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60% of all students in a class commute by public

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by AAPL » Mon Mar 25, 2019 3:16 am
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e-GMAT

60% of all students in a class commute by public transportation. If 30% of the students aspire to be scientists, which of the following can be the percentage of students who do not commute by public transportation and do not aspire to be scientists?
I. 5%
II. 30%
III. 60%

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III

OA B
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by GMATGuruNY » Mon Mar 25, 2019 3:47 am
AAPL wrote:e-GMAT

60% of all students in a class commute by public transportation. If 30% of the students aspire to be scientists, which of the following can be the percentage of students who do not commute by public transportation and do not aspire to be scientists?
I. 5%
II. 30%
III. 60%

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III
Use a DOUBLE-MATRIX to organize the data.
Let P = public transportation, NP = not public transportation, S = science, NS = not science.

60% of all students in a class commute by public transportation.
30% of the students aspire to be scientists.
The following matrix is yielded:
Image

I: 5% do not commute by public transportation and do not aspire to be scientists
The following matrix is yielded:
Image
Not viable: the red value cannot be greater than the blue value.
Eliminate any answer that includes Statement I (A, D, and E).

II: 30% do not commute by public transportation and do not aspire to be scientists
The following matrix is yielded:
Image
This works.
Eliminate any answer that does not include Statement II (C).

The correct answer is B.

III: 30% do not commute by public transportation and do not aspire to be scientists
Image
Not viable: the red value cannot be greater than the blue value.
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