Problem Solving

In a certain physics class, the ratio of the number of physics
majors to non-physics majors is 3 to 5. If two of the physics
majors were to change their major to biology, the ratio would
be 1 to 2. How many physics majors are in the class?
(A) 16
(B) 18
(C) 24
(D) 30
(E) 32

I am getting 12 as answer.
Please help incase I have misunderstood the problem.

The ratio of physics:biology is 3:5. So, suppose we have 3 physics majors and 5 biology majors. Then if two of the physics majors were to change their major to biology, the ratio will be 1:7. So, the ratio of p to total is 1:8. So, the total number should be divisible by 8.
On the other hand the ratio of p:b should be 1:2, or p:T should be equal to 1:3, therefore the total number should be divisible by 3.
So the total number should be divisible by 24. We have:
3/8 = p/24 => p = 9. Therefore the correct answer is the answer choice that is divisible by 9. So the correct answer is B

tapanmittal wrote:In a certain physics class, the ratio of the number of physics
majors to non-physics majors is 3 to 5. If two of the physics
majors were to change their major to biology, the ratio would
be 1 to 2. How many physics majors are in the class?
(A) 16
(B) 18
(C) 24
(D) 30
(E) 32

I am getting 12 as answer.
Please help incase I have misunderstood the problem.

OA is B ?
Please post question along with OA.

p:b = 3:5 => p = (3/5)b
and
(p-2 / b+2) = 1/2
Therefore,
b = 30
p = 18

tapanmittal wrote:In a certain physics class, the ratio of the number of physics
majors to non-physics majors is 3 to 5. If two of the physics
majors were to change their major to biology, the ratio would
be 1 to 2. How many physics majors are in the class?
(A) 16
(B) 18
(C) 24
(D) 30
(E) 32

Let p = the number of physics majors and n = the number of non-physics majors.

We can PLUG IN THE ANSWERS, which represent the value of p.
Since p:n = 3:5, the value of p must be a MULTIPLE OF 3.
Eliminate A and E.
The correct answer choice must satisfy the following constraint:
After two students switch from physics to biology, (new p)/(new n) = 1/2.

Answer choice D: p=30
Since p:n = 3:5, p=30 and n=50.
After two students switch from physics to biology, (new p)/(new n) = (30-2)/(50+2) = 28/52 = 7/13.
Since 7/13 > 1/2, eliminate D.

Answer choice B: p=18
Since p:n = 3:5 = 18:30, p=18 and n=30.
After two students switch from physics to biology, (new p)/(new n) = (18-2)/(30+2) = 16/32 = 1/2.
Success!

The correct answer is B.

Two nice approaches:

First approach

p/n = 3/5

(p - 2)/(n + 2) = 1/2

then crossmultiply and solve for p.

Second approach

Suppose the number of physics majors = p. We know that (p - 2) is half of (5/3)p + 2, so we simply solve

(p - 2) = (1/2)*((5/3)p + 2)

and find p = 18.

I think the question is not rightly worded. It should have been "How many physics majors are in the class now?" or "How many physics majors were in the class before?"

Does anyone agree with me on this ?

tapanmittal wrote:In a certain physics class, the ratio of the number of physics
majors to non-physics majors is 3 to 5. If two of the physics
majors were to change their major to biology, the ratio would
be 1 to 2. How many physics majors are in the class?
(A) 16
(B) 18
(C) 24
(D) 30
(E) 32

I am getting 12 as answer.
Please help incase I have misunderstood the problem.

jawwadali wrote:I think the question is not rightly worded. It should have been "How many physics majors are in the class now?" or "How many physics majors were in the class before?"

Does anyone agree with me on this ?

I wish I could, but the question is fine as is. Since it used the word "if" to describe what would happen IF some students were added, there was no actual change in reality. So we don't need to distinguish between now and before, because no students ever actually joined (or left) the class.

Just a general question. In this question are they not asking the amount of students who are now MAJORING in PHYSICS so should it not be 18 -'2' as two people left?

nasahtahir wrote:Just a general question. In this question are they not asking the amount of students who are now MAJORING in PHYSICS so should it not be 18 -'2' as two people left?

No, because the questions asks what were to happen IF two physics majors were to defect to biology. Those two people haven't ACTUALLY switched their majors yet, so we don't need to subtract them.

Hi All,
We get 16 when we use only a single variable, calculation is as below:
(3x-2) / (5x + 2) = 1/2

This solves to x = 6

Now, 3x-2 = 16.

Could you kindly point if there is some mistake.

Thanks

Vikasx wrote:Hi All,
We get 16 when we use only a single variable, calculation is as below:
(3x-2) / (5x + 2) = 1/2

This solves to x = 6

Now, 3x-2 = 16.

Could you kindly point if there is some mistake.

Thanks

The algebra is correct. If 2 physics majors had switched to biology, the number of physics majors would have been 16. But since the switch appears to be a hypothetical that hasn't actually happened, there'd be 3x, or 18 Physics majors now.

Vikasx wrote:Hi All,
We get 16 when we use only a single variable, calculation is as below:
(3x-2) / (5x + 2) = 1/2

This solves to x = 6

Now, 3x-2 = 16.

Could you kindly point if there is some mistake.

Thanks

The expression in red represents the number of REMAINING physics majors if two were to change their major to biology.
The question stem asks for the ACTUAL number of physics major NOW.
The actual number of physics majors = 3x = 3*6 = 18.