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# Are x, y, and z consecutive integers?

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Manager
Joined: 30 Oct 2012
Posts: 62
Location: India
WE: Marketing (Manufacturing)
Are x, y, and z consecutive integers?  [#permalink]

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25 Jun 2018, 01:38
1
3
00:00

Difficulty:

45% (medium)

Question Stats:

56% (01:25) correct 44% (01:44) wrong based on 46 sessions

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Are x, y, and z consecutive integers?

(1) The remainder when x + y + z is divided by 3 is 2.
(2) The remainder when xyz is divided by 3 is 1.

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Joined: 02 Aug 2009
Posts: 7106
Re: Are x, y, and z consecutive integers?  [#permalink]

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25 Jun 2018, 01:48
3
Are x, y, and z consecutive integers?

We cannot say for sure if x,y&z are integers since nit given in question

(1) The remainder when x + y + z is divided by 3 is 2.
Of course we cannot say these are integers or not, but had these been consecutive integers then x=y-1 and z=y+1...
So x+y+z=y-1+y+y+1=3y.
So should be div by 3
But here it leaves a remainder of 2, so ans is NO..
Sufficient

(2) The remainder when xyz is divided by 3 is 1.
Again if x , y and z are consecutive, one of them will be surely a multiple of atleast 3 so xyz will also be a multiple of 3...
But here it leaves a remainder of 1, so ans is NO
Sufficient

D
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Are x, y, and z consecutive integers? &nbs [#permalink] 25 Jun 2018, 01:48
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