GMAT PREP PROB??

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dferm: Master | Next Rank: 500 Posts; Posts: 446; Joined: Thu Jul 26, 2007 1:07 pm; Thanked: 6 times

by dferm » Fri Apr 11, 2008 12:28 pm

PLEASE EXPLAIN.. THANKS.

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Source: Beat The GMAT — Problem Solving | Fri Apr 11, 2008 12:28 pm

Musiq: Senior | Next Rank: 100 Posts; Posts: 93; Joined: Thu Apr 10, 2008 1:42 pm; Location: Chicago; Thanked: 20 times

by Musiq » Fri Apr 11, 2008 2:58 pm

Your question is very interesting. It combines a lot of simple (but very easy to miss on test day) combiniatorics issues.

First we have 2 Sizes. Lets for simplicity's sake call them LARGE and SMALL. Then there's 4 colors in each kind.

Now the question wants us to generate all the ways in which we can package (Same Color AND Same Size) OR (Same Size and 3 different colors). The AND and the OR are important here. The OR tells us to add the 2 different numbers arrived at.

Lets do the Same Color AND Same Size first :
Since there must be 3 notepads of the same color, it could be either:
BBB
GGG
YYY
PPP
( B = Blue, G= Green, Y= Yellow and P= Pink). Thats 4 ways.

But, we have to account for the 2 sizes also. And since it is an "AND" condition, multiply 4 with 2 = 8 ways.

Now, let's do the Same Size AND Different Colors:
The number of ways to pick 3 different colors from 4 given colors (when order is not important) is 4 C 3. This combination gives us 4 ways.
But, to account for the 2 sizes, we multiply this by 2. Again, the "AND" in the condition is key.

Now , we have an "OR", which in combinatorics is an addition.

So, 8 + 8 = 16 ways in which to fulfill the 2 given conditions of filling these boxes.

Hope this helps!

For love, not money.

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sampleresume: Senior | Next Rank: 100 Posts; Posts: 55; Joined: Sun Apr 06, 2008 5:04 pm

by sampleresume » Sun Apr 13, 2008 5:11 pm

Why not copy the original questions here so everyone can see?

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