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Re: x is an integer. [#permalink]
4
IlCreatore wrote:
Here we have that quantity A is equal to \((-1)^{2x}+(-1)^{3x}+(-1)^{4x}\), while column B is equal to \((-1)^x+(-1)^{2x}+(-1)^{3x}+(-1)^{4x}\).
Then if we subtract the equal quantities from both sides we have to compare \(1\) and \((-1)^x\). Since we just know that x is an integer, which column is greater should depend on x being even or odd.

So, why the answer is B?


I think you have misinterpret the ques

QTy A is

\((-1)^{x^2}+(-1)^{x^3}+(-1)^{x^4}\)

In this even if x= odd or x= even then QTY B is always greater
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Re: x is an integer. [#permalink]
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pranab01 wrote:
IlCreatore wrote:
Here we have that quantity A is equal to \((-1)^{2x}+(-1)^{3x}+(-1)^{4x}\), while column B is equal to \((-1)^x+(-1)^{2x}+(-1)^{3x}+(-1)^{4x}\).
Then if we subtract the equal quantities from both sides we have to compare \(1\) and \((-1)^x\). Since we just know that x is an integer, which column is greater should depend on x being even or odd.

So, why the answer is B?


I think you have misinterpret the ques

QTy A is

\((-1)^{x^2}+(-1)^{x^3}+(-1)^{x^3}\)

In this even if x= odd or x= even then QTY B is always greater


I hope they will be more properly written in the real test! Thanks!
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Re: x is an integer. [#permalink]
pranab01 wrote:
IlCreatore wrote:
Here we have that quantity A is equal to \((-1)^{2x}+(-1)^{3x}+(-1)^{4x}\), while column B is equal to \((-1)^x+(-1)^{2x}+(-1)^{3x}+(-1)^{4x}\).
Then if we subtract the equal quantities from both sides we have to compare \(1\) and \((-1)^x\). Since we just know that x is an integer, which column is greater should depend on x being even or odd.

So, why the answer is B?


I think you have misinterpret the ques

QTy A is

\((-1)^{x^2}+(-1)^{x^3}+(-1)^{x^4}\)

In this even if x= odd or x= even then QTY B is always greater



WHY?
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Re: x is an integer. [#permalink]
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Expert Reply
Edited the first quantity in the original post.

Thank you, Guys.

Regards
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Re: x is an integer. [#permalink]
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Carcass wrote:
Edited the first quantity in the orifinal post.

Thank you Guys.

Regards


the second one is also misleading since there is no addition mark b/t the middle
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Re: x is an integer. [#permalink]
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Expert Reply
Done.

Thank you so much.
Regards
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Re: x is an integer. [#permalink]
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Carcass wrote:

This question is part of GREPrepClub - The Questions Vault Project




x is an integer.

Quantity A
Quantity B
\((-1)^{x^2}+(-1)^{x^3}+(-1)^{x^4}\)
\((-1)^x + (-1)^{2x} + (-1)^{3x} + (-1)^{4x}\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


I think answer is D ,because B is smaller than A.if we put the value of x=0
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Re: x is an integer. [#permalink]
kiransokande007 wrote:
i think answer is D
if we consider value of x=2 then a will be 3 and will be 4

if we consider x=3 then A will be -3 and B will be 0


In both the case, B is greater than A. So the answer is B.
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Re: x is an integer. [#permalink]
IlCreatore wrote:
Here we have that quantity A is equal to \((-1)^{2x}+(-1)^{3x}+(-1)^{4x}\), while column B is equal to \((-1)^x+(-1)^{2x}+(-1)^{3x}+(-1)^{4x}\).
Then if we subtract the equal quantities from both sides we have to compare \(1\) and \((-1)^x\). Since we just know that x is an integer, which column is greater should depend on x being even or odd.

So, why the answer is B?


I think it should be D. Try when x = 0. A > B because 0 is an integer
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Re: x is an integer. [#permalink]
Sir,

Even then the quantity \(B\) will be greater than \(A\).

\(x^0 = 1\), where \(x\) is any number.

Calculator123 wrote:
I think it should be D. Try when x = 0. A > B because 0 is an integer
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Re: x is an integer. [#permalink]
1
solve both sides with following values,
x=-1,0,1 and solve both sides.
for above values,
Qty A < Qty. B
therefore,
Answer is B
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x is an integer. [#permalink]
5
Carcass wrote:

This question is part of GREPrepClub - The Questions Vault Project




x is an integer.

Quantity A
Quantity B
\((-1)^{x^2}+(-1)^{x^3}+(-1)^{x^4}\)
\((-1)^x + (-1)^{2x} + (-1)^{3x} + (-1)^{4x}\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Key properties: (-1)^(even integer) = 1, and (-1)^(odd integer) = -1.

So, we need only consider two possible cases: x is EVEN, and x is ODD.

Case i: x is ODD
If x is ODD, then x^2 is odd, x^3 is odd, and x^4 is odd.
Also, if x is ODD, then 2x is even, 3x is odd and 4x is even
So, we get:
QUANTITY A: \((-1)^{x^2}+(-1)^{x^3}+(-1)^{x^4}=(-1)+(-1)+(-1)=-3\)
QUANTITY B: \((-1)^x + (-1)^{2x} + (-1)^{3x} + (-1)^{4x}=(-1) + 1 + (-1) + 1 = 0\)
In this case, Quantity B is greater.


Case ii: x is EVEN
If x is even, then x^2 is even, x^3 is even, and x^4 is even.
Also, if x is EVEN, then 2x is even, 3x is even and 4x is even.
So, we get:
QUANTITY A: \((-1)^{x^2}+(-1)^{x^3}+(-1)^{x^4}=1+1+1=3\)
QUANTITY B: \((-1)^x + (-1)^{2x} + (-1)^{3x} + (-1)^{4x}=1 + 1 + 1 + 1 = 4\)
In this case, Quantity B is greater.

In both possible cases, Quantity B is greater.

Answer: B
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Re: x is an integer. [#permalink]
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