3 digit integers

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3 digit integers

by kartikshah » Fri Jul 27, 2012 5:55 pm
What is the sum of all 3 digit positive integers that can be formed using the digits 1, 5, and 8, if the digits are allowed to repeat within a number?

A. 126

B. 1386

C. 3108

D. 308

E. 13986

My working:
3 spots: d1, d2, d3
d1 = 3 ways
d2 = 3 ways
d3 = 3 ways
total 27 ways in which number can be made using the given three digits.

So, the sum will have (9*1)+(9*5)+(9*8) = an 8 in the unit's digit.

But how do I choose between 3108 and 308?

Is there another way to solve?[/b]
Source: — Problem Solving |

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by eagleeye » Fri Jul 27, 2012 6:08 pm
kartikshah wrote:What is the sum of all 3 digit positive integers that can be formed using the digits 1, 5, and 8, if the digits are allowed to repeat within a number?

A. 126

B. 1386

C. 3108

D. 308

E. 13986

My working:
3 spots: d1, d2, d3
d1 = 3 ways
d2 = 3 ways
d3 = 3 ways
total 27 ways in which number can be made using the given three digits.

So, the sum will have (9*1)+(9*5)+(9*8) = an 8 in the unit's digit.

But how do I choose between 3108 and 308?

Is there another way to solve?[/b]
Total numbers = 3*3*3= 27.
Each digit is at 100s, 10s, and 1s place equal to 27/3 = 9 times. Hence:
Sum = 100*9*(1+5+8)+10*9*(1+5+8)+9*(1+5+8)
= 111*9*14
= 999*14
= 13986
E is correct. :)

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by kartikshah » Fri Jul 27, 2012 6:14 pm
I conveniently forgot about the hundreds, tens places!!
Thanks!