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

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:

GMAT assassins aren't born, they're made,
Rich

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)

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.

Answer: B

Aren’t we supposed to plug the value of x in the new ratio??
Why we are plugging in the original one?

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
Answer : B


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