is the value of y? [#permalink]

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12 Sep 2017, 00:14
MathRevolution wrote:
If x, y and z are different integers, what is the value of y?

1) The average (arithmetic mean) of x, y and z is 2
2) x<y<z

Ans is E

1) x+y+z = 3x2 = 6

1+2+3 =6 where y =2
-1+3+4 = 6 where y = 3
Insufficient
A,D eliminated

2) x<y<z
1<2<3
1<5<10
B eliminated

Combine both

1<2<3 y=2
-1<3<4 y=3
C eliminated

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Re: If x, y and z are different integers, what is the value of y?   [#permalink] 12 Sep 2017, 00:14
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