then how many negative values can z take ?a)Noneb)Onec)Twod)Threee)A finite number greater than threeCorrect answer is option 'B'. Can you explain this answer?

GMAT Exam > GMAT Questions > then how many negative values can z take ?a)N...

then how many negative values can z take ?

a)
None
b)
One
c)
Two
d)
Three
e)
A finite number greater than three

Correct answer is option 'B'. Can you explain this answer?

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then how many negative values can z take ?a)Noneb)Onec)Twod)Threee)A f...

To Find: Number of negative values of z

Approach:

Solve the given equation
- Note that the denominator is z - 1.
- To remove the denominator, we will need to multiply each term of this equation with z - 1.
- This will be time consuming (because we will have to multiply each term with z as well as with -1. Example: and is likely to result in a tedious calculation.
- To simplify this process, we will substitute (z - 1) as x
Find the value of z
Count the number of negative values of z

Substitute z - 1 = x

Therefore z = x + 1 ; z - 2 = x -1

Hence

This is a cubic equation (involves x³) and you may feel that you do not know how to solve a cubic equation.

However, before giving up, think about how you solve a quadratic equation? By rewriting the given equation into its factors.

Let’s try if the cubic equation above can be similarly written into factors. We’ll find that the middle term, -21x, can be broken down as under:

That is

z - 1 = 1 or 4 or -5
z = 2 or 5 or -4
Thus, we get three values of z. However, the question asks specifically about the number of negative values of z.
Among the 3 possible values of z, we see that only one value of z is negative.

Correct Answer: Option B

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