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

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

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22 Oct 2009, 15:11
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Question Stats:

68% (01:47) correct 32% (00:31) wrong based on 379 sessions

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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?

A. 6 to 1
B. 3 to 2
C. 2 to 3
D. 1 to 5
E. 1 to 6

[Reveal] Spoiler:
Hi,

I have a problem reading such questions.

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.

[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Dec 2013, 01:48, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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26 Oct 2009, 12:04
1
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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

Last edited by GMATBootcamp on 27 Oct 2009, 22:17, edited 2 times in total.
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27 Oct 2009, 17:16
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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?

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 $$\frac{H}{M}$$?

$$H=\frac{E}{2}$$, $$M=\frac{E}{3}$$ --> $$\frac{H}{M}=\frac{3}{2}$$

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27 Oct 2009, 18:19
HAHA you are right. I can't believe I did that. Just goes to show you how two wrongs can make a right?

Kudos to you sir, thanks for pointing out my blunder.
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16 Dec 2013, 19:20
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Re: At a certain college there are twice as many english majors [#permalink]

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15 Feb 2015, 10:56
Hello from the GMAT Club BumpBot!

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

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15 Feb 2015, 14:35
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Hi All,

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...

H:M
3:2

[Reveal] Spoiler:
B

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# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Intern Joined: 28 Jul 2015 Posts: 1 Followers: 0 Kudos [?]: 0 [0], given: 0 Re: At a certain college there are twice as many english majors [#permalink] ### Show Tags 12 Jan 2016, 13:57 I've seen different solutions to this exercise. I wanted to share how I approached it. I looked for the unknown multiplier. This is what I wrote down: E : H : M 2 : 1 : ? 3 : ? : 1 Multiplied line 1 by 3 Multiplied line 2 by 2 The combined ratio is E : H : M 6 : 3 : 2 Therefore, the ratio of H : M is 3 : 2 Hope it helps! GMAT Club Legend Joined: 09 Sep 2013 Posts: 15517 Followers: 651 Kudos [?]: 210 [0], given: 0 Re: At a certain college there are twice as many english majors [#permalink] ### Show Tags 19 Jan 2017, 09:07 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Manager Joined: 19 Aug 2016 Posts: 83 Location: India Schools: ISB '20 (WD) GMAT 1: 610 Q38 V35 GPA: 3.82 Followers: 1 Kudos [?]: 23 [0], given: 25 Re: At a certain college there are twice as many english majors [#permalink] ### Show Tags 22 Apr 2017, 14:39 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 $$\frac{H}{M}$$? $$H=\frac{E}{2}$$, $$M=\frac{E}{3}$$ --> $$\frac{H}{M}=\frac{3}{2}$$ Answer: B. Hi Bunuel, 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? _________________ Consider giving me Kudos if you find my posts useful, challenging and helpful! EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 9127 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 446 Kudos [?]: 2880 [0], given: 169 Re: At a certain college there are twice as many english majors [#permalink] ### Show Tags 22 Apr 2017, 16:29 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 _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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

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23 Apr 2017, 02:57
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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Re: At a certain college there are twice as many english majors   [#permalink] 23 Apr 2017, 02:57
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