If x, y, z are non-zero numbers and x + xy2 = z3, then which of the following is NOT equal to 1?
  • a)
  • b)
  • c)
  • d)
  • e)
Correct answer is option 'C'. Can you explain this answer?

GMAT Question

By DEEPAK PRAJAPAT · Apr 05, 2020 ·GMAT
Harmanjot Singh answered Apr 07, 2020
Given equation is  
x+xy2 = z3
This can be rewritten as:
x(1+y2) = z …………….. (I)
We need to find the option statement whose value is not equal to 1.
Now let us look at each option.
Option A:
This is same as
 …………….. Expression A
From (I), we know that the numerator and denominator of Expression A are equal.
Therefore the value of Expression A is 1.
Option B:
This can be rewritten as:
We already saw in the previous option that this is equal to 1.
Option C:
This can be rewritten as: 
From I, we can rewrite this as:
 ………….. Expression C
It is given that y is a non-zero number. Therefore, the value of  (1+y2) is always greater than 1.
So, Expression C cannot be equal to 1.
Option D:
This can be rewritten as:
From options A and B, we already know that this expression is equal to 1.
Option E:
We already know that this expression is equal to 1.
Correct Answer: C
 

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