Question: Which of the following is greater than \(\frac{2}{3}\)?

1. \(\frac{33}{50}\)
2. \(\frac{8}{11}\)
3. \(\frac{3}{5}\)
4. \(\frac{13}{27}\)
5. \(\frac{5}{8}\)

Answer:
Approach Solution (1):

1. \(\frac{33}{50}=\frac{99}{150}\)

\(\frac{2}{3}=\frac{2*50}{3*50}=\frac{100}{150}\)​

\(As, \frac{99}{150}<\frac{100}{150},so\frac{33}{50}<\frac{2}{3}\)

2. \(\frac{8}{11}=\frac{24}{33}\)

​\(\frac{2}{3}=\frac{2*11}{3*11}=\frac{22}{33}\)

\(As,\frac{24}{33}>\frac{22}{33},so\frac{8}{11}>\frac{2}{3}\)

3. ​\(\frac{3}{5}=\frac{9}{15}\)

\(\frac{2}{3}=\frac{10}{15}\)​

\(As,\frac{9}{15}<\frac{10}{15},so\frac{3}{5}<\frac{2}{3}\)

4. \(\frac{2}{3}=\frac{2*9}{3*9}=\frac{18}{27}\)

​\(As,\frac{13}{27}<\frac{18}{27},so \frac{13}{27} < \frac{2}{3}\)

5. \(\frac{5}{8}=\frac{5*3}{8*3}=\frac{15}{24}\)

\(As,\frac{15}{24}<\frac{16}{24},so\frac{5}{8}<\frac{2}{3}\)​

Correct Option: B

Approach Solution (2):

\(\frac{2}{3}=0.(66)\approx0.67\)

1. \(\frac{33}{50}=0.66\)Eliminate
2. \(\frac{8}{11}=\frac{72}{99}=0.(72)\)BINGO!
3. \(\frac{3}{5}=0.6\)Eliminate
4. \(\frac{13}{27}\)less than 0.5 Eliminate
5. \(\frac{5}{8}=0.625\)Eliminate

Correct Option: B

“Which of the following is greater than \(\frac{2}{3}\)?”- 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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