A certain scholarship committee awarded scholarships in the

Translation is the same for both questions.

Twice as many $2500 scholarships as $4000 means that if the number of $4000 scholarships was x, then the number of $2500 scholarships was 2x.

Three times as many $1250 scholarships as $2500 scholarships means that if the number of $2500 scholarships was 2x, then the number of $1250 scholarships was 3*(2x)=6x.

As for another question:
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?

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 \(\frac{H}{M}\)?

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

This question is discussed here: at-a-certain-college-there-are-twice-as-many-english-majors-85632.html

Does this make sense?

This is a ratio question. So first find out the ratio of all three scholarships awarded

$1250 : $2500 : $4000 = 6:2:1
How - let x be the number of scholarships of $4000, then number of scholarship of $2500 will be 2x (twice than the other). then $1250 scholarships will be 6x (thrice of $2500 scholarship)
Ratio 6x:2x:x = 6:2:1

Now $37500 is the total amount of $1250 scholarship. Hence, total 30
If $1250 scholarship are 30 then $4000 scholarship are 5 (divide 30 by 6)

IMO A

Here is my approach
Let X, Y and Z be numbers of awards for $1250, $2500 and $4000 . (X = 3Y; Y = 2Z ==> X:Y:Z = 1:1/3:1/6
We know from the stem that X = 30 ($37500/$1250). Thus Y = 10 (30/3) and Z = 5 (30/6)
Brother Karamazov

We can let the number of $1250 scholarships = a, the number of $2500 scholarships = b, and the number of $4000 scholarships = c.

Since the committee awarded twice as many $2500 scholarships as $4000 scholarships:

b = 2c

Since it awarded three times as many $1250 scholarships as $2500 scholarships:

a = 3b

Since b = 2c, we see that a = 3(2c) = 6c.

Since a total of $37500 was awarded in $1250 scholarships:

1250a = 37,500

a = 30

Since a = 6c, we see that c = a/6 = 30/6 = 5.

Answer: A

My answer was 180 because I switch numbers in the question then when I did not find 180 I said ok do the opposite, then I got the right answer.

these kind of phrases are killing me
"twice as many $2500 scholarships as $4000"
"three times as many $1250 scholarships as $2500"

which is which .. Can anyone give me the right way of figuring these kind of phrases out very quickly? LOOL

Hi All,

We're told that there are 3 types of scholarships; I'm going to assign a variable to each type:

A = the number of $1250 scholarships
B = the number of $2500 scholarships
C = the number of $4000 scholarships

From the prompt, we're told that there were twice as many $2500 scholarships as $4000 scholarships. This ratio can be written as…

B:C
2:1

We're also told that the number of $1250 scholarships is three times the number of $2500 scholarships. This ratio can be written as…

A:B
3:1

So, we have…

A:B
3:1
...B:C
...2:1

Combining ratios, we get…

A:B:C
6:2:1

This means that the number of $1250 scholarships is some multiple of 6 and the number of $2500 scholarships is an equivalent multiple of 2.

We're told that the number of $1250 scholarships totaled $37500….

37,500/1250 = 30

Thus, there ere were thirty $1250 scholarships awarded. Using the final ratio, we can deduce that there were ten $2500 scholarships and five $4000 scholarships.

Final Answer:

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

Thank you hardnstrong and msand. Its more clear now. +1Kudos to both.

Also,

If $4000 were the only scholarships then max number was 9 since 10*4000 = 40000> 37500.

Once you know just work out the problems with option A or B. Just a shortcut to use once u iron out the concepts.

I had the same problem to

Lets assume 1250 as X, 2500 as Y and 4000 as Z

Z=2X Statement 1
Y = 3X Statement 2

Now we get (X + 3x + 2X ) 1250 = 37500

after we solve we get 30/6 = 5 answer A

Yes, I'm also confused with the phrases (twice as many XXX as XXX). Remember we have a very similar question, that is, (see below)

"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?" The correct answer is 3:2 (rather than 2:3).

The expression is the same in these TWO questions, but why not the same understanding?

Who can help? Thank you.

Hi Bunuel,

I got it. Your explanation is very clear. Thank you so much!

Since the starting point is given as the $4000 scholarship,
Assume $4000 scholarships to be x
By the given information, $2500 scholarships = 2x
and $1250 scholarships = 6x

Gievn: Total $1250 scholarships = $37500
6x*1250 = 37500
Solve for x = 5
Option A

\(\left. \matrix{\\
A\,\,:\,\,\,\$ 125 \cdot 10\,\, \hfill \cr \\
B:\,\,\,\$ 250 \cdot 10 \hfill \cr \\
C:\,\,\,\$ 400 \cdot 10\, \hfill \cr} \right\}\,\,\,{\rm{each}}\)

\(A:B:C = 6:2:1\,\,\,\left( {{\rm{quantities}}} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\{ \matrix{\\
A = 6k \hfill \cr \\
B = 2k \hfill \cr \\
C = k \hfill \cr} \right.\,\,\,\,\,\,\,\left( {k \ge 1\,\,{\mathop{\rm int}} } \right)\)

\(? = k\)

\(6k\,\,\,A\,\,{\rm{units}}\,\, \cdot \,\,\left( {{{\$ 125 \cdot 10} \over {1\,\,A\,\,{\rm{unit}}}}\,\,\matrix{\\
\nearrow \cr \\
\nearrow \cr \\
\\
} } \right)\,\,\,\,\,\, = \,\,\,\,\,\$ \,3750 \cdot 10\,\,\,\,\)

Obs.: arrows indicate licit converter (UNITS CONTROL technique).


\(? = k = \frac{{3750}}{{6 \cdot 125}} = \underleftrightarrow {\frac{{3750}}{{3 \cdot 250}} = \frac{{375}}{{3 \cdot 25}}} = \frac{{125}}{{25}} = 5\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

What is GMATH method? Why you use all of those symbols we don't understand? Please clarify them.

Posted from my mobile device

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.