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11 Dec 2025, 02:22
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In a group of men and women, what is the average (arithmetic mean) weight of the entire group?
(1) Of everyone in the group, 3/7 are men and have an average weight of 175 pounds.
(2) Of everyone in the group, 4/7 are women and have an average weight of 140 pounds.
(1) Of everyone in the group, 3/7 are men and have an average weight of 175 pounds.
(2) Of everyone in the group, 4/7 are women and have an average weight of 140 pounds.
11 Dec 2025, 02:31
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We can easily solve this question using alligation and to apply that, we need both the equations to solve
Here's how we can solve this
Hence, C
GMAT-Club-Forum-pv1h2jxn.png [ 2.26 KiB | Viewed 633 times ]
Here's how we can solve this
Hence, C
Attachment:
GMAT-Club-Forum-pv1h2jxn.png [ 2.26 KiB | Viewed 633 times ]
msignatius
11 Dec 2025, 02:41
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First, I'd assume the total number of people - men and women - to be 7 for the sake of simplicity.
Clearly, with Statement I, where the average of 3 of the 7 people - men - is given, the entire group's average isn't calculable, as we don't know what weight the women average.
With Statement II taken in isolation, the same problem exists, but for calculating the average weight of the men.
Taken together: The men weigh in total - 3*175 = 525; the women weigh in total 4*140 = 560. Added together - 525 + 560 = 1085. Divided by 7, i.e., the total number of people, gives us the combined average (1085 / 7 = 155).
Clearly, with Statement I, where the average of 3 of the 7 people - men - is given, the entire group's average isn't calculable, as we don't know what weight the women average.
With Statement II taken in isolation, the same problem exists, but for calculating the average weight of the men.
Taken together: The men weigh in total - 3*175 = 525; the women weigh in total 4*140 = 560. Added together - 525 + 560 = 1085. Divided by 7, i.e., the total number of people, gives us the combined average (1085 / 7 = 155).
