GRE® Math Practice | Statistics & Averages #4

The GRE maths sample question given below is a problem solving question in statistics. This sample question is a GRE medium difficulty math question.

Question 4: The average weight of the women in a group is 60 kg and that of the men is 72 kg. If the average weight of the group is 68 kg, what is the ratio of women to men in the group?

1. 1 : 3
2. 2 : 3
3. 3 : 2
4. 1 : 2
5. 2 : 1

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Video Explanation

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Explanatory Answer | GRE Averages Practice Question 4

Given Data

Average weight of women in the group = 60 kg
Average weight of men in the group= 72 kg
Average weight of the entire group = 68 kg

Let the number of men in the group be m.
Let the number of women in the group be w.
Then, the total number of people in the group is (m + w)

Standard Framework to Compute the Ratio:

Number	Average	Total Sum
w	60	60w
m	72	72m
(w + m)	68	68(w + m)

Total weight of the group = Total weight of men in the group + Total weight of women in the group
68(w + m) = 72m + 60W ......(1)

Simplifying equation (1), 68m + 68w = 72m + 60w
68w – 60w = 72m – 68m
8w = 4m
\\frac{w}{m}) = \\frac{4}{8}) → \\frac{w}{m}) = \\frac{1}{2})
Ratio of number of women to men in the group w : m :: 1 : 2

Choice D is the correct answer

Note: Make sure you watch the video explanation to learn how to solve this question using the rule of alligation. Using the rule of alligation, this question can be solved in less than 20 seconds.