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gmatclub test question M18, Q39 : ST

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Senior Manager
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gmatclub test question M18, Q39 : ST [#permalink] New post 19 Mar 2009, 02:37
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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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Re: gmatclub test question M18, Q39 : ST [#permalink] New post 19 Mar 2009, 04:26
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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, 04:26
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