Question

What is the sum of all the possible three-digit numbers that can be constructed using the digits 3, 4, and 5 if each digit can be used only once in each number?

• A. $3224$
• B. $2664$
• C. $1778$
• D. $1336$

Answer 1

Answer: (B)

$2664$

There are 6 ways in which to arrange these digits: 345, 354, 435, 453, 534, and 543. Notice that each digit appears twice in the hundreds column, twice in the tens column, and twice in the ones column. Therefore, you can use your knowledge of place value to find the sum quickly. Because each digit appears twice in the hundreds column, you have 3 + 3 + 4 + 4 + 5 + 5 = 24 in the hundreds column. If you multiply 24 by 100, you get the value of all of the numbers in that column. Repeat this reasoning for the tens column and the ones column:100(24) + 10(24) + (24) = 2,400 + 240 + 24 = 2,664.