The expression above is defined for which of the following values of x

Question

\frac{1}{3 - \frac{6}{x - 4}} The expression above is defined for which of the following values of x? I. x = 4 II. x = 6 III. x = 8 A. I only B. II only C. III only D. II and III only E. I, II, and III 2024-01-27_15-54-59.png

Bunuel · Answer

For the given expression to be defined, the denominators must not be zero.

Therefore, x - 4 should not equal 0, implying that x cannot be 4.

Similarly, 3 - 6/(x - 4) must not equal 0, meaning 6/(x - 4) should not equal 3. From this, it follows that (x - 4) must not equal 2, and therefore, x cannot be 6.

Answer: C.

gmatophobia · Answer

The denominator should not be equal to zero, therefore  x 
eq 4

\frac{1}{3 - \frac{6}{x - 4}}

\frac{1}{\frac{3(x-4) - 6}{x-4}}

\frac{x-4}{3(x-4) - 6}

\frac{x-4}{3x-18}

3x-18 
eq 0

x 
eq \frac{18}{3}

x 
eq 6

Therefore, x cannot be 4 or 6. It can be any other value such as 8.

Option C

AK1501 · Answer

Bunuel   gmatophobia  - if we solve and make this (x-4)/ (3(x-4)-6) in this case taking 4 will only make the numerator zero which is acceptable for a defined fraction right?

Bunuel · Answer

You should consider the initial, unsimplified fraction. For example, if we had 1/(1/x), then x clearly cannot be 0. However, if you simplify it to just x, you might incorrectly conclude that x can take any value, which is not correct.

adarshravindra · Answer

I have a question here, wrt the above quant, i strongly feel the answer can be 4 too along 8, because in the original equationif i append 4 the value is 1/indefinite which is still zero and valid right? WHat am i missing here, is it wrong to assume that 1/indefinite is zero?

Bunuel · Answer

Division by 0 is not allowed, so any number divided by 0 is undefined, not equal to 0. Furthermore, anything divided by an undefined expression is also undefined, not equal to 0.

divyasaxena2825 · Answer

Hi Bunuel,

Could you please solve this by using options?

bumpbot · Answer

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The expression above is defined for which of the following values of x

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The expression above is defined for which of the following values of x

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