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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At a particular grade school, there are two math classes
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Statements combined: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.
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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