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by [email protected] » Tue Apr 08, 2014 9:37 pm
Hi shibsriz,

You'll have to do a bit of algebra to deduce the number of solutions to this equation...

5 - 6/x = x

First, multiply everything by x...

5x - 6 = x^2

Now, move everything "to the right"....

0 = x^2 - 5x + 6

You can now factor this into two terms...

0 = (x -2)(x - 3)

And answer the question...

Final Answer: C

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Last edited by [email protected] on Wed Apr 09, 2014 12:59 pm, edited 1 time in total.
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by Brent@GMATPrepNow » Wed Apr 09, 2014 7:48 am
I just have one small point to make.
Rich's approach is great, but his factorization of x² - 5x + 6 should be (x - 2)(x - 3), rather than (x - 6)(x +1)

So, the two solutions are actually x = 2 and x = 3

Cheers,
Brent
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by [email protected] » Wed Apr 09, 2014 12:58 pm
Hi All,

Brent is absolutely correct - I rushed it and made a silly mistake (I've edited the original post). As it stands, my mistake doesn't actually affect the answer to this question, but it's worth noting that the details DO matter on Test Day.

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by Jeff@TargetTestPrep » Tue Jul 17, 2018 3:44 pm
[email protected] wrote:If 5 - 6/x = x, then x has how many possible values?

(A) None
(B) One
(C) Two
(D) A finite number greater than two
(E) An infinite number
We need to simplify the equation 5 - 6/x = x. We start by multiplying the entire equation by x and we obtain:

5x - 6 = x^2

x^2 - 5x + 6 = 0

(x - 3)(x - 2) = 0

x = 3 or x = 2

We see that x has 2 possible values.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
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