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A certain scholarship committee awarded scholarships in the

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A certain scholarship committee awarded scholarships in the  [#permalink]

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New post Updated on: 10 Nov 2012, 03:36
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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

Originally posted by zz0vlb on 24 Apr 2010, 15:07.
Last edited by Bunuel on 10 Nov 2012, 03:36, edited 1 time in total.
Renamed the topic and edited the question.
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Re: How many scholarships were awarded?  [#permalink]

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New post 25 Apr 2010, 00:17
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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




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
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Re: How many scholarships were awarded?  [#permalink]

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New post 25 Apr 2010, 00:26
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$37500/$1250 = 30 Schols...
therefore , 30/3 = 10 Schols for $2500
And, 10/2 = 5 Schols for $4000.

Ans A.
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Re: How many scholarships were awarded?  [#permalink]

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New post 25 Apr 2010, 04:57
Thank you hardnstrong and msand. Its more clear now. +1Kudos to both.
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Re: How many scholarships were awarded?  [#permalink]

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New post 25 Apr 2010, 07:34
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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Re: How many scholarships were awarded?  [#permalink]

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New post 09 Nov 2012, 12:13
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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)
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Re: A certain scholarship committee awarded scholarships in the  [#permalink]

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New post 10 Nov 2012, 03:42
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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.

Answer: A.
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Re: A certain scholarship committee awarded scholarships in the  [#permalink]

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New post 26 Feb 2013, 18:19
1
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
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Re: A certain scholarship committee awarded scholarships in the  [#permalink]

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New post 27 Feb 2013, 01:41
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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Re: A certain scholarship committee awarded scholarships in the  [#permalink]

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New post 19 Jan 2014, 00:38
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.
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Re: A certain scholarship committee awarded scholarships in the  [#permalink]

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New post 19 Jan 2014, 08:34
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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Re: A certain scholarship committee awarded scholarships in the  [#permalink]

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New post 20 Jan 2014, 03:54
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! :-D
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Re: A certain scholarship committee awarded scholarships in the  [#permalink]

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New post 08 Dec 2015, 22:40
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]

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New post 13 Mar 2018, 12:04
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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.

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Re: A certain scholarship committee awarded scholarships in the  [#permalink]

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New post 15 Mar 2018, 09:15
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


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
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A certain scholarship committee awarded scholarships in the  [#permalink]

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New post 07 Oct 2018, 06:43
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

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

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

\(? = k\)

\(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.
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