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Ratio

by tapanmittal » Fri Jun 19, 2015 4:21 am
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.
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by talaangoshtari » Fri Jun 19, 2015 4:50 am
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
Last edited by talaangoshtari on Fri Jun 19, 2015 5:20 am, edited 2 times in total.
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by Uva@90 » Fri Jun 19, 2015 4:54 am
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.
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by talaangoshtari » Fri Jun 19, 2015 4:59 am
p:b = 3:5 => p = (3/5)b
and
(p-2 / b+2) = 1/2
Therefore,
b = 30
p = 18
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by GMATGuruNY » Fri Jun 19, 2015 5:49 am
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.
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by Brent@GMATPrepNow » Fri Jun 19, 2015 8:13 am
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 new ratio (of physics majors to non-physics majors) would be 1 to 2. How many physics majors are in the class?

(A) 16
(B) 18
(C) 24
(D) 30
(E) 32
The ratio of the number of physics majors to non-physics majors is 3 to 5
Let P = number of Physics majors
Let N = number of Non-physics majors
So, we get: P/N = 3/5
Cross multiply to get: 5P = 3N
Rearrange to get: 5P - 3N = 0

If two of the physics majors were to change their major to biology, the new ratio of physics majors to non-physics majors would be 1 to 2
This means that P - 2 = the NEW number of Physics majors
And N + 2 = the NEW number of Non-physics majors
So, we get: (P - 2)/(N + 2) = 1/2
Cross multiply to get: 2(P - 2) = 1(N + 2)
Expand: 2P - 4 = N + 2
Rearrange to get: 2P - N = 6

We now have two equations:
5P - 3N = 0
2P - N = 6

Multiply BOTTOM equation by 3 to get:
5P - 3N = 0
6P - 3N = 18

Subtract top equation from bottom to get: P = 18
Answer: B

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by Matt@VeritasPrep » Tue Jun 23, 2015 6:18 pm
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.
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by jawwadali » Thu Oct 27, 2016 11:33 am
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.
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by [email protected] » Thu Oct 27, 2016 11:39 am
Hi jawwadali,

The first sentence describes the CURRENT ratio of the class. The second sentence describes a 'hypothetical' (IF two of the physics majors were to change...), so that change has not happened (and might not happen at all). As such, when the question asks how many physics majors ARE in the class, it has to be referring to the current number of physics majors.

If the author of this question made the second sentence into an actual fact (re: "Two of the physics majors changed their major to biology and then the ratio became 1 to 2"), then the question - "how many physics majors are left in the class?" would make sense.

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by Matt@VeritasPrep » Thu Oct 27, 2016 11:10 pm
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.
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by nasahtahir » Fri Nov 25, 2016 5:07 am
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?
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by Matt@VeritasPrep » Fri Nov 25, 2016 2:33 pm
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.
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by Vikasx » Wed Feb 01, 2017 3:55 am
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
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by DavidG@VeritasPrep » Wed Feb 01, 2017 4:26 am
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.
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by GMATGuruNY » Wed Feb 01, 2017 4:33 am
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.
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