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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 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.. _________________

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.
_________________

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

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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?
_________________

Do not pray for an easy life, pray for the strength to endure a difficult one - Bruce Lee

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

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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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