make 45 cents in change

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Thu May 13, 2010 4:57 am

In how many ways can one make 45 cents in change using only nickels, dimes, and quarters, when any coin can be used for any possible number of times?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

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Source: Beat The GMAT — Problem Solving | Thu May 13, 2010 4:57 am

tpr-becky: GMAT Instructor; Posts: 509; Joined: Wed Apr 21, 2010 1:08 pmFollowed by: 85 members; Location: Irvine, CA; Thanked: 199 times; GMAT Score:750

by tpr-becky » Thu May 13, 2010 4:53 pm

While I am sure there is a formula I did this quickly through logic-

Can't have 2 Quarters because that is too much
so if you have on quarter you need to add $.20 -

you can do $.20 with 2 dimes, 1 dime with 2 nickels, or 4 nickels (3 ways)

Or you can use zero quarters you'd need 4 dimes and 1 nickel, 3 dimes and 3 nickels, 2 dimes and 5 nickels, 1 dime and 7 nickels or 0 dimes and 9 nickels (5 ways)

For a total of 8 ways.

My logic went - how many ways if I use a quarter, and how many ways if I don't use a quarter.

Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA

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pardeep_10sharma: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Tue Mar 02, 2010 9:38 amFollowed by: 1 member; Location: India; GMAT Score:540

by pardeep_10sharma » Fri May 14, 2010 4:54 am

Great mam.u did in awsome manner..........U r so intelligent. Thanks for sharing ur super duper soln and keep on sharing in future too........

tpr-becky wrote:While I am sure there is a formula I did this quickly through logic-

Can't have 2 Quarters because that is too much
so if you have on quarter you need to add $.20 -

you can do $.20 with 2 dimes, 1 dime with 2 nickels, or 4 nickels (3 ways)

Or you can use zero quarters you'd need 4 dimes and 1 nickel, 3 dimes and 3 nickels, 2 dimes and 5 nickels, 1 dime and 7 nickels or 0 dimes and 9 nickels (5 ways)

For a total of 8 ways.

My logic went - how many ways if I use a quarter, and how many ways if I don't use a quarter.

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cager: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Mon May 10, 2010 1:40 pm; Location: Toronto, ON

by cager » Fri May 14, 2010 6:26 am

thanks. does anyone know the formula?
in case there are questions that have more combination's than this.

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