GRE® Quant Q5 | Number Properties

The GRE maths sample Quantitative Comparison question given below is from the topic number properties. It tests the concept of Prime Factorisation of numbers and Irrational Numbers.

Question 5

Quantity A	Quantity B
\\sqrt{\frac{143}{208}}) × \\sqrt{\frac{169}{77}})	\\sqrt{\frac{459}{306}}) × \\sqrt{\frac{224}{675}})

1. Quantity A is greater
2. Quantity B is greater
3. The two quantities are equal
4. Cannot be determined

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Video Explanation

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Explanatory Answer | GRE Quantitative Comparison Question 5

Step 1 of solving this GRE question : Evaluate Quantity A

Quantity A: \\sqrt{\frac{143}{208}}) × \\sqrt{\frac{169}{77}})

Prime Factorizing the numerator and the denominator of each term,
\\sqrt{\frac{143}{208}}) × \\sqrt{\frac{169}{77}}) = \\sqrt{\frac{11 \times 13}{13 \times 2^{4}}}) × \\sqrt{\frac{13 \times 13}{7 \times 11}})
→ \\sqrt{\frac{11 \times 13 \times 13 \times 13}{13 \times 2^{4} \times 7 \times 11}})
→ \\frac{13}{4 \sqrt{7}})

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Step 2 of solving this GRE question : Evaluate Quantity B

Quantity B: \\sqrt{\frac{459}{306}}) × \\sqrt{\frac{224}{675}})

Prime Factorizing the numerator and the denominator of each term,
\\sqrt{\frac{459}{306}}) × \\sqrt{\frac{224}{675}}) = \\sqrt{\frac{17 \times 3^{3}}{2 \times 3^{2} \times 17}}) × \\sqrt{\frac{2^{5} \times 7}{3^{3} \times 5^{2}}})
→ \\sqrt{\frac{3 \times 2^{5} \times 7}{2 \times 3^{3} \times 5^{2}}})
→ \\frac{4 \sqrt{7}}{15})

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Step 4 of solving this GRE question : The Comparison

Quantity A: \\frac{13}{4 \sqrt{7}}) is greater than 1 since numerator is greater than the denominator.

Quantity B: \\frac{4 \sqrt{7}}{15}) is lesser than 1 since numerator is lesser than the denominator.

Quantity A > Quantity B

Choice A is the correct answer