In a certain calculus class, the ratio of the number of math majors to

Question

In a certain calculus class, the ratio of the number of math majors to the number of students who are not math majors is 2 to 5. If 2 more math majors were to enter the class, the ratio would be 1 to 2. How many students are in the class?

A. 10
B. 12
C. 21
D. 28
E. 35

Show Answer

Official Answer

D

A. 10 
B. 12 
C. 21 
D. 28 
E. 35

Makky07 · Accepted Answer

Another easy way:

2x/5x is original ratio

(2x + 2)/5x = 1/2 new ratio
cross multiply
2(2x + 2) = 5x
x = 4

2(4) + 5(4) = 28.

stoolfi · Answer

My way of solving:

The number of students is a multiple of seven. Rule out A and B.

That leaves C, D, and E: 21,28,35, or, 6/15, 8/20, 10/25.

To get 50% (a fraction that reduces to 1/2), you must have an EVEN denominator.

D is the only possible solution.

EMPOWERgmatRichC · Answer

Hi All,

Since the question asks for the total number of students in the class, and the answer choices are numbers, we can TEST THE ANSWERS.

From the prompt, we know that the current ratio of math-majors to non-math-majors is 2:5. This means that the number of math-majors MUST be a multiple of 2 and the number of non-math-majors MUST be an equivalent multiple of 5. By extension, the TOTAL number of students MUST be a multiple of 7. We're then told that adding 2 math majors to the class with change the ratio to 1:2

Since the total number of students MUST be a multiple of 7, we can eliminate Answers A and B.

Let's TEST Answer D.....
IF.....
There are 28 total students.....
math-majors = 8
non-math-majors = 20

Adding 2 more math-majors --> 8+2 = 10
Ratio of math-majors to non-math-majors is now 10:20, which is 1:2
This is a MATCH to what we were told, so this MUST be the answer.

Final Answer:  D

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

ScottWalsh · Answer

I didn't pick up on the fact that the total number of students needs to be a multiple of 7. That's why we practice!

MATH:NON-MATH=2:5
M=2/5N
2/5N+2=1/2N
2=1/2N-2/5N
2=5/10N-4/10N
2=1/10N

N=20
M=2/5*20=8

TOTAL=28

ketkichaudhary1992 · Answer

but 2 more maths major were added so why it cant be 2(4)+2 + 5(4)= 30

EMPOWERgmatRichC · Answer

Hi ketkichaudhary1992,

The question asks for the number of students that are in the class (NOT the number of students that would be in the class IF 2 more math majors were added; that information is a 'hypothetical' that is used to show us how the ratio of students would change). Another reason why we know that 30 is not the answer is because it does not appear among the 5 answer choices. On Test Day, if that type of situation occurs, then you know that something about "your way" of interpreting the prompt was incorrect - so you should go back and double-check your work.

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

ArnauG · Answer

Let's solve the problem step by step. Let's assume the number of math majors in the class is "2x" and the number of students who are not math majors is "5x".

According to the given information, the initial ratio of math majors to non-math majors is 2:5. Therefore, we have:

Math Majors: 2x
Non-Math Majors: 5x

Next, it states that if 2 more math majors were to enter the class, the ratio would be 1:2. This means that the new ratio of math majors to non-math majors would be 1:2. Therefore, we have:

Math Majors: 2x + 2
Non-Math Majors: 5x

Now, we can set up an equation using the ratios:

(2x + 2) / (5x) = 1 / 2

To solve this equation, we can cross-multiply:

2(2x + 2) = 5x

4x + 4 = 5x

4 = 5x - 4x

4 = x

Now, we can substitute the value of x back into the original equations to find the total number of students in the class:

Total Students = Math Majors + Non-Math Majors

Total Students = 2x + 5x

Total Students = 7x

Total Students = 7 * 4

Total Students = 28

Therefore, there are 28 students in the class.

The correct answer is (D) 28.

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