GRE® Math | Ratios Q3

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

---

---

Video Explanation

---

---

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