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Re: If X, Y and Z are non-zero numbers, is X^2−Y^3−2Z odd?
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04 Feb 2019, 00:40
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
If X, Y and Z are non-zero numbers, is X^2−Y^3−2Z odd?
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05 Feb 2019, 03:51
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
_________________
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.
Re: If X, Y and Z are non-zero numbers, is X^2−Y^3−2Z odd?
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05 Feb 2019, 04:03
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..
Re: If X, Y and Z are non-zero numbers, is X^2−Y^3−2Z odd?
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05 Feb 2019, 04:26
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
_________________
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, 21:18
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
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, 21:40
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.
_________________
Even x and y can also be fractions along with z... Are we accounting for them as well....For some values the result can turn out to be a negative fraction as well...
if z= 1/4...then 2z=1/2...an even fraction....but for z=1/6..2z=1/3....So 2 different nature of the fraction may be obtained which could give us different(even/odd) value..
Even x and y can also be fractions along with z... Are we accounting for them as well....For some values the result can turn out to be a negative fraction as well...
if z= 1/4...then 2z=1/2...an even fraction....but for z=1/6..2z=1/3....So 2 different nature of the fraction may be obtained which could give us different(even/odd) value..
Thanks in advance
When we say a number or a variable is odd or even, it means they are integers. Only integers can be even and odd, so you cannot take fractions here for x, y and z.
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18% (01:28) correct 
