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

Question

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%

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

BrushMyQuant · Accepted Answer

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!

PareshGmat · Answer

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

TGC · Answer

Attached is the solution:

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

3X-15=90

X=35

Hence 2X-15 = 55

KarishmaB · Answer

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)

federig · Answer

When the problem states Algebra OR Geometry = 90%, should't we just consider 2G-15 + G-15 = 90?
Wouldn't writing 2G-15 + G-15 + 15 = 90 be equal to saying Algebra OR Geometry OR Both?

bumpbot · Answer

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

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