GRE® Quant Q5 | Number Properties

Quantitative Comparison | Irrational Numbers | Prime Factorization

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 Get to 170 in GRE Quant Online GRE Courses From INR 2999 Video Explanation GRE Live Online Classes Starts Mon, May 6, 2024 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, $\sqrt{\frac{143}{208}}$ × $\sqrt{\frac{169}{77}}$ = $\sqrt{\frac{11 \times 13}{13 \times 2^{4}}}$ × $\sqrt{\frac{13 \times 13}{7 \times 11}}$ → $\sqrt{\frac{11 \times 13 \times 13 \times 13}{13 \times 2^{4} \times 7 \times 11}}$ → $\frac{13}{4 \sqrt{7}}$ 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, $\sqrt{\frac{459}{306}}$ × $\sqrt{\frac{224}{675}}$ = $\sqrt{\frac{17 \times 3^{3}}{2 \times 3^{2} \times 17}}$ × $\sqrt{\frac{2^{5} \times 7}{3^{3} \times 5^{2}}}$ → $\sqrt{\frac{3 \times 2^{5} \times 7}{2 \times 3^{3} \times 5^{2}}}$ → $\frac{4 \sqrt{7}}{15}$ 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 GRE Online Course - QuantTry it free! Register in 2 easy steps and Start learning in 5 minutes! Already have an Account? GRE Live Online Classes Next Batch May 6, 2024 Work @ Wizako How to reach Wizako? Mobile:$91) 93800 48484
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