Question

When n is divided by 14, the remainder is 10. What is the remainder when n is divided by 7? Can you explain how to do pls. thanks!

Answer 1

n mod 14 =10
n=14t+10
n=7k+5

thus n mod 7=5

got it ?

Answer 2

thank you. answer in PSAT book is actually 3. Says - you 1st have to pick a # for n. Easiest strategy is to pick n=24 (because 14 +10=24). Now try your number out: 24 divided by 7=3r3. So remainder answer is 3. This doesn't make sense to me but this is what the book says - can you explain? tks.

Answer 3

this is the way I did it:
\[\frac{n}{14}=Q_1+\frac{10}{14} \text{ \implies } \frac{n}{7}=2Q_1+\frac{10}{7}=2Q_1+\frac{7}{7}+\frac{3}{7}=(2Q_1+1)+\frac{3}{7}\]

Answer 4

I multiply the first equation by 2 on both sides

Answer 5

when n is divided by 7 the quotient is 2Q_1+1 and the remainder is 3
where Q_1 was the quotient when was divided by 14

Answer 6

when n was divided by 14*

Answer 7

mmmm are u sure its 3 ?
i tried this to get 3 but not sure if its correct
n mod 14=10 =-4
-4 mod 7=3

@ganeshie8 what do u think ?

Answer 8

yup - sure it's 3. what is mod?

Answer 9

example:
let's take your n=24
\[\frac{24}{14}=1+\frac{10}{14} \\ \text{ mutliply both sides by 2 ->} \frac{24}{7}=2(1)+\frac{10}{7} \\ \frac{24}{7}=2(1)+\frac{7}{7}+\frac{3}{7}=2(1)+1+1+\frac{3}{7}=[2(1)+1]+\frac{3}{7}\]
and just as i said the remainder 3

Answer 10

2(1)+1 is 3
that is the quotient when dividing 24 by 7
and 3 is the remainder

Answer 11

but we really didn't need that example to find the remainder

Answer 12

wait lol yeah im sure now its 3
see
n=14t + 10
now 14t/7=m + remainder 0
10/7=1 + remainder of 3
so 0+3=3

ok for sure its 3 ^_^