Sum of numbers

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bosky: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Sat Nov 27, 2010 11:39 am

by bosky » Sun Dec 12, 2010 6:50 pm

Hello,

I am not find understanding the example from Kaplan 2011 Premier on Sum of numbers. It says sum = average * number of terms. I am having trouble with example on Pg 247:

What is the sum of all 27 3 digit integers that can be created by 1,2 & 3?

The solution calculates average of these numbers as (111+333)/2. Why is the average as given when clearly the group of these numbers is not consecutive. eg if I had 3, 6 & 18 and I had to average of these 3, the average is not is not the same as (3+18)/2...

Thanks,
Bosky

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Source: Beat The GMAT — Problem Solving | Sun Dec 12, 2010 6:50 pm

Tani: Legendary Member; Posts: 1255; Joined: Fri Nov 07, 2008 2:08 pmFollowed by: 90 members; Location: St. Louis; Thanked: 312 times

by Tani » Sun Dec 12, 2010 8:12 pm

First think about how the 27 numbers you need to sum are derived.

Look at the 100s digit. There will be nine numbers that start with 1, 9 starting with 2 and 9 starting with three. When you add these you get: 9*1 + 9*2 + 9*3 = 54 for 54 100s.

You get the same in the tens and units digits. The sum of all 27 numbers will be 54*100 + 54*10 + 54*1 = 5,994

Divide that by 27 and you get 222.

Tani Wolff

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bosky: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Sat Nov 27, 2010 11:39 am

by bosky » Mon Dec 13, 2010 8:49 am

Thanks Tani. Is there any other way to solve these problems?

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KapTeacherEli: GMAT Instructor; Posts: 578; Joined: Tue Aug 25, 2009 6:00 pmFollowed by: 62 members; Thanked: 136 times

by KapTeacherEli » Mon Dec 13, 2010 3:03 pm

Hi bosky,

There actually isn't another way to solve it aside from Tani's. The solution you quoted from the GMaT Premier 2011 is scheduled for revision the next printing; sorry for the confusion it may have caused.

Fortunately, Tani's solution is quick, efficient, and a great way to crack this type of problem. And although Kapln does occasionally make mistakes, we take pride in our solutions and strategies, so don't let this error deter you from using the mathematical shortcuts and rules for actual consecutive sets. I checked those personally, and I can assure you that they're error free and extremely valuable!

Let me or Tani know if there is anything else we can do to help you, and thanks for choosing Kaplan.

Eli Meyer
Kaplan GMAT Teacher
Cambridge, MA
www.kaptest.com/gmat

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bosky: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Sat Nov 27, 2010 11:39 am

by bosky » Mon Dec 13, 2010 9:37 pm

Thanks Tania and Eli for help in this question. The solution does make sense.

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