SOLUTION: Numbers are formed using the digits 4,5,6,7 and 8 with no digit being used more than once. How many odd number are less than 700? I got the answer as 15 but was told the answer

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Question 1135440: Numbers are formed using the digits 4,5,6,7 and 8 with no digit being used more than once. How many odd number are less than 700?
I got the answer as 15 but was told the answer is 25. This is my working
First digit is an even number which is either 4 or 6 and last digit is either 5 or 7
thus possible combination is 2*3(ie remaining numbers)*2(ie. possible combination of last digit) = 12
First digit is an odd number ie 5 and last digit is just 7 therefore
possible combination is 1*3*1 = 3
Therefore the answer is 12+3 = 15 possible ways. Is this correct? Thanks

Answer by greenestamps(13198) (Show Source):
You can put this solution on YOUR website!

You read something into the problem that wasn't there -- you only counted the 3-digit numbers....

There are also 1- and 2-digit numbers that satisfy the requirements.

You will find the correct answer is indeed 25.

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The question asks for the number of odd numbers you can make that are less than 700, using the given digits. You found and counted only the 3-digit numbers that satisfy the requirements; the problem didn't specify 3-digit numbers.

5 is an example of a 1-digit number that is odd and less than 700; 67 is an example of a 2-digit number that is less than 700.

And there are more... making 25 the total number of odd numbers that are less than 700 and use only the given digits.