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

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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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New post 03 Feb 2019, 09:52
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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.
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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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New post 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

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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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New post 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
Nothing about X and Y
insuff

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

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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
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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New post 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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New post 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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New post 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

Let me know what you think about this
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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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New post 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

Let me know what you think about this


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

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New post 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

Let me know what you think about this


EVEN or ODD means they are integer also
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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
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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New post 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

Let me know what you think about this





Is EVEN or ODD mean INTEGER Only?

So 2.2 is not even fraction ?
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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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New post 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

Let me know what you think about this





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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