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A school give scholarship of a total of $940,000 to students, the scho

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A school give scholarship of a total of $940,000 to students, the scho  [#permalink]

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New post 01 Apr 2016, 08:09
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Difficulty:

  55% (hard)

Question Stats:

66% (02:15) correct 34% (02:18) wrong based on 107 sessions

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A school give scholarship of a total of $940,000 to students, the scholarship consist of 3 types $95,000, $35,000, and $10,000. What is the smallest possible number of students who take the scholarship?

A. 13
B. 14
C. 15
E. 16
E. 17


* A solution will be posted in two days.

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Re: A school give scholarship of a total of $940,000 to students, the scho  [#permalink]

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New post 01 Apr 2016, 08:41
MathRevolution wrote:
A school give scholarship of a total of $940,000 to students, the scholarship consist of 3 types $95,000, $35,000, and $10,000. What is the smallest possible number of students who take the scholarship?

A. 13
B. 14
C. 15
E. 16
E. 17


* A solution will be posted in two days.



let the three be a,b,c..
so 95000a+35000b+10000c=940000..
lets simplify..
19a+7b+2c=188..

for min a+b+c, we have to have max number of bigger scholarship..

so lets substitute a as 9 , a as 10 goes more than 940..
19*9 + 7b+2c=188
7b+2c=188-171=17..
we have to have b as odd since 2c is even and SUM is ODD..
so b=1...
7*1+2c=17
or 2c=10..
c=5..
total a+b+c=9+1+5=15..
C

Ofcourse to be SURE we should check when a=8 too
Reason:- we have been forced to take FIVE 10000s instead of ONE 35000 and ONE 10000 as 5000 is left over..
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Re: A school give scholarship of a total of $940,000 to students, the scho  [#permalink]

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New post 04 Apr 2016, 00:58
A school give scholarship of a total of $940,000 to students, the scholarship consist of 3 types $95,000, $35,000, and $10,000. What is the smallest possible number of students who take the scholarship?

A. 13
B. 14
C. 15
E. 16
E. 17


The number of first-place students=f
The number of second-place students=s
The number of third-place students=t
Then, an equation 95,000f+35,000s+10,000t=940,000 is derived.
In order for f+s+t to be minimum, f should be maximum followed by s and t.
Then, f=9, s=1, t=5 are derived and f+s+t=9+1+5=15.
Thus, C is the answer.
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Re: A school give scholarship of a total of $940,000 to students, the scho  [#permalink]

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New post 12 Aug 2017, 19:25
chetan2u wrote:
MathRevolution wrote:
A school give scholarship of a total of $940,000 to students, the scholarship consist of 3 types $95,000, $35,000, and $10,000. What is the smallest possible number of students who take the scholarship?

A. 13
B. 14
C. 15
E. 16
E. 17


* A solution will be posted in two days.



let the three be a,b,c..
so 95000a+35000b+10000c=940000..
lets simplify..
19a+7b+2c=188..

for min a+b+c, we have to have max number of bigger scholarship..

so lets substitute a as 9 , a as 10 goes more than 940..
19*9 + 7b+2c=188
7b+2c=188-171=17..
we have to have b as odd since 2c is even and SUM is ODD..
so b=1...
7*1+2c=17
or 2c=10..
c=5..
total a+b+c=9+1+5=15..
C

Ofcourse to be SURE we should check when a=8 too
Reason:- we have been forced to take FIVE 10000s instead of ONE 35000 and ONE 10000 as 5000 is left over..


So, the total value of $940,000 must be taken by students without any remainder?
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Re: A school give scholarship of a total of $940,000 to students, the scho  [#permalink]

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New post 12 Aug 2017, 20:33
don't get it, why the question is marked as hard
I resolved it mentally for C right away, and then spent 6 minutes thinking I might be wrong, hard questions can't be so easy...
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Re: A school give scholarship of a total of $940,000 to students, the scho   [#permalink] 12 Aug 2017, 20:33
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A school give scholarship of a total of $940,000 to students, the scho

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