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Need help!!!

by paosilvestre » Tue Feb 01, 2011 1:09 pm
I know that this is a very simple math problem but I need help.......

A basketball team plays only against the other five teams in its league and always in the following order: Croton, Darby, Englewood, Fiennes, and Garvin. If the team´s final game of the season is against Fiennes, which of the following could be the number of games in the team´s schedule?

a. 18
b. 24
c. 56
d. 72
e. 81
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by Stuart@KaplanGMAT » Tue Feb 01, 2011 1:15 pm
paosilvestre wrote:I know that this is a very simple math problem but I need help.......

A basketball team plays only against the other five teams in its league and always in the following order: Croton, Darby, Englewood, Fiennes, and Garvin. If the team´s final game of the season is against Fiennes, which of the following could be the number of games in the team´s schedule?

a. 18
b. 24
c. 56
d. 72
e. 81
Hi,

we could solve this as a complicated remainder problem, or we could just use good old fashioned (but quick) brute force. On the GMAT, you should always choose fast and dirty over long and elegant.

We know that the order of teams is CDEFG; we know that the last game is against F. We want to know what could be the total number of games played.

Well, the schedule could simply be CDEF, making F the 4th game.
The schedule could be CDEFG/CDEF, making F the 9th game.
The schedule could be CDEFG/CDEFG/CDEF, making F the 14th game.

See the pattern yet? If not, do one more:

The schedule could be CDEFG/CDEFG/CDEFG/CDEF, making F the 19th game.

By now, I'm sure you see that the final game has to end in either "4" or "9"; scan the choices, only (B) is a match - choose (B)!
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by paosilvestre » Tue Feb 01, 2011 1:25 pm
Thanks!!!
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by Night reader » Tue Feb 01, 2011 1:46 pm
paosilvestre wrote:I know that this is a very simple math problem but I need help.......

A basketball team plays only against the other five teams in its league and always in the following order: Croton, Darby, Englewood, Fiennes, and Garvin. If the team´s final game of the season is against Fiennes, which of the following could be the number of games in the team´s schedule?

a. 18
b. 24
c. 56
d. 72
e. 81
:) nothing to be stamped

n-number of games
5 games - required number for cycle
4th game - remainder
n=5i+4 {i - integer}
a. (18-4)/5 not integer --> cross over as Incorrect
b. (24-4)/5 integer --> correct
c. (56-4)/5 not integer --> cross over as Incorrect
d. (72-4)/5 not integer --> cross over as Incorrect
e. (81-4)/5 not integer --> cross over as Incorrect
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