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

Question

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

Bunuel · Answer

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.

EMPOWERgmatRichC · Answer

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:  B

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

KarishmaB · Answer

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)

ScottTargetTestPrep · Answer

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

Animesh2691 · Answer

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

Bunuel · Answer

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?

arup1590 · Answer

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

Sent from my iPhone using  GMAT Club Forum mobile app

Hoozan · Answer

Similar Question: https://gmatclub.com/forum/in-a-certain ... 48061.html

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