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.

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

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.

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