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# A physics class has majors and non-majors in a ratio of 4 to

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A physics class has majors and non-majors in a ratio of 4 to [#permalink]

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02 Jun 2012, 17:01
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A physics class has majors and non-majors in a ratio of 4 to 10. If two more majors were to be added to the class, the ratio would then be 2 to 4. How many people are in the class?

A. 14
B. 28
C. 42
D. 56
E. 70
[Reveal] Spoiler: OA

Last edited by Bunuel on 22 Jul 2013, 03:53, edited 1 time in total.
Edited the OA.
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Re: A physics class has majors and non-majors in a ratio of 4 to [#permalink]

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03 Jun 2012, 01:55
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Expert's post
phoenix9801 wrote:

A physics class has majors and non-majors in a ratio of 4 to 10. If two more majors were to be added to the class, the ratio would then be 2 to 4. How many people are in the class?

A. 14
B. 28
C. 42
D. 56
E. 70

Given: $$\frac{majors}{non-majors}=\frac{4x}{10x}$$, for some positive multiple $$x$$.

Also: $$\frac{4x+2}{10x}=\frac{2}{4}$$ --> $$x=2$$ --> $$total=majors+non-majors=4x+10x=14x=28$$.

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Re: A physics class has majors and non-majors in a ratio of 4 to [#permalink]

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04 Mar 2015, 09:55
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Re: A physics class has majors and non-majors in a ratio of 4 to [#permalink]

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04 Mar 2015, 17:09
Hi All,

While most Test Takers would approach this question with Algebra (which is fine), the numbers involved are relatively "easy", so you can get to the correct answer with a bit of Arithmetic and TESTing THE ANSWERS.

We're told that the starting ratio of majors:non-majors is 4:10, which means that the starting number of majors MUST be a multiple of 4, the starting number of non-majors MUST be a multiple of 10 and the total number of students MUST be a multiple of 14 (for every 14 total people, 4 are majors and 10 are non-majors).

We're told that by adding 2 more majors to the class, the ratio changes to 2:4. We're asked for the TOTAL number of students in the class.

14 total
4 majors
10 non-majors

4+2 = 6 majors
10 non-majors
majors:non-majors is 6:10 = 3:5, which is NOT what we're looking for.

Answer B: 28 total students....notice how this is EXACTLY DOUBLE the number in Answer A.....this should make some of the math go faster....
28 total
8 majors
20 non-majors

8+2 = 10 majors
20 non-majors
majors:non-majors = 10:20 = 2:4, which IS a match for what we were told.

[Reveal] Spoiler:
B

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Re: A physics class has majors and non-majors in a ratio of 4 to   [#permalink] 04 Mar 2015, 21:26
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