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If X, Y and Z are nonzero numbers, is X^2−Y^3−2Z odd?
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03 Feb 2019, 10:52
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If X, Y and Z are nonzero 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 nonzero numbers, is X^2−Y^3−2Z odd?
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03 Feb 2019, 11:14
Manat wrote: If X, Y and Z are nonzero 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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Re: If X, Y and Z are nonzero 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 nonzero 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 nonzero numbers, so they can be fractions or integers... (1) X and Y are odd. \(x^2Y^3\) 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 C
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Re: If X, Y and Z are nonzero numbers, is X^2−Y^3−2Z odd?
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04 Feb 2019, 01:16
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 nonzero numbers, is X^2−Y^3−2Z odd?
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Updated on: 05 Feb 2019, 04:04
Manat wrote: If X, Y and Z are nonzero 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
Originally posted by Archit3110 on 05 Feb 2019, 03:39.
Last edited by Archit3110 on 05 Feb 2019, 04:04, edited 1 time in total.



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If X, Y and Z are nonzero 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 nonzero 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(nonzero 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 35  0.8 Even  Even Even Let me know what you think about this
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Re: If X, Y and Z are nonzero 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 nonzero 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(nonzero 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 35  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 nonzero 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 nonzero 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(nonzero 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 35  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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Re: If X, Y and Z are nonzero numbers, is X^2−Y^3−2Z odd?
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05 Feb 2019, 21:18
KanishkM wrote: Archit3110 wrote: Manat wrote: If X, Y and Z are nonzero 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(nonzero 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 35  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 nonzero numbers, is X^2−Y^3−2Z odd?
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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(nonzero 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 35  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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If X, Y and Z are nonzero numbers, is X^2−Y^3−2Z odd?
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01 Mar 2019, 07:31
chetan2u VeritasKarishmafrom 1&2 x & y are odd and z is even 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



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Re: If X, Y and Z are nonzero numbers, is X^2−Y^3−2Z odd?
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01 Mar 2019, 19:30
Debashis Roy wrote: chetan2u VeritasKarishmafrom 1&2 x & y are odd and z is even 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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Re: If X, Y and Z are nonzero numbers, is X^2−Y^3−2Z odd?
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01 Mar 2019, 19:30






