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

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Joined: 19 Jan 2010
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A physics class has majors and non-majors in a ratio of 4 to [#permalink]

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Updated on: 22 Jul 2013, 04:53
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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

Originally posted by phoenix9801 on 02 Jun 2012, 18:01.
Last edited by Bunuel on 22 Jul 2013, 04:53, edited 1 time in total.
Edited the OA.
Math Expert
Joined: 02 Sep 2009
Posts: 47077
Re: A physics class has majors and non-majors in a ratio of 4 to [#permalink]

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03 Jun 2012, 02:55
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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, 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.

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.

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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, 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

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

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28 Feb 2018, 11:27
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

We see that the ratio of majors to non-majors = 4x : 10x. When two more majors were to be added to the class, the ratio would then be 2 to 4, and thus:

(4x + 2)/10x = 2/4

4(4x + 2) = 20x

16x + 8 = 20x

8 = 4x

2 = x

So there are 4(2) + 10(2) = 28 people in the class.

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Joined: 12 Oct 2017
Posts: 4
Re: A physics class has majors and non-majors in a ratio of 4 to [#permalink]

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13 Apr 2018, 22:26
Aren’t we supposed to plug the value of x in the new ratio??
Why we are plugging in the original one?
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Joined: 02 Sep 2009
Posts: 47077
Re: A physics class has majors and non-majors in a ratio of 4 to [#permalink]

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14 Apr 2018, 00:48
Animesh2691 wrote:
Aren’t we supposed to plug the value of x in the new ratio??
Why we are plugging in the original one?

We do not have new ratio. Adding two more majors is a hypothetical scenario: 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?

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

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16 Apr 2018, 01:53
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
let the major =4x and n-major = 14x
As per the question,major to be increased by 2 I.e. 4x+2 now ratio 4x+2/10x=2/4
Solving this we get x=2
Now total strength = major +N-Major=14x=14*2=28

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Re: A physics class has majors and non-majors in a ratio of 4 to   [#permalink] 16 Apr 2018, 01:53
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