aeros232 wrote:

A certain organization presents reward to some people. There are 3 kinds of reward that respectively are $125, $40, $15. If the total reward is $1,735, what is the least possible value of the number of the people who received reward?

a. 17

b. 22

c. 32

d. 47

e. 90

from question :

1735= 125A + 40B +15C

Since we have 3 variables and only other information we can infer is that each of A, B and C should be non negative integer (>=0). Hence, we need to plug in numbers to find out.

Now since the question is asking for 'least' number of rewards, best approach to start with is -finding least 'possible' number of rewards - it can happen when every award is 125. So number of reward in this case 1735/125 = 13 + some remainder. hence ans must be greater than 14.

So we can start with A=13

This gives us

1735 = 13*125 + 40B +15C

or 40B + 15C =110

or 8B + 3C =22

Do we have any combination for B and C that works for this? yes.. if B=C=2.

Hence total number of rewards = A+B+C=13+2+2 = 17

same is given in A.

At this point, some observations could also be made. There could be a doubt in mind, what if A=12 and B+C <5? but note, it is not possible because for every A reduced, difference (125) is to be filled by at least 4 of Bs and Cs (40 and 15 respectively). Second, none of the answer choices is below 17.

Hence Ans A it is.

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