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

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In a certain calculus class, the ratio of the number of math majors to  [#permalink]

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New post Updated on: 03 Apr 2015, 04:21
1
4
00:00
A
B
C
D
E

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Question Stats:

82% (01:25) correct 18% (01:43) wrong based on 217 sessions

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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

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shubhangi


Originally posted by shubhangi on 21 Nov 2003, 14:10.
Last edited by Bunuel on 03 Apr 2015, 04:21, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: In a certain calculus class, the ratio of the number of math majors to  [#permalink]

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New post 21 Nov 2003, 15:40
4
1
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.
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Re: In a certain calculus class, the ratio of the number of math majors to  [#permalink]

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New post 21 Nov 2003, 14:41
1
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.
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Re: In a certain calculus class, the ratio of the number of math majors to  [#permalink]

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New post 03 Apr 2015, 11:14
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.

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Re: In a certain calculus class, the ratio of the number of math majors to  [#permalink]

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New post 28 Dec 2015, 02:03
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
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Re: In a certain calculus class, the ratio of the number of math majors to  [#permalink]

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New post 22 Jul 2018, 07:05
Makky07 wrote:
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.


but 2 more maths major were added so why it cant be 2(4)+2 + 5(4)= 30
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Re: In a certain calculus class, the ratio of the number of math majors to  [#permalink]

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New post 22 Jul 2018, 11:11
ketkichaudhary1992 wrote:
Makky07 wrote:
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.


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


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.

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Rich
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Re: In a certain calculus class, the ratio of the number of math majors to &nbs [#permalink] 22 Jul 2018, 11:11
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