Question: If S and T are non-zero numbers and \(\frac{1}{S}+\frac{1}{T}=S+T\), which of the following must be true?

1. ST = 1
2. S + T = 1
3. \(\frac{1}{S}=T\)
4. \(\frac{S}{T}=1\)
5. None of the above

“If S and T are non-zero numbers and \(\frac{1}{S}+\frac{1}{T}=S+T\) , which of the following must be true?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:

Approach Solution (1):

\(\frac{1}{S}+\frac{1}{T}=S+T\)

\(\frac{T+S}{ST}=S+T\rightarrow\)

Cross multiply: \(S+T=(S+T)*ST\)

(S+T)(ST-1) = 0

Either S + T = 0 or ST = 1. Now notice that if S+T = 0 is true then none of the options must be true.

Correct option: E

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