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

I hope they will be more properly written in the real test! Thanks!

WHY?

Edited the first quantity in the original post.

Thank you, Guys.

Regards

the second one is also misleading since there is no addition mark b/t the middle

Done.

Thank you so much.
Regards

I think answer is D ,because B is smaller than A.if we put the value of x=0

In both the case, B is greater than A. So the answer is B.

I think it should be D. Try when x = 0. A > B because 0 is an integer

Sir,

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

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

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

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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