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Of the students at a certain high school, 90 percent took a [#permalink]

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02 Dec 2012, 06:53

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A

B

C

D

E

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85% (hard)

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55% (03:08) correct
45% (02:40) wrong based on 165 sessions

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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?

Re: Of the students at a certain high school [#permalink]

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02 Dec 2012, 08:16

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Quote:

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]

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07 Jun 2013, 02:58

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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]

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17 Aug 2013, 13:07

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Attached is the solution:

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

3X-15=90

X=35

Hence 2X-15 = 55

Attachments

gasa.JPG [ 12.42 KiB | Viewed 1781 times ]

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Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________

Re: Of the students at a certain high school, 90 percent took a [#permalink]

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15 Apr 2015, 19:15

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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%

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]

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02 Aug 2016, 08:08

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: Of the students at a certain high school, 90 percent took a [#permalink]

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12 Aug 2016, 05:03

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?

gmatclubot

Re: Of the students at a certain high school, 90 percent took a
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12 Aug 2016, 05:03

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