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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
The OA is A.
A certain scholarship committee awarded scholarships in the
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$$\left. \matrix{BTGmoderatorLU wrote:Source: GMAT Prep
A certain scholarship committee awarded scholarships in the amounts of $1250, $2500 and $4000. The Committee awarded twice as many $2500 scholarships as $4000 and it awarded three times as many $1250 scholarships as $2500 scholarships. If the total of $37500 was awarded in $1250 scholarships, how many $4000 scholarships were awarded?
A. 5
B. 6
C. 9
D. 10
E. 15
A\,\,:\,\,\,\$ 125 \cdot 10\,\, \hfill \cr
B:\,\,\,\$ 250 \cdot 10 \hfill \cr
C:\,\,\,\$ 400 \cdot 10\, \hfill \cr} \right\}\,\,\,{\rm{each}}$$
$$A:B:C = 6:2:1\,\,\,\left( {{\rm{quantities}}} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\{ \matrix{
A = 6k \hfill \cr
B = 2k \hfill \cr
C = k \hfill \cr} \right.\,\,\,\,\,\,\,\left( {k \ge 1\,\,{\mathop{\rm int}} } \right)$$
$$6k\,\,\,A\,\,{\rm{units}}\,\, \cdot \,\,\left( {{{\$ 125 \cdot 10} \over {1\,\,A\,\,{\rm{unit}}}}\,\,\matrix{
\nearrow \cr
\nearrow \cr
} } \right)\,\,\,\,\,\, = \,\,\,\,\,\$ \,3750 \cdot 10\,\,\,\,$$
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)
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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.
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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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
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
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We can let a = the number of $1250 scholarships, b = the number of $2500 scholarships, and c = he number of $4000 scholarships.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
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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