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CrossRoads with OG 13th Edition/Math/Q154

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CrossRoads with OG 13th Edition/Math/Q154

by im_mba » Sun May 11, 2014 11:15 am
SPOILER ALERT!!!

A club collected exactly $599 from its members. If each member contributed at least $12, what is the
greatest number of members the club could have?
A) 43
B) 44
C) 49
D) 50
E) 51

Option C ,49 , is the OGA for this Question.
However I think there's one problem if we go by this answer choice i.e 49.
The question states two things :
1. $599 is the exact amount collected
2. Each member contributed atleast $12.

Assuming that 49 is the maximum # of people that could have contributed $12 each so the total amount contributed from $12-club people would be $588. This leaves us with needing $11($599-$588) more for making up to the total contribution($599). However the second point clearly states that each member contributed atleast $12. So this answer choice leaves us with $11 contributed by nobody.

The answer should be 48 , which is not even in the option , because this way both the conditions to the questions are satisfied.
1. 48 * $12 = $576 ;
2. Remaining $23 is a valid contribution for any member to make since there's no upper limit.

Please correct me if I'm wrong anywhere in my approach.



[spoiler][/spoiler]
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by Brent@GMATPrepNow » Sun May 11, 2014 11:59 am
im_mba wrote:
A club collected exactly $599 from its members. If each member contributed at least $12, what is the
greatest number of members the club could have?
A) 43
B) 44
C) 49
D) 50
E) 51
To maximize the number of members, we must MINIMIZE the amount each person contributed.
The minimum contribution is $12.
So, how many $12-contributions will divide into $599?

599 divided by 12 equals 49 with remainder 11.
So, there can be AT MOST 49 members.

Answer: C

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by Brent@GMATPrepNow » Sun May 11, 2014 12:02 pm
im_mba wrote:SPOILER ALERT!!!

A club collected exactly $599 from its members. If each member contributed at least $12, what is the
greatest number of members the club could have?
A) 43
B) 44
C) 49
D) 50
E) 51

Option C ,49 , is the OGA for this Question.
However I think there's one problem if we go by this answer choice i.e 49.
The question states two things :
1. $599 is the exact amount collected
2. Each member contributed atleast $12.

Assuming that 49 is the maximum # of people that could have contributed $12 each so the total amount contributed from $12-club people would be $588. This leaves us with needing $11($599-$588) more for making up to the total contribution($599). However the second point clearly states that each member contributed atleast $12. So this answer choice leaves us with $11 contributed by nobody.

The answer should be 48 , which is not even in the option , because this way both the conditions to the questions are satisfied.
1. 48 * $12 = $576 ;
2. Remaining $23 is a valid contribution for any member to make since there's no upper limit.

Please correct me if I'm wrong anywhere in my approach.

[spoiler][/spoiler]
You may be forgetting that the MINIMUM contribution is $12.
So, it's possible that 48 people contributed $12 (total = $576), and 1 person contributed $23.
This gives us a total of $599 (and a total of 49 people)

Cheers,
Brent
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by im_mba » Sun May 11, 2014 12:05 pm
hi Brent,
Thanks for replying.
What you are saying is exactly the same as as OG explanation for this answer.But i see a major flaw going by this answer. I will appreaciate if you can spend a more time on the approach that i've taken and point a flaw in it.
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by [email protected] » Sun May 11, 2014 2:10 pm
Hi im_mba,

Your approach assumes that each member contributed the SAME amount of money, but the prompt does NOT state that. We're told that each member contributed AT LEAST $12, but it's possible that the members all contributed different amounts of money (that were each at least $12).

Also, your answer gives us only $576, but the prompt states that it's supposed to be $599 (this should have been the first "clue" that something was wrong with your approach).

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by im_mba » Sun May 11, 2014 3:07 pm
Rich
What my thinking is that the total amount of money contributed by each member should add upto 599 which doesnt happen when I take the number of people of contributed $12 to be 49 since ut leaves me with $11 short for the entire total . Since the question bounds each member from contributing less than $12,those $11 will not be adding up to the total money contributed by 49 people to make grand total of 599 which despise the foundation of the question that the club had gatherd EXACT $599.
[email protected] wrote:Hi im_mba,

Your approach assumes that each member contributed the SAME amount of money, but the prompt does NOT state that. We're told that each member contributed AT LEAST $12, but it's possible that the members all contributed different amounts of money (that were each at least $12).

Also, your answer gives us only $576, but the prompt states that it's supposed to be $599 (this should have been the first "clue" that something was wrong with your approach).

GMAT assassins aren't born, they're made,
Rich
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by im_mba » Sun May 11, 2014 3:15 pm
My Bad..All the time I thought that the question asked only for the number of people who contributed by $12.

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by Jeff@TargetTestPrep » Tue Jul 07, 2015 3:34 am
im_mba wrote:SPOILER ALERT!!!

A club collected exactly $599 from its members. If each member contributed at least $12, what is the
greatest number of members the club could have?
A) 43
B) 44
C) 49
D) 50
E) 51

Option C ,49 , is the OGA for this Question.
However I think there's one problem if we go by this answer choice i.e 49.
The question states two things :
1. $599 is the exact amount collected
2. Each member contributed atleast $12.

Assuming that 49 is the maximum # of people that could have contributed $12 each so the total amount contributed from $12-club people would be $588. This leaves us with needing $11($599-$588) more for making up to the total contribution($599). However the second point clearly states that each member contributed atleast $12. So this answer choice leaves us with $11 contributed by nobody.

The answer should be 48 , which is not even in the option , because this way both the conditions to the questions are satisfied.
1. 48 * $12 = $576 ;
2. Remaining $23 is a valid contribution for any member to make since there's no upper limit.

Please correct me if I'm wrong anywhere in my approach.



[spoiler][/spoiler]
Solution:

Let's first divide= 599 by 12 (the minimum amount each member could contribute) and then use the remainder to finish the problem.

599/12 = 49 R 11

This means that: 49 x $12 + $11 = $599

In other words, if 49 members each contribute $12, someone would have to contribute the extra $11. Note that, since each member contributed at least $12, the $11 could not have come from an additional member. Therefore, the extra $11 must have been contributed by one (or more) of the existing 49 members. Regardless of who contributed the extra $11, the maximum number of members that the club could have is 49.

Answer: C

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