At a particular grade school, there are two math classes

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

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: Beat The GMAT — Data Sufficiency | Sat Apr 07, 2018 12:51 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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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