Minimum no# of children required

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rakaisraka: Senior | Next Rank: 100 Posts; Posts: 37; Joined: Mon Jul 06, 2015 2:46 am

by rakaisraka » Tue Aug 18, 2015 1:27 pm

Four friends have 24 , 36 , 40 and 60 coins respectively. They want to distribute all these coins among children in such a way that each friend gives equal number of coins to to each child and no child receives coins from more than one of the four friends.
What is the minimum number of children needed to above condition to hold true.?
Thanks

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Source: Beat The GMAT — Problem Solving | Tue Aug 18, 2015 1:27 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Aug 18, 2015 1:32 pm

rakaisraka wrote:Four friends have 24 , 36 , 40 and 60 coins respectively. They want to distribute all these coins among children in such a way that each friend gives equal number of coins to to each child and no child receives coins from more than one of the four friends.
What is the minimum number of children needed to above condition to hold true.?
Thanks

This question would be much easier to solve if the 5 answer choices were provided. Where are they?

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Brent

Brent Hanneson - Creator of GMATPrepNow.com

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by [email protected] » Tue Aug 18, 2015 6:32 pm

Hi rakaisraka,

As Brent as already pointed out, this question would be considerably easier to solve if we TESTed THE ANSWERS. Since you have not included the 5 choices, we're force to take more of a 'math-centric' approach.

Since the prompt states that each child must receive the SAME number of coins and that no child can receive coins from more than one of the four people, we're looking for a number that is the Greatest Common Factor of all four numbers (24, 36, 40 and 60). There are a couple of different ways to figure that out - regardless of which way you choose, you should find that it's 4.

So, if each child receives 4 coins, there would have to be...

24/4 = 6 children
36/4 = 9 children
40/4 = 10 children
60/4 = 15 children

[spoiler]6+9+10+15 = 40 children.[/spoiler]

GMAT assassins aren't born, they're made,
Rich

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rakaisraka: Senior | Next Rank: 100 Posts; Posts: 37; Joined: Mon Jul 06, 2015 2:46 am

by rakaisraka » Wed Aug 19, 2015 11:34 am

Thanks , This question did not had answer choices..Can you explain why are we looking for GCF?
Thanks

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Sheri Kim: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Thu Aug 20, 2015 2:15 am

by Sheri Kim » Thu Aug 20, 2015 2:23 am

rakaisraka wrote:Thanks , This question did not had answer choices..Can you explain why are we looking for GCF?
Thanks

Each friend gives out the same number of coins to each child.

If we lay this out:

1 coin per child : 24+36+40+60 children
2 coins per child : 12+18+20+30 children
4 coins per child (greatest common factor) : 6+9+10+15 children

GCF = the maximum number of coins they can give to each child
Therefore, by using GCF we can get the minimum number of children needed.

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by [email protected] » Thu Aug 20, 2015 9:15 am

Hi rakaisraka,

Since the question did not include answer choices, then what is the SOURCE of the question? Is it a GMAT-based resource or a general "math" resource?

We're looking for the GCF because the question asked for the MINIMUM number of children needed (to satisfy all of the conditions in the prompt). When dealing with questions that ask for a minimum or maximum number, you often have to look at maximizing or minimizing some OTHER number in the calculation.

GMAT assassins aren't born, they're made,
Rich

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Fri Aug 21, 2015 6:58 pm

Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

Four friends have 24 , 36 , 40 and 60 coins respectively. They want to distribute all these coins among children in such a way that each friend gives equal number of coins to to each child and no child receives coins from more than one of the four friends.
What is the minimum number of children needed to above condition to hold true.?
Thanks

==> 24=(2^3)3, 36=(2^2)(3^2), 40=(2^3)5, 60=(2^2)(3)(5). The problem is asking for the Greatest common divisor. Since the GCD is the minimum value of the index, 2^2 =4 is the answer. Thus, 24=4*6(6to each 4 children), 36=4*9(9 to each 4 children), 40=4*10(10 to each 4 children), 60=4*15(15 to each 4 children). 4 is the answer.

In case of minimum number 1 would be the answer, hence the problem asks for maximum number where the answer is 4.

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