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Of the students at a certain high school, 90 percent took a

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Of the students at a certain high school, 90 percent took a [#permalink] New post 02 Dec 2012, 05:53
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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%
[Reveal] Spoiler: OA

Last edited by ritumaheshwari02 on 02 Dec 2012, 08:08, edited 1 time in total.
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Re: Of the students at a certain high school [#permalink] New post 02 Dec 2012, 07:16
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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%


Let the total number of students be 100
A OR G = 90
A AND G = 15
A = 2G
(A OR G) = A + G - (A AND G)
90 = 2G + G - 15
=> 3G = 105
=> G = 35
=> A = 2G = 70

A AND NOTG = A - (A AND G) = 70 - 15 = 55
So, Answer will be C
Hope it helps!
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Re: Of the students at a certain high school [#permalink] New post 07 Jun 2013, 01:58
Solved using overlapping sets:
Total No. of students taking algebra = a
Total No. of students taking geometry = g
Students taking both = 15

So from the information above,
Total No. of students taking only algebra = (a-15)
Total No. of students taking only geometry = (g-15)

Total No of students = (a-15) + (g-15) + 15 = 90;
So, a+g = 105
From the condition given, 2g = a, so substituting
a = 70 & Total No. of students taking only algebra = (a-15) = 55 %
Answer = C
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Re: Of the students at a certain high school, 90 percent took a [#permalink] New post 17 Aug 2013, 12:07
Attached is the solution:

2X-15+15+X-15=90

3X-15=90

X=35


Hence 2X-15 = 55
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Re: Of the students at a certain high school, 90 percent took a [#permalink] New post 15 Apr 2015, 18:15
Hello from the GMAT Club BumpBot!

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Re: Of the students at a certain high school, 90 percent took a [#permalink] New post 16 Apr 2015, 00:02
Expert's post
ritumaheshwari02 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%


You can also just use the formula
n(A or B) = n(A) + n(B) - n(A and B)
90 = 2X + X - 15
X = 35
2X = 70

This is the number of people who took algebra including those who took both. To get the number of people who took only algebra, 70 - 15 = 55%
Answer (C)
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Re: Of the students at a certain high school, 90 percent took a   [#permalink] 16 Apr 2015, 00:02
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