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17 Feb 2024, 23:04
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C
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61% (02:17) correct
39%
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All of the m men and w women who were members of club G last year are still members this year. From last year to this year, was the percent increase in the membership of men in club G greater than the percent increase in the membership of women in Club G?
(1) This year (m/2 + x) men and (w/2 + x) women became new members of club G, and x > 0
(2) More women than men became new members of club G this year
(1) This year (m/2 + x) men and (w/2 + x) women became new members of club G, and x > 0
(2) More women than men became new members of club G this year
Can someone exaplain why the answer is not E? Isn't it true that we know the number of new members is higher for women, and then we also know that the number of old members had more women than men. but the growth could be larger for either men or women depending on what the ratios are?
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18 Feb 2024, 02:49
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All of the m men and w women who were members of club G last year are still members this year. From last year to this year, was the percent increase in the membership of men in club G greater than the percent increase in the membership of women in Club G?
(1) This year (m/2 + x) men and (w/2 + x) women became new members of club G, and x > 0
This implies that men gained more than half, by x members, of their initial number, and women also gained more than half, also by x members, of their initial number. If the initial numbers of men and women were 10 and 20, and 6 (10/2 + 1) and 11 (20/2 + 1) men and women became new members, then the number of men increased by 60%, while the number of women increased by less than 60%. However, if we reverse men and women's numbers, then we'd get the opposite answer. Hence, this statement alone is not sufficient.
(2) More women than men became new members of club G this year
This statement alone is also insufficient. For example, if the initial numbers of men and women were 1 and 10, and 1 and 2 men and women became new members, then the number of men increased by 100%, while the number of women increased by 20%. However, if the initial numbers of men and women were 100 and 10, and 1 and 2 men and women became new members, then the number of men increased by 1%, while the number of women increased by 20%.
(1)+(2) Since more women than men became new members according to (2), we have (m/2 + x) < (w/2 + x), which gives m < w. Since initially there were fewer men than women, x would constitute a greater percentage of m than of w. Therefore, half plus x for men would constitute a greater percentage than half plus x for women. Thus, the percent increase in the membership of men was greater than the percent increase in the membership of women. Hence, the combined statements are sufficient.
Answer: C.
P.S. Is this a GMAT Prep Focus question? Could you please post a screenshot of it? Thank you!
(1) This year (m/2 + x) men and (w/2 + x) women became new members of club G, and x > 0
This implies that men gained more than half, by x members, of their initial number, and women also gained more than half, also by x members, of their initial number. If the initial numbers of men and women were 10 and 20, and 6 (10/2 + 1) and 11 (20/2 + 1) men and women became new members, then the number of men increased by 60%, while the number of women increased by less than 60%. However, if we reverse men and women's numbers, then we'd get the opposite answer. Hence, this statement alone is not sufficient.
(2) More women than men became new members of club G this year
This statement alone is also insufficient. For example, if the initial numbers of men and women were 1 and 10, and 1 and 2 men and women became new members, then the number of men increased by 100%, while the number of women increased by 20%. However, if the initial numbers of men and women were 100 and 10, and 1 and 2 men and women became new members, then the number of men increased by 1%, while the number of women increased by 20%.
(1)+(2) Since more women than men became new members according to (2), we have (m/2 + x) < (w/2 + x), which gives m < w. Since initially there were fewer men than women, x would constitute a greater percentage of m than of w. Therefore, half plus x for men would constitute a greater percentage than half plus x for women. Thus, the percent increase in the membership of men was greater than the percent increase in the membership of women. Hence, the combined statements are sufficient.
Answer: C.
P.S. Is this a GMAT Prep Focus question? Could you please post a screenshot of it? Thank you!
General Discussion
17 Feb 2024, 23:26
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Let's analyze each statement separately:
Statement 1: This year (m/2 + x) men and (w/2 + x) women became new members of club G, and x > 0.
This statement tells us that the number of new male members is (m/2 + x) and the number of new female members is (w/2 + x), where x is some positive value. However, without knowing the values of m and w, we cannot determine if the percent increase in the membership of men is greater than the percent increase in the membership of women. This statement alone is not sufficient.
Statement 2: More women than men became new members of club G this year.
This statement tells us that the number of new female members is greater than the number of new male members, but it does not give us enough information to determine if the percent increase in the membership of men is greater than the percent increase in the membership of women. Without knowing the original number of male and female members, we cannot determine if the increase in membership for each group is significant enough to meet the condition in the question stem. Statement 2 alone is not sufficient.
Together:
From Statement 1, we have the number of new male members as (m/2 + x) and the number of new female members as (w/2 + x), where x is some positive value. From Statement 2, we know that more women than men became new members this year, meaning that (w/2 + x) > (m/2 + x).
We can simplify this inequality as (w - m)/2 > -x. Since x is positive, this inequality tells us that the difference in the number of new male and female members is less than the difference in the original number of male and female members.
To determine if the percent increase in the membership of men is greater than the percent increase in the membership of women, we need to calculate the percent increase for each group. The percent increase for the men is given by:
(new male members - original male members) / original male members \* 100
= [(m/2 + x) - m] / m \* 100
= (-m/2 + x) / m \* 100
Similarly, the percent increase for the women is given by:
(new female members - original female members) / original female members \* 100
= [(w/2 + x) - w] / w \* 100
= (-w/2 + x) / w \* 100
To compare these percentages, we can divide the above two equations:
[(m/2 + x)/m] / [(w/2 + x)/w]
Simplifying this expression, we get:
(2x + m) / (2x + w)
Since (w - m)/2 > -x, we know that w > m. This means that the denominator of the above expression is greater than the numerator, which implies that the percent increase in the membership of men is less than the percent increase in the membership of women.
Therefore, both statements together are sufficient to determine that the percent increase in the membership of men is less than the percent increase in the membership of women, but neither statement alone is sufficient.
Answer: C) Both together sufficient, but neither alone is sufficient.
Statement 1: This year (m/2 + x) men and (w/2 + x) women became new members of club G, and x > 0.
This statement tells us that the number of new male members is (m/2 + x) and the number of new female members is (w/2 + x), where x is some positive value. However, without knowing the values of m and w, we cannot determine if the percent increase in the membership of men is greater than the percent increase in the membership of women. This statement alone is not sufficient.
Statement 2: More women than men became new members of club G this year.
This statement tells us that the number of new female members is greater than the number of new male members, but it does not give us enough information to determine if the percent increase in the membership of men is greater than the percent increase in the membership of women. Without knowing the original number of male and female members, we cannot determine if the increase in membership for each group is significant enough to meet the condition in the question stem. Statement 2 alone is not sufficient.
Together:
From Statement 1, we have the number of new male members as (m/2 + x) and the number of new female members as (w/2 + x), where x is some positive value. From Statement 2, we know that more women than men became new members this year, meaning that (w/2 + x) > (m/2 + x).
We can simplify this inequality as (w - m)/2 > -x. Since x is positive, this inequality tells us that the difference in the number of new male and female members is less than the difference in the original number of male and female members.
To determine if the percent increase in the membership of men is greater than the percent increase in the membership of women, we need to calculate the percent increase for each group. The percent increase for the men is given by:
(new male members - original male members) / original male members \* 100
= [(m/2 + x) - m] / m \* 100
= (-m/2 + x) / m \* 100
Similarly, the percent increase for the women is given by:
(new female members - original female members) / original female members \* 100
= [(w/2 + x) - w] / w \* 100
= (-w/2 + x) / w \* 100
To compare these percentages, we can divide the above two equations:
[(m/2 + x)/m] / [(w/2 + x)/w]
Simplifying this expression, we get:
(2x + m) / (2x + w)
Since (w - m)/2 > -x, we know that w > m. This means that the denominator of the above expression is greater than the numerator, which implies that the percent increase in the membership of men is less than the percent increase in the membership of women.
Therefore, both statements together are sufficient to determine that the percent increase in the membership of men is less than the percent increase in the membership of women, but neither statement alone is sufficient.
Answer: C) Both together sufficient, but neither alone is sufficient.
(IYKYK)
