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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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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, 04:53, 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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New post 03 Jun 2012, 02:55
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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]

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

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New post 04 Mar 2015, 18:09
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.

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]

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New post 04 Mar 2015, 22:26
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, 22:26
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