Combination problem and a few more.

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torofish: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Mon Nov 24, 2008 6:41 am

by torofish » Sat Jan 02, 2010 11:18 am

1.) Kris is purchasing a gear to ride his bike. He wants 2 gloves, 1 parka, 2 hats, 3 boots. A catalog offers 5 types of gloves, 3 parkas, 4 hats, 6 boots. How much different order could he place?
1.) 360
2.) 720
3.) 3600
4.) 7200
5.) 36000

Couldn't do

2.) S is non-negative integers.
So, all possible value = 0, 5, 0.6, -0.7, am I correct?

3.) A, B, C, D are consecutive integers in increasing order.
I thought it could by either 13, 14, 15, 16, 17 and 13, 15, 17, 19, 21. Both sequences are increasing, and consecutive.
But solution seems to interpret that as 13, 14, 15, 16, 17 only.
Is my 13, 15, 17, 19, 21 correct?
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Source: Beat The GMAT — Problem Solving | Sat Jan 02, 2010 11:18 am

cameronwu: Senior | Next Rank: 100 Posts; Posts: 34; Joined: Wed Jun 17, 2009 6:15 am; Thanked: 4 times

by cameronwu » Sat Jan 02, 2010 1:03 pm

Hi. I couldn't really understand what you meant by question 2) and 3)... it seems like you left out information in the question.

I think I can help with Question 1 though.

This is a basic combinations problem that involves figuring out how many combinations you can make of each different gear type, and multiplying them all together. So the basic formula would look like (Combos of Gloves) * (C. of Parks) * (C. of Hats) * (C. of boots) = Answer.

In case you don't know how to do a combination, it looks like this. Take gloves for example. You have 5 types and make 2 choices, so it would be (# of types)! / [(choices)!*(types-choices)!]. 5! / (2!*3!) = 120 / 2*6 = 10. So you have 10 total combinations of gloves to choose from.

Expanding that for the problem, you end up getting (10)*(3)*(6)*(20) = 3600 combinations.

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Testluv: GMAT Instructor; Posts: 1302; Joined: Mon Oct 19, 2009 2:13 pmFollowed by: 164 members; Location: Toronto; Thanked: 539 times; GMAT Score:800

by Testluv » Sat Jan 02, 2010 7:03 pm

torofish,

please review the posting guidelines: you need to post questions in full with the answer choices.

For your second question:

2.) S is non-negative integers.
So, all possible value = 0, 5, 0.6, -0.7, am I correct?

0 and 5 are non-negative integers. But 0.6 and -0.7 are not non-negative integers because 0.6 isn't an integer and because -0.7 isn't an integer and is negative.

3.) A, B, C, D are consecutive integers in increasing order.
I thought it could by either 13, 14, 15, 16, 17 and 13, 15, 17, 19, 21. Both sequences are increasing, and consecutive.
But solution seems to interpret that as 13, 14, 15, 16, 17 only.
Is my 13, 15, 17, 19, 21 correct?

13, 15, 17, 19, 21 are NOT consecutive integers; instead, they are consecutive odd integers.

Kaplan Teacher in Toronto

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