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# A certain scholarship committee awarded scholarships in the

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Manager
Joined: 27 Feb 2010
Posts: 105
Location: Denver
A certain scholarship committee awarded scholarships in the [#permalink]

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24 Apr 2010, 16:07
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Question Stats:

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A certain scholarship committee awarded scholarships in the amounts of $1250,$2500 and $4000. The Committee awarded twice as many$2500 scholarships as $4000 and it awarded three times as many$1250 scholarships as $2500 scholarships. If the total of$37500 was awarded in $1250 scholarships, how many$4000 scholarships were awarded?

A. 5
B. 6
C. 9
D. 10
E. 15
[Reveal] Spoiler: OA

Last edited by Bunuel on 10 Nov 2012, 04:36, edited 1 time in total.
Renamed the topic and edited the question.
Manager
Joined: 05 Mar 2010
Posts: 217
Re: How many scholarships were awarded? [#permalink]

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25 Apr 2010, 01:17
1
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zz0vlb wrote:
A certain scholarship committee awarded scholarships in the amounts of $1250,$2500 and $4000. The Committe awarded twice as many$2500 scholarships as $4000 and it awarded three times as many$1250 scholarships as $2500 scholarships. If the total of$37500 was awarded in $1250 scholarships, how many$4000 scholarships were awarded?

A.5
B.6
C.9
D.10
E.15

[Reveal] Spoiler:
A

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

And, 10/2 = 5 Schols for $4000. Ans A. Manager Joined: 27 Feb 2010 Posts: 105 Location: Denver Re: How many scholarships were awarded? [#permalink] ### Show Tags 25 Apr 2010, 05:57 Thank you hardnstrong and msand. Its more clear now. +1Kudos to both. Senior Manager Joined: 12 Jan 2010 Posts: 256 Schools: DukeTuck,Kelogg,Darden Re: How many scholarships were awarded? [#permalink] ### Show Tags 25 Apr 2010, 08:34 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.
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Joined: 11 Jul 2012
Posts: 46
Re: How many scholarships were awarded? [#permalink]

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09 Nov 2012, 13:13
1
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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 Math Expert Joined: 02 Sep 2009 Posts: 39622 Re: A certain scholarship committee awarded scholarships in the [#permalink] ### Show Tags 10 Nov 2012, 04:42 1 This post received KUDOS Expert's post zz0vlb wrote: A certain scholarship committee awarded scholarships in the amounts of$1250, $2500 and$4000. The Committee awarded twice as many $2500 scholarships as$4000 and it awarded three times as many $1250 scholarships as$2500 scholarships. If the total of $37500 was awarded in$1250 scholarships, how many $4000 scholarships were awarded? A. 5 B. 6 C. 9 D. 10 E. 15 Say the number of$4,000 scholarships awarded was x, then the number of $2,500 scholarships awarded would be 2x and the number of$1,250 scholarships awarded would be 6x.

We are given that 6x*1,250=37,500 --> x=5.

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Joined: 22 Jan 2013
Posts: 9
Re: A certain scholarship committee awarded scholarships in the [#permalink]

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26 Feb 2013, 19:19
1
KUDOS
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
Director
Joined: 29 Nov 2012
Posts: 878
Re: A certain scholarship committee awarded scholarships in the [#permalink]

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27 Feb 2013, 02:41
aiha85 wrote:
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

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
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Intern
Joined: 17 Jan 2014
Posts: 8
Re: A certain scholarship committee awarded scholarships in the [#permalink]

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19 Jan 2014, 01:38
aiha85 wrote:
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

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.
Math Expert
Joined: 02 Sep 2009
Posts: 39622
Re: A certain scholarship committee awarded scholarships in the [#permalink]

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19 Jan 2014, 09:34
Expert's post
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BOOKMARKED
smallapple wrote:
aiha85 wrote:
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

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.

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?
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Intern
Joined: 17 Jan 2014
Posts: 8
Re: A certain scholarship committee awarded scholarships in the [#permalink]

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20 Jan 2014, 04:54
Bunuel wrote:
smallapple wrote:
aiha85 wrote:
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

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.

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

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

Does this make sense?

Hi Bunuel,

I got it. Your explanation is very clear. Thank you so much!
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Posts: 15929
Re: A certain scholarship committee awarded scholarships in the [#permalink]

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08 Dec 2015, 00:46
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Re: A certain scholarship committee awarded scholarships in the [#permalink]

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08 Dec 2015, 23:40
Quote:
A certain scholarship committee awarded scholarships in the amounts of $1250,$2500 and $4000. The Committee awarded twice as many$2500 scholarships as $4000 and it awarded three times as many$1250 scholarships as $2500 scholarships. If the total of$37500 was awarded in $1250 scholarships, how many$4000 scholarships were awarded?

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
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Re: A certain scholarship committee awarded scholarships in the   [#permalink] 08 Dec 2015, 23:40
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