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A school has a students and b teachers. If a < 150, b < 25, and classes have a...

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by swerve » Fri May 08, 2020 10:56 am

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A school has a students and b teachers. If a < 150, b < 25, and classes have a maximum of 15 students, can the a students be distributed among the b teachers so that each class has the same number of students? (Assume that any student can be taught by any teacher)

1) It is possible to divide the students evenly into groups of 2, 3, 5, 6, 9, 10, or 15.
2) The greatest common factor of a and b is 10.

OA E
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Source: — Data Sufficiency |
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Re: A school has a students and b teachers. If a < 150, b < 25, and classes have a...

by deloitte247 » Sun May 10, 2020 1:26 am
Given that => a < 150 and b < 25
Classes have a maximum of 15 students

Target question => Can the ''a'' students be distributed among the b teachers so that the class has the same number of students?

Statement 1 => It is possible to divide the students evenly into groups of 2, 3, 5, 6, 9, 10 or 15
Number of students = LCM of 2,3,5,6,9,10 and 15 = 90 Since b < 25
If b = 15, then students can be evenly distributed 90/15 = 6 but if b = 24, then students cannot be distributed evenly.
Since the exact value of b is unknown. Statement 1 is NOT SUFFICIENT

Statement 2 => The greatest common factor of a and b is 10
This doesn't give us the exact value of a and b and there are more than 1 combination of 2 numbers with 10 as their HCF. So, we cannot ascertain if the student can be evenly distributed because of the variation in a and b. Statement 2 is NOT SUFFICIENT

Combining both statements together =>
None of the statements give the exact value of b so we cannot determine if students can be evenly distributed.
Both statements together ARE NOT SUFFICIENT

Answer = E
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