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# If X, Y and Z are non-zero numbers, is X^2−Y^3−2Z odd?

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Manager
Joined: 11 Jun 2018
Posts: 67
GMAT 1: 500 Q39 V21
If X, Y and Z are non-zero numbers, is X^2−Y^3−2Z odd?  [#permalink]

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03 Feb 2019, 09:52
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Difficulty:

85% (hard)

Question Stats:

10% (01:07) correct 90% (01:18) wrong based on 39 sessions

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If X, Y and Z are non-zero numbers, is X^2−Y^3−2Z odd?

(1) X and Y are odd.

(2) Z is even.
VP
Joined: 09 Mar 2018
Posts: 1003
Location: India
Re: If X, Y and Z are non-zero numbers, is X^2−Y^3−2Z odd?  [#permalink]

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03 Feb 2019, 10:14
1
Manat wrote:
If X, Y and Z are non-zero numbers, is X^2−Y^3−2Z odd?

(1) X and Y are odd.

(2) Z is even.

So

z can be even or fractions as well

1) X and Y are odd.

X^2−Y^3−2Z
Can be even or odd.

2) This doesn't tell anything about x and y

Lets combine both of them

X^2 - Y^3 - 2z

Will always be even - 2 * z

Even - Even

Even

Answers the question as a No

C
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Quote which i can relate to.
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Posts: 7335
Re: If X, Y and Z are non-zero numbers, is X^2−Y^3−2Z odd?  [#permalink]

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03 Feb 2019, 23:40
Manat wrote:
If X, Y and Z are non-zero numbers, is X^2−Y^3−2Z odd?

(1) X and Y are odd.

(2) Z is even.

$$X^2−Y^3−2Z$$

X, y and Z are non-zero numbers, so they can be fractions or integers...

(1) X and Y are odd.
$$x^2-Y^3$$ is surely even. Now it depends on 2Z..
say z is an integer ans is EVEN
say Z is a fraction, $$\frac{1}{2}$$, then ans is ODD
Insuff

(2) Z is even
insuff

Combined..
all are integers, so ans is always EVEN
Sufficient

C
_________________

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
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Re: If X, Y and Z are non-zero numbers, is X^2−Y^3−2Z odd?  [#permalink]

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04 Feb 2019, 00:16
good question.. missed the part that z can also be a fraction and marked A
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If X, Y and Z are non-zero numbers, is X^2−Y^3−2Z odd?  [#permalink]

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Updated on: 05 Feb 2019, 03:04
Manat wrote:
If X, Y and Z are non-zero numbers, is X^2−Y^3−2Z odd?

(1) X and Y are odd.

(2) Z is even.

#1
x& y are odd
X^2−Y^3−2Z ; would always be even ;
X^2−Y^3−2Z; would be odd only if z is even i.e "1/2 "fraction ;
insufficieint

#2
z even ; not sufficient , values of x,y not given

from 1&2
x & y are odd and z is even

so in that case X^2−Y^3−2Z would be odd if z is even fraction 1/2 and even when z is an integer..

IMO C
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Originally posted by Archit3110 on 05 Feb 2019, 02:39.
Last edited by Archit3110 on 05 Feb 2019, 03:04, edited 1 time in total.
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If X, Y and Z are non-zero numbers, is X^2−Y^3−2Z odd?  [#permalink]

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05 Feb 2019, 02:51
Archit3110 wrote:
Manat wrote:
If X, Y and Z are non-zero numbers, is X^2−Y^3−2Z odd?

(1) X and Y are odd.

(2) Z is even.

#1
x& y are odd
X^2−Y^3−2Z ; would always be even ;
X^2−Y^3−2Z; would be odd only if z is even i.e "1/2 "fraction ;
insufficieint

#2
z even ; not sufficient , values of x,y not given

from 1&2
x & y are odd and z is even

so in that case X^2−Y^3−2Z would be odd if z is even fraction 1/2 and even when z is an integer..

in #2 its given z is even ; it can be an integer or fraction as well...
X^2−Y^3−2Z
x & y are odd and z = 2 or even integer ; we would get even value
and
x& y are odd and z = 1/2 , we would get odd value
IMO E

Archit3110 but z = 1/2 is not even, because when you solve it, 0.5, is an odd fraction(non-zero number), this when used in statement A could have answered the question as Yes

That is why when we combine, it says that z is even

We could have taken 0.4 which is 2/5

odd -odd - 4/5
3-5 - 0.8
Even - Even
Even

_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

SVP
Joined: 18 Aug 2017
Posts: 1928
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If X, Y and Z are non-zero numbers, is X^2−Y^3−2Z odd?  [#permalink]

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05 Feb 2019, 03:03
KanishkM wrote:
Archit3110 wrote:
Manat wrote:
If X, Y and Z are non-zero numbers, is X^2−Y^3−2Z odd?

(1) X and Y are odd.

(2) Z is even.

#1
x& y are odd
X^2−Y^3−2Z ; would always be even ;
X^2−Y^3−2Z; would be odd only if z is even i.e "1/2 "fraction ;
insufficieint

#2
z even ; not sufficient , values of x,y not given

from 1&2
x & y are odd and z is even

so in that case X^2−Y^3−2Z would be odd if z is even fraction 1/2 and even when z is an integer..

in #2 its given z is even ; it can be an integer or fraction as well...
X^2−Y^3−2Z
x & y are odd and z = 2 or even integer ; we would get even value
and
x& y are odd and z = 1/2 , we would get odd value
IMO E

Archit3110 but z = 1/2 is not even, because when you solve it, 0.5, is an odd integer(non-zero number), this when used in statement A could have answered the question as Yes

That is why when we combine, it says that z is even

We could have taken 0.4 which is 2/5

odd -odd - 4/5
3-5 - 0.8
Even - Even
Even

KanishkM ; fractions cannot be even or odd ; only whole numbers can be categorised as even or odd..
I understood where i went wrong in my approach ; thanks..
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Joined: 02 Aug 2009
Posts: 7335
Re: If X, Y and Z are non-zero numbers, is X^2−Y^3−2Z odd?  [#permalink]

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05 Feb 2019, 03:26
KanishkM wrote:
Archit3110 wrote:
Manat wrote:
If X, Y and Z are non-zero numbers, is X^2−Y^3−2Z odd?

(1) X and Y are odd.

(2) Z is even.

#1
x& y are odd
X^2−Y^3−2Z ; would always be even ;
X^2−Y^3−2Z; would be odd only if z is even i.e "1/2 "fraction ;
insufficieint

#2
z even ; not sufficient , values of x,y not given

from 1&2
x & y are odd and z is even

so in that case X^2−Y^3−2Z would be odd if z is even fraction 1/2 and even when z is an integer..

in #2 its given z is even ; it can be an integer or fraction as well...
X^2−Y^3−2Z
x & y are odd and z = 2 or even integer ; we would get even value
and
x& y are odd and z = 1/2 , we would get odd value
IMO E

Archit3110 but z = 1/2 is not even, because when you solve it, 0.5, is an odd fraction(non-zero number), this when used in statement A could have answered the question as Yes

That is why when we combine, it says that z is even

We could have taken 0.4 which is 2/5

odd -odd - 4/5
3-5 - 0.8
Even - Even
Even

EVEN or ODD means they are integer also
_________________

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
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Joined: 17 Mar 2014
Posts: 439
Re: If X, Y and Z are non-zero numbers, is X^2−Y^3−2Z odd?  [#permalink]

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05 Feb 2019, 20:18
KanishkM wrote:
Archit3110 wrote:
Manat wrote:
If X, Y and Z are non-zero numbers, is X^2−Y^3−2Z odd?

(1) X and Y are odd.

(2) Z is even.

#1
x& y are odd
X^2−Y^3−2Z ; would always be even ;
X^2−Y^3−2Z; would be odd only if z is even i.e "1/2 "fraction ;
insufficieint

#2
z even ; not sufficient , values of x,y not given

from 1&2
x & y are odd and z is even

so in that case X^2−Y^3−2Z would be odd if z is even fraction 1/2 and even when z is an integer..

in #2 its given z is even ; it can be an integer or fraction as well...
X^2−Y^3−2Z
x & y are odd and z = 2 or even integer ; we would get even value
and
x& y are odd and z = 1/2 , we would get odd value
IMO E

Archit3110 but z = 1/2 is not even, because when you solve it, 0.5, is an odd fraction(non-zero number), this when used in statement A could have answered the question as Yes

That is why when we combine, it says that z is even

We could have taken 0.4 which is 2/5

odd -odd - 4/5
3-5 - 0.8
Even - Even
Even

Is EVEN or ODD mean INTEGER Only?

So 2.2 is not even fraction ?
Math Expert
Joined: 02 Sep 2009
Posts: 53066
Re: If X, Y and Z are non-zero numbers, is X^2−Y^3−2Z odd?  [#permalink]

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05 Feb 2019, 20:40
ammuseeru wrote:
KanishkM wrote:
Archit3110 wrote:

#1
x& y are odd
X^2−Y^3−2Z ; would always be even ;
X^2−Y^3−2Z; would be odd only if z is even i.e "1/2 "fraction ;
insufficieint

#2
z even ; not sufficient , values of x,y not given

from 1&2
x & y are odd and z is even

so in that case X^2−Y^3−2Z would be odd if z is even fraction 1/2 and even when z is an integer..

in #2 its given z is even ; it can be an integer or fraction as well...
X^2−Y^3−2Z
x & y are odd and z = 2 or even integer ; we would get even value
and
x& y are odd and z = 1/2 , we would get odd value
IMO E

Archit3110 but z = 1/2 is not even, because when you solve it, 0.5, is an odd fraction(non-zero number), this when used in statement A could have answered the question as Yes

That is why when we combine, it says that z is even

We could have taken 0.4 which is 2/5

odd -odd - 4/5
3-5 - 0.8
Even - Even
Even

Is EVEN or ODD mean INTEGER Only?

So 2.2 is not even fraction ?

2.2 is NOT even or ODD.

Only integers can be even or odd:

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder.

An odd number is an integer that is not evenly divisible by 2.
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Re: If X, Y and Z are non-zero numbers, is X^2−Y^3−2Z odd?   [#permalink] 05 Feb 2019, 20:40
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