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01 Apr 2016, 08:09
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
61% (02:22) correct
39%
(02:28)
wrong
based on 247
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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. 13
B. 14
C. 15
E. 16
E. 17
01 Apr 2016, 08:41
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MathRevolution
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..
04 Apr 2016, 00:58
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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
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.
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.
