Number of small containers filled?

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sat Feb 22, 2014 5:09 pm

Hello,

Can you please assist with this:

A manufacturer packages soap powder in containers of three different sizes. The amount of soap powder
in a full large container could fill exactly 3 of the medium containers or exactly 5 of the small containers. If an equal number of small and large containers are to be filled with the amount of soap powder that would fill 90 medium containers, how many small containers will be filled?

OA: 25

I am getting 54 though.

Let x be the amount of soap powder in a full large container.

This would fill 3 medium containers i.e. x/3
or 5 small containers i.e. x/5

If x/3 = 90 => x = 270

Hence, number of small containers = 270/5 = 54

Can you please tell me where I am going wrong here?

Thanks,
Sri

Source: Beat The GMAT — Problem Solving | Sat Feb 22, 2014 5:09 pm

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[email protected]: Elite Legendary Member; Posts: 10391; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sat Feb 22, 2014 7:00 pm

Hi Sri,

This question is essentially about the relationships between small, medium and large containers. Instead of trying to solve this with complex equations, I'm going to go about this in as easy a way as I can.

From the prompt we know that….

L = 3M 1 large = 3 medium
L = 5S 1 large = 5 smalls

We also know that we have the equivalent of 90 medium containers full of soap. Using the above information, we know that we would have 30 full large containers OR 150 small containers

The question asks us to have an EQUAL number of large and small containers, so we have to "move soap" around until we have the same total amount of soap as can fill 90 mediums, BUT have an equal number of large and small containers.

We'll start with….
30 larges and 0 smalls

For every large container we remove, we gain 5 smalls
29 large and 5 smalls
28 large and 10 smalls
27 large and 15 smalls
26 large and 20 smalls
25 large and 25 smalls

And then we're done.

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

Contact Rich at [email protected]

Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members; Thanked: 335 times

by Patrick_GMATFix » Sat Feb 22, 2014 7:20 pm

Hope that helped Sri,
-Patrick

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