Packages in GMATPrep

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mysseo: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Tue Nov 15, 2011 3:28 pm; Thanked: 1 times

Packages in GMATPrep

by mysseo » Sun Dec 04, 2011 11:05 pm

A certain office supply stocks 2 size of self stick notepads, each in 4 colors: blue, green, yellow or pink. The store packs the notepads in packages that contain either 3 notepads of the same size and same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?

A.6
B.8
C.16
D.24
E.32

It was on GMATPrep. I have no idea how to solve it. The answer was C. Please help me. Thank you.

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Source: Beat The GMAT — Problem Solving | Sun Dec 04, 2011 11:05 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Sun Dec 04, 2011 11:17 pm

mysseo wrote:A certain office supply stocks 2 size of self stick notepads, each in 4 colors: blue, green, yellow or pink. The store packs the notepads in packages that contain either 3 notepads of the same size and same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?

A.6
B.8
C.16
D.24
E.32

It was on GMATPrep. I have no idea how to solve it. The answer was C. Please help me. Thank you.

Let the two sizes be 1 and 2.
Let the varieties in size 1 be B1, G1, Y1, and P1 where B, G, Y and P are the four given colors, blue, green, yellow and pink.
Also let the varieties in size 2 be B2, G2, Y2 and P2.

The first kind of package has 3 notepads of same size and color.
This means all three are either all B1, or all B2 , or all G1, or all G2, or all Y1, or all Y2, or all P1 or all P2.
So we have 8 possibilities.

The second kind of package has 3 notepads of same size but different colors.
This means all 3 are either selected from B1, G1, Y1 and P1 in 4C3 = 4 ways or all 3 are selected from B2, G2, Y2 and P2 in 4C3 = 4 ways.
This means we can have 4 + 4 = 8 possibilities.

Adding the possibilities of both types of packages, we get 8 + 8 = 16 ways.

The correct answer is C.

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
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