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uttom: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Wed Jul 09, 2014 8:59 pm

by uttom » Wed Jul 09, 2014 9:02 pm

how many ways i select a+b=12 where 0<=a, b<=9

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Source: Beat The GMAT — Problem Solving | Wed Jul 09, 2014 9:02 pm

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by [email protected] » Thu Jul 10, 2014 8:39 am

Hi uttom,

When posting a prompt, you should post the ENTIRE question, including the answer choices. My guess is that there are some additional "restrictions" to this question, even though you have not listed them.

Do A and B have to be integers?
Do A and B have to be positive?
Can A and B be the same value?
If A=3, B=8, is that considered different from A=8, B=3?

GMAT questions are carefully worded so that there should be no confusion about the information provided or the question that you are expected to answer.

Assuming that A and B have to be positive integers, then you can list out all of the possibilities (there aren't that many):

3, 9
4, 8
5, 7
6, 6
7, 5
8, 4
9, 3
10, 2
11, 1

Here we have 9 possible pairs of numbers.

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Rich

Last edited by [email protected] on Fri Jul 11, 2014 10:20 am, edited 1 time in total.

Contact Rich at [email protected]

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netdiag2015: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Wed Feb 26, 2014 10:56 am; Thanked: 1 times

by netdiag2015 » Fri Jul 11, 2014 6:57 am

As b must be <=9 so
b value a value
9 3
8 4
7 5
6 6
5 7
4 8
3 9
2 10
1 11
0 12
There are 10 ways

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Fri Jul 11, 2014 7:29 am

how many ways i select a+b=12 where 0<=a, b<=9

For any linear equation (where (a,b,c...>=0)

The number of Whole Number solutions is given by (n+r-1)C(r-1)

Where n = Sum of all the variables
and r = Number of Variables

Here,
Since b<=9 therefore a>=3
So If we assign 3 to a in the beginning then we have to distribute remaining (12-3=9) between a and b

Therefore, n = 9 and r = 2
Therefore, The number of Whole Number solutions of the given equation is (9+2-1)C(2-1)

i.e. (10)C(1) = 10 Answer

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Fri Jul 11, 2014 7:39 am

For any linear equation (where (a,b,c...>=0)

The number of Whole Number solutions is given by (n+r-1)C(r-1)

Where n = Sum of all the variables
and r = Number of Variables

This method is essentially beneficial for questions as mentioned below

Questions: A fruit vendor want to prepare the fruit baskets using Apple, Bananas and Cherries. He wants to ensure that every basket has 8 Fruits. How many different baskets can be prepared if a basket with a different composition of No. of fruits of any one type is considered a different basket.

Solution: A+B+C=8
A,B,C>=0
n=8, r=3
Total solution = (8+3-1)C(3-1) = (10)C(2)= 45

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Jul 12, 2014 7:12 am

Here, a sum of 12 is to be DISTRIBUTED between 2 integers.
Distribution problems can be solved with the SEPARATOR METHOD.
Examples:

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https://www.beatthegmat.com/lets-have-a- ... 69973.html
https://www.beatthegmat.com/experts-any- ... 82307.html
https://www.beatthegmat.com/algebra-t215423.html

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