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QUANTITY A The ratio of male to female professors at 6. University X
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30 Jan 2024, 01:50
30 Jan 2024, 01:50
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At University X, 30% of the professors are tenured. More than half of the tenured professors are men.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The ratio of male to female professors at University X |
1 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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QUANTITY A The ratio of male to female professors at 6. University X
[#permalink]
30 Jan 2024, 14:02
30 Jan 2024, 14:02
1
Using 100 as the total number of professors, you can set up a double matrix with the given info.
The total number of tenured professors is 30. Half of that is 15, so the number of male AND tenured professors must be more than 15, while the number of female AND tenured professors must be less than 15.
7.png [ 14.88 KiB | Viewed 533 times ]
However, we aren't given any info about the gender ratios within the non-tenured group. Thus, we can't determine the ratios of male to female of all the tenured AND non-tenured professors.
8.png [ 17.14 KiB | Viewed 519 times ]
For example, if there are 20 male AND tenured professors, there are 10 female AND tenured professors. This works, since 20 is more than half of 30.
Say of the 70 non-tenured professors, 40 are male and 30 are female. This means there are 20+40=60 male and 10+30=40 female professors total. This makes Quantity A = 3/2, which is greater than B.
10.png [ 17.32 KiB | Viewed 515 times ]
However, let's say of the 70 non-tenured professors, 20 are male and 50 are female. This means there are 20+20=40 male and 10+50=60 female professors total. This makes Quantity A = 2/3, which is less than B.
The total number of tenured professors is 30. Half of that is 15, so the number of male AND tenured professors must be more than 15, while the number of female AND tenured professors must be less than 15.
Attachment:
7.png [ 14.88 KiB | Viewed 533 times ]
However, we aren't given any info about the gender ratios within the non-tenured group. Thus, we can't determine the ratios of male to female of all the tenured AND non-tenured professors.
Attachment:
8.png [ 17.14 KiB | Viewed 519 times ]
For example, if there are 20 male AND tenured professors, there are 10 female AND tenured professors. This works, since 20 is more than half of 30.
Say of the 70 non-tenured professors, 40 are male and 30 are female. This means there are 20+40=60 male and 10+30=40 female professors total. This makes Quantity A = 3/2, which is greater than B.
Attachment:
10.png [ 17.32 KiB | Viewed 515 times ]
However, let's say of the 70 non-tenured professors, 20 are male and 50 are female. This means there are 20+20=40 male and 10+50=60 female professors total. This makes Quantity A = 2/3, which is less than B.
gmatclubot
QUANTITY A The ratio of male to female professors at 6. University X [#permalink]
30 Jan 2024, 14:02
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