Question: If \((\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6})=r(\frac{1}{9}+\frac{1}{12}+\frac{1}{15}+\frac{1}{18})\)then r =

1. \(\frac{1}{3}\)
2. \(\frac{4}{3}\)
3. 3
4. 4
5. 12

Answer:
Solution with Explanation:
Approach Solution (1):

To solve this question, we need to recognize that there’s a \((\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6})\) ”hiding” in \((\frac{1}{9}+\frac{1}{12}+\frac{1}{15}+\frac{1}{18})\)

We can reveal this by factoring \(\frac{1}{3}\)out of \((\frac{1}{9}+\frac{1}{12}+\frac{1}{15}+\frac{1}{18})\)

We get: \((\frac{1}{9}+\frac{1}{12}+\frac{1}{15}+\frac{1}{18})\) = \(\frac{1}{3}\)\((\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6})\)

So,

Given: \((\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6})\) = r\((\frac{1}{9}+\frac{1}{12}+\frac{1}{15}+\frac{1}{18})\)

Factor right side to get:\((\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6})\) =(r)\(\frac{1}{3}\)\((\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6})\)

Divide \((\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6})\) from both sides to get: 1 = r*\(\frac{1}{3}\)

Multiply both sides by 3 to get: 3 = r

Correct Option: C

“If \((\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6})=r(\frac{1}{9}+\frac{1}{12}+\frac{1}{15}+\frac{1}{18})\)then r =”- 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.

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