# 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 Fri, August 26, 2022 ### 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 August 26, 2022 ##### Where is Wizako located? Wizako - GMAT, GRE, SAT Prep An Ascent Education Initiative 14B/1 Dr Thirumurthy Nagar 1st Street Nungambakkam Chennai 600 034. India Work @ Wizako ##### How to reach Wizako? Mobile:$91) 93800 48484
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