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At a certain college there are twice as many english majors [#permalink]

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22 Oct 2009, 14:11

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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 the number of history majors to the number of mathematics majors?

Does it mean for each one English major, there are 2 history majors and 3 math majors? or is it for every one history major there are 2 english majors and for each math major, there are 3 english ones.

Re: how to read math questions in English? [#permalink]

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26 Oct 2009, 11:04

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This is how I translated the question:

At a certain college there are twice as many english majors as history majors E = 2H and three times as many english majors as mathematics majors. E = 3M What is the ratio of the number of history majors to the number of mathematics majors? What is H:M?

Just set E equal to each other to get the ratio in terms of H and M.

2H = 3M H/M = 3/2

The answer is 3:2

Last edited by GMATBootcamp on 27 Oct 2009, 21:17, edited 2 times in total.

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 the number of history majors to the number of mathematics majors?

Think above is not correct, though the final answer IS correct. But again there is a mistake in calculations, if it were as it's written above answer would be 2/3. So there are two mistakes in the solution, one in ratio translation and the second in calculation.

At a certain college there are twice as many english majors as history majors: E = 2H (as there are MORE english majors)

and three times as many english majors as mathematics majors: E = 3M (as there are MORE english majors)

What is the ratio of the number of history majors to the number of mathematics majors? What is \(\frac{H}{M}\)?

Since this question just describes how 1 variables relates to 2 other variables, we can TEST VALUES to put those relationships in terms of real numbers...

We're told that: 1) There are TWICE as many English majors as History majors. 2) There are THREE TIMES as many English majors as Math majors.

Since, the number of English majors is 2 times a number and 3 times another number, let's choose...

English majors = 6

Using the two given facts, we have....

History majors = 3 Math majors = 2

The question asks for the ratio of the number of History majors to the number of Math majors. Using the numbers above, we have...

Re: At a certain college there are twice as many english majors [#permalink]

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22 Apr 2017, 13:39

Bunuel wrote:

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 the number of history majors to the number of mathematics majors?

Think above is not correct, though the final answer IS correct. But again there is a mistake in calculations, if it were as it's written above answer would be 2/3. So there are two mistakes in the solution, one in ratio translation and the second in calculation.

At a certain college there are twice as many english majors as history majors: E = 2H (as there are MORE english majors)

and three times as many english majors as mathematics majors: E = 3M (as there are MORE english majors)

What is the ratio of the number of history majors to the number of mathematics majors? What is \(\frac{H}{M}\)?

I also marked my answer as 2:3 only to find it wrong. Can you please explain what am I doing wrong if I am directly putting 2H/3M to take out the ratio?
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It's important to remember what the question ASKS for...

You have not shown any of the work that you've done, so I assume that when you get to 2H/3M in your work, you were actually looking at 2H = 3M. In math terms, this means "2 times the number of History majors is equal to 3 times the number of Math majors."

From here, you can either continue to do algebra or you can think in terms of real-world numbers.

Algebraically, you'd have...

2H = 3M 2H/M = 3 H/M = 3/2

So the ratio of H to M is 3:2

In real-world terms, you cannot have a 'fraction' of a person, so let's look for a number that's both a multiple of 2 and a multiple of 3.... 6

Re: At a certain college there are twice as many english majors [#permalink]

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23 Apr 2017, 01:57

EMPOWERgmatRichC wrote:

Hi ashikaverma13,

It's important to remember what the question ASKS for...

You have not shown any of the work that you've done, so I assume that when you get to 2H/3M in your work, you were actually looking at 2H = 3M. In math terms, this means "2 times the number of History majors is equal to 3 times the number of Math majors."

From here, you can either continue to do algebra or you can think in terms of real-world numbers.

Algebraically, you'd have...

2H = 3M 2H/M = 3 H/M = 3/2

So the ratio of H to M is 3:2

In real-world terms, you cannot have a 'fraction' of a person, so let's look for a number that's both a multiple of 2 and a multiple of 3.... 6

2H = 3M 6 = 6

So, if 2H = 6 and 3M = 6, then...

H = 3 and M = 2...

So the ratio of H to M is 3:2

GMAT assassins aren't born, they're made, Rich

Hi,

Yea, I miscalculated at the last step. missed the last step of calculation actually and converted 2H=3M in the ratio of 2:3 and missed the conversion.

Thanks, it is clear to me now.
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