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gmatclub test question M18, Q39 : ST

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