Easy Digits & Decimals

[shonen]

Hey All,

Just starting out on my GMAT studies and I'm a bit rusty with the math section. I'm working on/looking over the digits and decimals chapter in Manhatten GMAT prep and was wondering if someone can give me help with the question below -

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

The solution states: There are 6 ways in which to arrange these digits: 345, 354, 435, 453, 534, 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:

100 (24) + 10 (24) + (24) = 2400 + 240 + 24 = 2664.

I follow most of the solution, but was wondering where they got the number 24 from? Thanks in advance for any help.

[clock60]

Originally Posted by shonen

Hey All,

Just starting out on my GMAT studies and I'm a bit rusty with the math section. I'm working on/looking over the digits and decimals chapter in Manhatten GMAT prep and was wondering if someone can give me help with the question below -

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

The solution states: There are 6 ways in which to arrange these digits: 345, 354, 435, 453, 534, 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:

100 (24) + 10 (24) + (24) = 2400 + 240 + 24 = 2664.

I follow most of the solution, but was wondering where they got the number 24 from? Thanks in advance for any help.

it is not too difficult
as we have 3 digit we have 3! =6 numbers
345
354
435
453
534
543
just sum the digit in every column
5+4+5+3+4+3=10+8+6=24

[shonen]

That makes good sense, I actually remember that rule.. just a bit rusty. Thanks again.

[Dr_GMAT]

Good explanation

[Crack_Mat]

nice one!