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by roc101 » Sun May 25, 2014 3:31 pm
why is this 3:2 and not 2:3?
At a certain college there are twice as many English majors as history majors and three times as many English majors as mathematics majors. What is the ratio of history majors to the number of mathematics majors?
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by Brent@GMATPrepNow » Sun May 25, 2014 4:16 pm
At a certain college there are twice as many English majors as History majors and three times as many English majors as Math's majors. What is the ratio of the number of history majors to the number of math's majors?
6:1
3:2
2:3
1:5
1:6
Goal: Find the value of H:M

Let's set this up:
There are twice as many English majors as History majors: E:H = 2:1
There are three times as many English majors as Math's majors: E:M = 3:1

Notice that the common "bond" here is E - it will connect the required H and M terms.

In order to use the E to connect the H and M terms, we must make the two E values equal by creating equivalent ratios.

E:H = 2:1
Multiply both terms by 3 to get E:H = 6:3
Important step: If E:H = 6:3, then H:E = 3:6

E:M = 3:1
Multiply both terms by 2 to get E:M = 6:2

Now that the two E terms are equal, we can combine the ratios to get: H:E:M = 3:6:2
This means that H:M = 3:2

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by [email protected] » Sun May 25, 2014 5:33 pm
Hi roc101,

For this question, you can TEST VALUES.

We're told that....

English = 2(History)

English = 3(Math)

We're asked for the ratio of History to Math (based on these answers.....History:Math)

We know that English has to be a multiple of 2 and a multiple of 3, so we need to pick a number that is a multiple of 6.

Let's keep things simple and pick 6. Now we can calculate the other values...

English = 6
History = 3
Math = 2

History: Math = 3:2

Final Answer: B

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by GMATGuruNY » Mon May 26, 2014 1:38 am
roc101 wrote:why is this 3:2 and not 2:3?
At a certain college there are twice as many English majors as history majors and three times as many English majors as mathematics majors. What is the ratio of history majors to the number of mathematics majors?
Since there twice as many English majors as history majors, E/H = 2/1.
Since there are three times as many English majors as math majors, E/M = 3/1.
Ratios can be MULTIPLIED.
H/M = H/E * E/M.
In the equation above, the values in red cancel out.
Thus:
H/M = H/E * E/M = (1/2) * (3/1) = 3/2.
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by theCodeToGMAT » Mon May 26, 2014 2:01 am
E:H = 2:1 = 6:3
E:M = 3:1 = 6:2

To find: H:M

If we normalize the ratios

E:H = 2:1 = 6:3
E:M = 3:1 = 6:2
So, H : M = 3 : 2
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