Of the students at a certain high school, 90 . . .

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Thu Nov 30, 2017 10:10 am

Of the students at a certain high school, 90 percent took a course in algebra or geometry and 15 percent took courses in both. If the percent of students who took a course in algebra was 2 times the percent of students who took a course in geometry, what percent of the students took a course in algebra but not geometry?

A. 35%
B. 50%
C. 55%
D. 60%
E. 70%

The OA is C.

I am not sure about how to solve this PS uqestion. May any expert give me some help? Thanks.

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Source: Beat The GMAT — Problem Solving | Thu Nov 30, 2017 10:10 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members; Thanked: 180 times

by EconomistGMATTutor » Thu Nov 30, 2017 2:15 pm

Hello Vjesus12.

Let's suppose that there are 100 students. So, we have the following equations:

A or G = 90.
A and G = 15.
A= 2G
A without G= ?

Now,

A or G = A + G - (A and G)
90 = 2G + G - 15
105 = 3G
G = 35.
A= 70.

A without G = A - (A and G) = 70 - 15 = 55.

So, the correct answer is 55%, that is to say C.

I really hope this way of explanation may help you to understand it better.

Feel free to ask me again if you have a doubt.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8139; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sun Sep 29, 2019 6:10 pm

VJesus12 wrote:Of the students at a certain high school, 90 percent took a course in algebra or geometry and 15 percent took courses in both. If the percent of students who took a course in algebra was 2 times the percent of students who took a course in geometry, what percent of the students took a course in algebra but not geometry?

A. 35%
B. 50%
C. 55%
D. 60%
E. 70%

The OA is C.

I am not sure about how to solve this PS uqestion. May any expert give me some help? Thanks.

Let x = the percent of students who took geometry; thus, 2x = the percent of students who took algebra. We can create the equation:

x + 2x - 15 = 90

3x = 105

x = 35

So 2(35) = 70 percent of the students took algebra, and 70 - 15 = 55 percent of the students took algebra but not geometry.

Answer: C

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