M28-22

Question

A team contributes a total of $399 from its members. If each member contributed at least $10, and no one contributed $19, what is the greatest number of members the club could have?

A.  37 
B.  38 
C.  39 
D.  40 
E.  41

Bunuel · Answer

Official Solution:

A team contributes a total of $399 from its members. If each member contributed at least $10, and no one contributed $19, what is the greatest number of members the club could have?

A.  37 
B.  38 
C.  39 
D.  40 
E.  41

Obviously, the team could not have 40 or more members, since $10*40 = $400 > $399. What about 39? If 37 members contribute $10 each ($10*37 = $370) and the remaining two members contributed, for example, $11 and $18, respectively, then the total number of members the team would have is 37 + 1 + 1 = 39.

Answer: C

souvik101990 · Answer

Hi  Bunuel . Shouldn't this be no one contributed MORE than $19 instead of  no one contributed $19

Otherwise you could have 37*10 + 29 = 399 with 38 members.

What do you think?

Bunuel · Answer

But the question asks what is the  greatest  number of members the club could have? Solution says 39, you got 38.

souvik101990 · Answer

UGH. Yes you are right, as always. Thanks man!

kapstone1996 · Answer

39 - C

40 will be high, 40*10 > $400

37 * 10 = 370 and still need $29
38 * 10 = 380 and still need $19, no one contributed no more than $19,

So leaves me to think, that G# of members can be 37 and 2 random people with any combination of $29, is above 10 person & less than 19. .

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

Cmulenga · Answer

$399/$10= 39.9
$399/$18= 22.2

Everyone contributed at least $10, but no one contributed $19. That’s why I divided the total by contribution amounts. So I just assumed everyone contributed the same amount for this problem.

It has to be a number in between 22.2-39.9 without going over.

And 39 is the highest number out of all the choices.

Posted from my mobile device

MBAToronto2024 · Answer

KarishmaB 
What is the best approach to solve such questions? My problem is that I'm missing some cases.

KarishmaB · Answer

No cases are required here. Think of it in this way:

Everyone must contribute at least $10. Since I need the greatest number of members, each should contribute the least possible. The least possible is $10. But that gives us 39.9 members which is not possible. 
This means that some people contributed a bit more to get the total to 399. Everybody did not give exactly $10. Since I want to maximise the number of members, I say perhaps some contributed $11 then and all others gave $10 only. So from 399, I remove some multiples of 11 to be left with a multiple of 10. If I remove one 11, I get 388 which is not a multiple of 10. If I remove 2 11s, I get 377 which is not a multiple of 10. So I have to keep removing. 
When I remove 9 11s from 399 I will get 300. 
So 9 people could have contributed $11 and 30 people could have contributed $10. Then total will be $399. So 39 people is possible.

Of course 40 is not possible as the answer because then we would have at least $400 collected.

Answer (C)

M28-22

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