Gumball Challenge

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beeparoo: Master | Next Rank: 500 Posts; Posts: 200; Joined: Sun Jun 17, 2007 10:46 am; Location: Canada; Thanked: 9 times

by beeparoo » Sat Aug 18, 2007 2:04 pm

A vending machine dispenses gumballs in a regularly repeating cycle of 10 different colours. If a quarter buys 3 gumballs, what is the minimum amount of money that must be spent before 3 gumballs of the same colour are dispensed?

A. $ 1.00

B. $ 1.75

C. $2.00

D. $2.25

E. $2.50

Correct answer: B You will need to highlight to see the answer

Source: Kaplan

++

I am confused about this one (I originally selected E) and the answer does not make any sense to me. I welcome anyone else to explain themselves. You got some 'splainin to do!

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Source: Beat The GMAT — Problem Solving | Sat Aug 18, 2007 2:04 pm

givemeanid: Master | Next Rank: 500 Posts; Posts: 277; Joined: Sun Jun 17, 2007 2:51 pmFollowed by: 1 member; Location: New York, NY; Thanked: 6 times

by givemeanid » Sat Aug 18, 2007 2:32 pm

To get 3 of same color, you need at least 21 gumballs. 3 for a quarter. 21 for $1.75.

So It Goes

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beeparoo: Master | Next Rank: 500 Posts; Posts: 200; Joined: Sun Jun 17, 2007 10:46 am; Location: Canada; Thanked: 9 times

by beeparoo » Sun Aug 19, 2007 4:39 pm

Here is my reasoning and perhaps someone can kindly let me know what I am doing wrong.

Let each colour be represented by the first 10 letters of the alphabet:
A B C D E F G H I J

Suppose your first quarter will give you the following colours: ABC

Your next quarter will give you DEF
And so on and so on...

To obtain the same colours again, you will spend money on the following sets of gumballs:

DEF GHI JAB CDE FGH IJA BCD EFG HIJ ABC (10 sets)

10 sets of three X $0.25 per set = $2.25

Therefore, how does one get to 21-gumballs dispensed??

Am I interpreting the question incorrectly?

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beny: Master | Next Rank: 500 Posts; Posts: 214; Joined: Fri Jul 20, 2007 1:35 am; Thanked: 3 times

by beny » Sun Aug 19, 2007 5:42 pm

You are looking for 3 colors of every gumball being dispensed, but the question asks for at least 1 color being dispensed.

According to your sequence:

DEF GHI JAB CDE FGH IJA BCD EFG HIJ ABC

Those 7 terms alread.y have 3 Ds, therefore, you know you have 3 of the same color. A quarter per trio equals $1.75.

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beeparoo: Master | Next Rank: 500 Posts; Posts: 200; Joined: Sun Jun 17, 2007 10:46 am; Location: Canada; Thanked: 9 times

by beeparoo » Tue Aug 21, 2007 12:22 pm

OooOooh. OK. Thanks Beny, your explanation really turned on the light.

When I read the question, I interpreted it differently which led me to pick another answer -- also a choice in the given answers. Yikes.

I think the question was ambiguous and I feel confidant that GMAT writers would ensure more explicit writings on the actual test.

Thanks again!

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