A certain scholarship committee awarded scholarships in the

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

A certain scholarship committee awarded scholarships in the

by BTGmoderatorLU » Sat Oct 06, 2018 2:20 pm

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Source: GMAT Prep

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

The OA is A.

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Source: Beat The GMAT — Problem Solving | Sat Oct 06, 2018 2:20 pm

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pm; Thanked: 59 times; Followed by:33 members

A certain scholarship committee awarded scholarships in the

by fskilnik@GMATH » Sun Oct 07, 2018 6:34 am

BTGmoderatorLU wrote:Source: GMAT Prep

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

$$\left. \matrix{
A\,\,:\,\,\,\$ 125 \cdot 10\,\, \hfill \cr
B:\,\,\,\$ 250 \cdot 10 \hfill \cr
C:\,\,\,\$ 400 \cdot 10\, \hfill \cr} \right\}\,\,\,{\rm{each}}$$
$$A:B:C = 6:2:1\,\,\,\left( {{\rm{quantities}}} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\{ \matrix{
A = 6k \hfill \cr
B = 2k \hfill \cr
C = k \hfill \cr} \right.\,\,\,\,\,\,\,\left( {k \ge 1\,\,{\mathop{\rm int}} } \right)$$
$$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.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

by deloitte247 » Sun Oct 07, 2018 9:02 am

There are 3 types of scholarships.
Let $1250 scholarships = A
Let $2500 scholarships = B
Let $4000 scholarships =C
There are twice as many $250 scholarships as $4000 scholarships. This is a ratio that can be written as B : C = 2 : 1
The number of $1250 scholarships is three time the number of $2500 scholarships. This is also certain and it can be written as A : B = 3 : 1 by combining ratio A : B and B : C we will get A : B : C = 6 : 2 : 1

Now $37500 is the total amount of $1250 scholarships and B is twice as many of C.
$$Hence,\ \frac{$37500}{$1250}=30\ scholarships$$
Number of A is three times the number of B
$$Hence,\ \frac{30}{3}\ =10\ scholarships\ for\ $2500$$
$$Hence,\ \frac{10}{2}\ =5\ scholarships\ for\ $4000$$

Option A is CORRECT.

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GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Sun Oct 07, 2018 2:52 pm

Hi All,

We're told that a certain scholarship committee awarded scholarships in the amounts of $1250, $2500 and $4000 - there are twice as many $2500 scholarships as $4000 and it awarded three times as many $1250 scholarships as $2500 scholarships. A total of $37500 was awarded in $1250 scholarships. We're asked for the number of $4000 scholarships that were awarded.

To start, 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 $37,500....

37,500/1250 = 30

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

Final Asnwer: A

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

Contact Rich at [email protected]

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GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Oct 10, 2018 5:52 pm

BTGmoderatorLU wrote:Source: GMAT Prep

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 a = the number of $1250 scholarships, b = the number of $2500 scholarships, and c = he number of $4000 scholarships.

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]