math
posted by Lucille
When a positive integer, n, is divided by 24 the remainder is 18. When n is divided by 8 the remainder is:
A.0 B.1 C.2 D.4 E.6
I tried doing n/24=18 and I got 432 and when I divided it by 8 I got 54; am I misinterpreting the question? I really see no other way to do it. Can someone please help me?

Reiny
The smallest value that n could be is 42 (42÷24 = 1 with a remainder of 18)
Adding 24 each time I got the sequence
42 66 90 114 138 162 ...
Now when you divide each of these by 8 you will have a remainder of 2 for each one 
Lucille
sorry, but I still don't get it...

Reiny
ok, let's try this
let N = 24x + 18
for whole number values of x isn't
N = 42,66,90,114,138,162,... ?
24x would give you multiples of 24, that is, all numbers that are exactly divible by 24, so by adding 18 we create a remainder of 18
now try dividing each of those by 8
What did you notice about the remainder? 
Lucille
I get decimals, well, a whole unti and a decimal

Reiny
this is one of the problems in using calculators, they give decimal answers.
try dividing 90 by 24 the old grade school method you learned in grade 4.
Does it not go 3 times with 18 left over?
Now do 90 divided by 8,
isn't that 11 times with 2 left over?
WELL ???? 
Lucille
I still don't think I'm doing this right, am I?

Lucille
I just don't get how I'm supposed to divide 90 by 18 and get a remainder of 2, according to your first reply...

Reiny
According to your own question when you divide by 8 you get a remainder of 2, not when you divide by 18

Lucille
I'm sorry, I'm just trying to figure out a way of actually colsing the problem and nothing seems to work

bobpursley
OK, n is divided by 24 and a remainder of 18.
if divided by 3, you will still have a "remainder"of 18, but that remainder is divisible by 3 twice, giving a final remainder of 2 
Lucille
so sorry, but I don't get how having a reminder works...

DrBob222
I think the point is this.
42/8 = 5 with remainder of 2.
66/8 = 8 with a remainder of 2.
90/8 = 11 with a remainder of 2.
114/8 = 14 with a remainder of 2.
Now read the last sentence of Reiny's response. What do you notice about the remainder? 
Lucille
oh, it makes sense now! thank you all very much! So sorry I had so many people helping me to finally get it, but you are all life savers! :D
Respond to this Question
Similar Questions

math
what is the least common positive integer that meets the following conditions: divided by 7 with remainder 4 divided by 8 with remainder 5 divided by 9 with remainder 6 i thought you could add 7 and 4 to get 13, then divide 13 and … 
math
what is the least common positive integer that meets the following conditions: divided by 7 with remainder 4 divided by 8 with remainder 5 divided by 9 with remainder 6 i thought you could add 7 and 4 to get 13, then divide 13 and … 
Algebra 2
Find a positive integer smaller than 500 that has a remainder of 3 when divided by 5, a remainder of 6 when divided by 9, and a remainder of 8 when divided by 11. 
math
You are given a positive integer such that when the integer is divided by 1995, the remainder is 75. What will the remainder be when the same positive integer is divided by 57? 
number theory
Find the least positive integer that leaves the remainder 3 when divided by 7, remainder 4 when divided by 9, and remainder 8 when divided by 11 
Math
Find the least positive integer that leaves the remainder 3 when divided by 7, remainder 4 when divided by 9, and remainder 8 when divided by 11. Using the Chinese Remainder Theorem. 
Math
How many integers bewteen 200 and 500 inclusive leave a remainder 1 when divided by 7 and a remainder 3 when divided by 4? 
Math
How many integers between 200 and 500 inclusive leave a remainder 1 when divided by 7 and a remainder 3 when divided by 4? 
Math
Find the smallest positive integer that leaves a remainder of 5 when divided by 7, a remainder of 6 when divided by 11, and a remainder of 4 when divided by 13. 
Math
When 14 is divided by 5, the remainder is 4. When 14 is divided by a positive integer n, the remainder is 2. For how many different values of n is this possible. Is listing it out the only way?