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# If x, y, and z are three integers, are they consecutive integers?

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Math Expert
Joined: 02 Sep 2009
Posts: 53865
If x, y, and z are three integers, are they consecutive integers?  [#permalink]

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10 Dec 2017, 00:51
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25% (medium)

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69% (00:56) correct 31% (01:00) wrong based on 87 sessions

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If x, y, and z are three integers, are they consecutive integers?

(1) z = x + 2
(2) None of the three integers are multiples of 3.

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If x, y, and z are three integers, are they consecutive integers?  [#permalink]

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10 Dec 2017, 03:33
Bunuel wrote:
If x, y, and z are three integers, are they consecutive integers?

(1) z = x + 2
(2) None of the three integers are multiples of 3.

Statement 1: Nothing mentioned about $$y$$. Insufficient

Statement 2: Among any three consecutive integers one of them have to be a multiple of $$3$$. As none are multiple of $$3$$, hence they are not consecutive. Sufficient

Option B
Intern
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Re: If x, y, and z are three integers, are they consecutive integers?  [#permalink]

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10 Dec 2017, 06:12
Hi,

Can someone clarify why the sequence can't be 0,1 and 2? Does 0*3=0 count as a multiple of 3?
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Joined: 02 Sep 2009
Posts: 53865
Re: If x, y, and z are three integers, are they consecutive integers?  [#permalink]

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10 Dec 2017, 06:19
6urra wrote:
Hi,

Can someone clarify why the sequence can't be 0,1 and 2? Does 0*3=0 count as a multiple of 3?

ZERO:

1. 0 is an integer.

2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

For more check below:
ALL YOU NEED FOR QUANT ! ! !

Hope it helps.
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Re: If x, y, and z are three integers, are they consecutive integers?  [#permalink]

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14 Dec 2017, 09:01
Bunuel wrote:
If x, y, and z are three integers, are they consecutive integers?

(1) z = x + 2
(2) None of the three integers are multiples of 3.

Statement 1 Since relation of y wrt x or z not clear. Therefore NOT SUFFICIENT

Statement 2 Case 1-> 0,1,2 None of the 3 integers divisible by 3 but are CONSECUTIVE
Case 2-> 1,3,7 None of the 3 integers divisible by 3 & are NOT CONSECUTIVE
Since no unique answer, therefore Statement 2 NOT SUFFICIENT

BOTH 1 & 2 -> does not give a UNIQUE ANSWER, since y relation wrt to x or z not clear it could be (0,1,2) or (1,3,7) or any 3 integers( none multiple of 3 and z=x+2)

Therefore IMHO option "E"
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Re: If x, y, and z are three integers, are they consecutive integers?  [#permalink]

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14 Dec 2017, 09:19
dineshril wrote:
Bunuel wrote:
If x, y, and z are three integers, are they consecutive integers?

(1) z = x + 2
(2) None of the three integers are multiples of 3.

Statement 1 Since relation of y wrt x or z not clear. Therefore NOT SUFFICIENT

Statement 2 Case 1-> 0,1,2 None of the 3 integers divisible by 3 but are CONSECUTIVE
Case 2-> 1,3,7 None of the 3 integers divisible by 3 & are NOT CONSECUTIVE
Since no unique answer, therefore Statement 2 NOT SUFFICIENT

BOTH 1 & 2 -> does not give a UNIQUE ANSWER, since y relation wrt to x or z not clear it could be (0,1,2) or (1,3,7) or any 3 integers( none multiple of 3 and z=x+2)

Therefore IMHO option "E"

Hi dineshril

the highlighted portion is not correct. 0 is divisible by every number 0/3=0.
Bunuel has explained the properties of 0 in the earlier post. You may check it for reference.
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Re: If x, y, and z are three integers, are they consecutive integers?  [#permalink]

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14 Dec 2017, 11:26
niks18 wrote:
dineshril wrote:
Bunuel wrote:
If x, y, and z are three integers, are they consecutive integers?

(1) z = x + 2
(2) None of the three integers are multiples of 3.

Statement 1 Since relation of y wrt x or z not clear. Therefore NOT SUFFICIENT

Statement 2 Case 1-> 0,1,2 None of the 3 integers divisible by 3 but are CONSECUTIVE
Case 2-> 1,3,7 None of the 3 integers divisible by 3 & are NOT CONSECUTIVE
Since no unique answer, therefore Statement 2 NOT SUFFICIENT

BOTH 1 & 2 -> does not give a UNIQUE ANSWER, since y relation wrt to x or z not clear it could be (0,1,2) or (1,3,7) or any 3 integers( none multiple of 3 and z=x+2)

Therefore IMHO option "E"

Hi dineshril

the highlighted portion is not correct. 0 is divisible by every number 0/3=0.
Bunuel has explained the properties of 0 in the earlier post. You may check it for reference.

Hi Niks
Thanks for the correction. Agree with BUNUEL

I then go with your analysis. Option "B" should be the right choice-since in any 3 consecutive Integers (1) One of the integer MUST be divisible by 3 and (2) SUM of 3 consecutive integers WILL ALWAYS be divisible by 3. So UNIQUE solution - all 3 integers are not consecutive.
Re: If x, y, and z are three integers, are they consecutive integers?   [#permalink] 14 Dec 2017, 11:26
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