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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

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

by BTGmoderatorLU » Mon Feb 26, 2018 11:46 am

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

The OA is B.

I'm confused by this PS question.

If the initial ratio is 4/10, then (4+2)/10=2/4.

I stuck here. Experts, any suggestion? Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Mon Feb 26, 2018 11:46 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Mon Feb 26, 2018 11:48 am

LUANDATO wrote: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

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

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Mon Feb 26, 2018 2:02 pm

LUANDATO wrote: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

We can PLUG IN THE ANSWERS, which present the total number of people in the class.
Let P = physics majors and N = non-physics majors.
When the correct answer is plugged in, adding 2 physics majors will yield the following ratio:
(New P)/N = 2/4 = 1/2.

B: total = 28
In this case:
Since P:N = 4:10 = 8:20, P=8 and N=20, with the result that the total number of students = 8+20 = 28.
After 2 physics majors are added -- increasing the value of P from 8 to 10 -- we get:
(new P)/N = 10/20 = 1/2.
Success!

The correct answer is B.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Feb 28, 2018 10:34 am

LUANDATO wrote: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

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

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