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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] New post 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] New post 03 Jun 2012, 01:55
Expert's post
phoenix9801 wrote:
Any help please. the book did not provide any answer. Thanks

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

Answer: B.
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Re: A physics class has majors and non-majors in a ratio of 4 to [#permalink] New post 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] New post 04 Mar 2015, 17:09
Expert's post
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.

Normally, we would start with Answers B or D first, but here I'm going to start with A to show you the pattern in the answers...

Answer A: 14 total students

14 total
4 majors
10 non-majors

adding 2 majors gives us...
4+2 = 6 majors
10 non-majors
majors:non-majors is 6:10 = 3:5, which is NOT what we're looking for.
Eliminate Answer A

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

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

Final Answer:
[Reveal] Spoiler:
B


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


Another option is to simply use brute force with some logic:

Say number of majors and non-majors are 4 and 10. If you add 2 more majors, you get 6 and 10. This ratio is higher than the required 1:2 so actual number of majors and non majors must be higher (so that the effect of 2 is slightly lower)
Say, if number of majors and non majors are 4*2 and 10*2. If you add 2 more majors, you get 10 and 20. This is the required ratio. So total number = 8+20 = 28

Answer (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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