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# gmatclub test question M18, Q39 : ST

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Senior Manager
Joined: 06 Jul 2007
Posts: 265
gmatclub test question M18, Q39 : ST [#permalink]

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19 Mar 2009, 03:37
If S and T are non-zero numbers and $$\frac{1}{S} + \frac{1}{T} = S + T$$ , which of the following is necessarily true?

A) $$ST = 1$$
B) $$S + T = 1$$
C) $$\frac{1}{S} = T$$
D) $$\frac{S}{T} = 1$$
E) none of the above

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GMAT Tutor
Joined: 24 Jun 2008
Posts: 1346
Re: gmatclub test question M18, Q39 : ST [#permalink]

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19 Mar 2009, 05:26
We can find a common denominator on the left side:

$$\frac{1}{S} + \frac{1}{T} = S + T \\ \frac{T}{ST} + \frac{S}{ST} = S+T \\ \frac{S + T}{ST} = S + T$$

Now, if $$S + T \neq 0$$, we can divide both sides by $$S + T$$ to get:

$$\frac{1}{ST} = 1 \\ ST = 1$$

So if $$S + T \neq 0$$, then $$ST = 1$$ must be true. However, we can't be sure that $$S + T \neq 0$$ is true, as you can see by plugging in, say, S = 2 and T = -2. So the answer is E.

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Re: gmatclub test question M18, Q39 : ST   [#permalink] 19 Mar 2009, 05:26
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# gmatclub test question M18, Q39 : ST

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