# 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?

1. 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

2. Lucille

sorry, but I still don't get it...

3. 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?

4. Lucille

I get decimals, well, a whole unti and a decimal

5. 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 ????

6. Lucille

I still don't think I'm doing this right, am I?

7. 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...

8. Reiny

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

9. Lucille

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

10. 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

11. Lucille

so sorry, but I don't get how having a reminder works...

12. 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?

13. 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

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