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At a particular grade school, there are two math classes

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At a particular grade school, there are two math classes

by M7MBA » Sat Apr 07, 2018 12:51 am
At a particular grade school, there are two math classes: math class w and math class z. The students in math class w can be broken up evenly into groups of 5 students; the students in math class z can be broken up evenly into groups of x students. What is the greatest common factor of the number of students in classes w and z?

(1) The number of students in math class w shares only one common prime factor with the number of students in math class z.
(2) The number of students in math class z is divisible by 9.

The OA is the option E.

I don't know how can I show that the correct answer is the option E. May anyone helps me?
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Source: — Data Sufficiency |
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by GMATGuruNY » Sat Apr 07, 2018 3:50 am
M7MBA wrote:At a particular grade school, there are two math classes: math class w and math class z. The students in math class w can be broken up evenly into groups of 5 students; the students in math class z can be broken up evenly into groups of x students. What is the greatest common factor of the number of students in classes w and z?

(1) The number of students in math class w shares only one common prime factor with the number of students in math class z.
(2) The number of students in math class z is divisible by 9.
Statements combined:
Case 1: W = 5*5 students and Z = 5*5*9*9 students
Here, 5 is the only prime factor common to W and Z, and Z is a multiple of 9
In this case, the GCF of W and Z is 25.

Case 2: W = 5*5*5 students, Z = 5*5*5*9*9*9 students
Here, 5 is the only prime factor common to W and Z, and Z is a multiple of 9.
In this case, the GCF of W and Z is 125.

Since the GCF can be different values, the two statements combined are INSUFFICIENT.

The correct answer is E.
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