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.
Of the students at a certain high school, 90 . . .
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- EconomistGMATTutor
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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.
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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Let x = the percent of students who took geometry; thus, 2x = the percent of students who took algebra. We can create the equation: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.
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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