# GRE® Math | Ratios Q3

#### GRE Practice Questions | Ratio and Proportion Questionbank

The GRE math sample question given below is a word problem in ratio and proportion. This GRE practice question also tests the basics of GRE Number Systems and GRE Number Properties.

Question 3: A box contains x red balls, thrice as many green balls and, half as many blue balls as there are red balls. If the box contains no other balls, which of the following could be the number of balls in the box?

1. 22
2. 44
3. 54
4. 33
5. 24

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### Explanatory Answer | GRE Practice Question 3

Number of red balls = x
Number of green balls → thrice as many as the number of red balls = 3x
Number of blue balls → half as many as the number of red balls = $$frac{\text{x}}{\text{2}}$ Total number of balls = x + 3x + $\frac{\text{x}}{\text{2}}$ = $\frac{\text{9x}}{\text{2}}$ Total number of balls and number of red balls are both integers. ∴ $\frac{\text{9x}}{\text{2}}$ and x are integers. If $\frac{\text{9x}}{\text{2}}$ is an integer, x has to be an even number. Four out of the five answer options are even. We need additional deduction to arrive at the answer. For any even value of x, $\frac{\text{9x}}{\text{2}}$ will be a multiple of 9. So, the total number of balls has to be a multiple of 9. The only multiple of 9 in the answer options is 54. Number of balls in the box = 54 #### Choice C 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 ## GRE Sample Questions | GRE Ratios, Percents, Fractions Videos On YouTube ##### 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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