SOLUTION: A 3-digit number when divided by 5 has an even quotient. When it is divided by 3, it also has an even quotient. a. what is the digit in the ones place? b. what can the number

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Question 654624: A 3-digit number when divided by 5 has an even quotient. When it is divided by 3, it also has an even quotient.
a. what is the digit in the ones place?
b. what can the number be?
(5th grade math and already we are having problems--eeks)

Found 2 solutions by solver91311, Edwin McCravy:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Not sure what you mean by an "even" quotient.

Do you mean that 5 divides the number evenly, or

the quotient is an even number, or

both?

Clarify.

John

My calculator said it, I believe it, that settles it
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Answer by Edwin McCravy(20063) About Me  (Show Source):
You can put this solution on YOUR website!
It has to be a multiple of 5.  All multiples of 5 either 
end in 0 or 5.  Since it has to be even it has to end in 0,
since if it ended in 5 it would be odd.

Therefore the answer to this 

a. what is the digit in the ones place?
must be 0, because the digit on the right end of the number is the
ones digit.


b. what can the number be?
Since it ends with a zero it is divisible by 10. So if you divide 
it by 10, the quotient will be a 2-digit number which is the same 
as the number without the 0 on the right end.  

But the quotient will still be divisible by 3.   

So the number could be any two digit number that is a 
multiple of 3 with a 0 on the right end of it for its ones digit.  

The smallest 2-digit number that is a multiple of 3 is 12, so the 
smallest the number could be is 120.  

The largest 2-digit number that is a multiple of 3 is 99, so the 
largest the number could be is 990. 

So it could be any of these thirty 3-digit numbers:

120, 150, 180, 210, 240, 270, 300, 330, 360, 390,
420, 450, 480, 510, 540, 570, 600, 630, 660, 690,
720, 750, 780, 810, 840, 870, 900, 930, 960, 990.

Edwin