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# If m is a positive integer and m = x + y + 2z, is m odd ?

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If m is a positive integer and m = x + y + 2z, is m odd ?  [#permalink]

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Updated on: 11 Jul 2015, 08:58
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7
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95% (hard)

Question Stats:

27% (01:30) correct 73% (01:10) wrong based on 126 sessions

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If m is a positive integer and m = x + y + 2z, is m odd ?

(1) x and y are consecutive positive integers.
(2) 4z is even.

Originally posted by abhinav008 on 11 Jul 2015, 08:51.
Last edited by Bunuel on 11 Jul 2015, 08:58, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If m is a positive integer and m = x + y + 2z, is m odd ?  [#permalink]

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11 Jul 2015, 09:07
Answer is E, as from I X and Y are consecutive positive integers lets take X=3 and Y=4 sum makes odd ie 7 and for 2z if we take value of z=1/2 then sum becomes even and if we take value of z=1 then sum becomes odd... so not sufficient.
From II nothing mention about X and Y so not sufficient and we combine even then again same scenario. So no statement is sufficient. Thnks
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If m is a positive integer and m = x + y + 2z, is m odd ?  [#permalink]

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Updated on: 11 Jul 2015, 09:14
1
abhinav008 wrote:
If m is a positive integer and m = x + y + 2z, is m odd ?

(1) x and y are consecutive positive integers.
(2) 4z is even.

Good question.

The trick here is to recognize that there is no mention that x,y,z have to be integers. Even if you dont recognise this initially, statement 1 should tell you that.

Given, m>0 and is an integer.
Qs: Is m = x+y+2z = odd?

Per statement 1, x, y are positive consecutive integers. We do not have any information about z (it can be an integer or maybe not). z can be either 1,2,3,4 etc or 3/4 , 4/5 etc.

Having x,y as consecutive integers means that x+y = odd (always) as 1 out of x or y will be odd and the other will be even.

Thus m= x+y+2z may or maybe not integer (or let alone even or odd). Thus this statement is not sufficient. To test the cases, we can have , m = 1+2+2*1/4= no or m = 1+2+2*3 = yes or m = 1+2+2*4=no

Per statement 2, 4 z is even ----> z = 1/4 or 1/2 or 1 or 2 or 3 etc. We do not know anything about x or y. They can be either integers or fractions. By testing cases, x = 1/4, y =1/5 , z=4 = No but x=1, y =2, 2z = 12 = Yes. Thus this statement is not sufficient

Combining, we still do not have enough information to say uniquely what values can z take. Thus the 2 statements are still not sufficient and hence E is the correct answer.

Originally posted by ENGRTOMBA2018 on 11 Jul 2015, 09:08.
Last edited by ENGRTOMBA2018 on 11 Jul 2015, 09:14, edited 2 times in total.
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Re: If m is a positive integer and m = x + y + 2z, is m odd ?  [#permalink]

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11 Jul 2015, 09:10
abhinav008 wrote:
If m is a positive integer and m = x + y + 2z, is m odd ?

(1) x and y are consecutive positive integers.
(2) 4z is even.

Hi,

the question tells us that m, x and y are integers but none of the statement helps in clearing the air around z..
it can be a fraction or integers and still satisfy the statements so insuff..
E
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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: If m is a positive integer and m = x + y + 2z, is m odd ?  [#permalink]

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12 Jul 2015, 03:01
1
abhinav008 wrote:
If m is a positive integer and m = x + y + 2z, is m odd ?

(1) x and y are consecutive positive integers.
(2) 4z is even.

Ans. E,
1. Not suff. as there is no information about Z, it can be integer (in this case 2z will be even) or Fraction (1/2 in this case 2z will be odd)
hence x+y+2z can be odd or even.
2. Not suff. no confirmed information about z and no information about x&y

1+2 Not suff--> from stmt.2, 4z = 2(2z) is even, so 2z can be odd or even and hence m can be odd or even.
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Re: If m is a positive integer and m = x + y + 2z, is m odd ?  [#permalink]

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26 Nov 2015, 10:58
a really good question
we are told that m!!! is an integer, but what about x, y, and z???

1 - x and y - consecutive integers, well, x+y is odd, thus we need to know whether 2z is odd or even to have a definitive answer to our question.
if z is integer, then m is odd. but if z is non integer, then m might be even. for ex: z=1 and z=1.5. 2 different results.

2. clearly this is insufficient. we do not know the value of x+y. and 4z = even might tell us that 2z=even or 2z=odd. clearly, 1.5*4=6 and is even. but 2*1.5=3 odd.

1+2
x+y - odd
2z might be even if z is integer, and 2z odd if z is not integer.

E.
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Re: If m is a positive integer and m = x + y + 2z, is m odd ?  [#permalink]

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11 Jul 2018, 02:00
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Re: If m is a positive integer and m = x + y + 2z, is m odd ? &nbs [#permalink] 11 Jul 2018, 02:00
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