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.
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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

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.

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

Final Answer:

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

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?

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
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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.

Page 133:

Question 6

The retailer has ... twice as many radios as clocks....

"twice as many radios as clocks" should be 2r = c but for some reason they state this as 2c = r??

wtf?
I am a native speaker and this doesn't make sense to me?

if I have 4 apples and 2 oranges, then I would say "I have twice as many apples as oranges" or in variable form "2a=o"

You say yourself that if you have 4 apples and 2 oranges, then you have twice as many apples as oranges, (4 apples) = 2*(2 oranges), a = 20, NOT 2a=o.

Similarly, "twice as many radios as clocks" means r = 2*c, there are more radios than clocks (twice as many), so you should multiply the number of clocks by 2 to get the number of radios.

The question you mention in your second post is discussed here: https://gmatclub.com/forum/at-a-certain ... 85632.html

Hope it helps.
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