Question

A number when divided by 97 leaves remainder 73. Then same number when divided by 83 has quotient 42. Find the remainder in the second case.

Answer 1

@ganeshie8

Answer 2

@mathmate

Answer 3

@Loser66

Answer 4

@confluxepic

Answer 5

@pooja195

Answer 6

@Kainui

Answer 7

@imqwerty

Answer 8

@loser66 hi

Answer 9

Hi, I didn't figure out how to solve it yet!! hehehe my brain is useless.

Answer 10

I have a bunch of solutions so that I don't know how to narrow down the answer.

Answer 11

options are 47,69,79,53

Answer 12

oh, so 79 works

Answer 13

If you have options, that is easy. just put it into the equation to get the answer

Answer 14

Like this: Let n is the given number, then
\(n = 97* t + 73\\n=83*s+ r\)

So, you have \(97t+73 = 83s+r\) then \(97t-83s+73=r\)

We know that \(0\leq r\leq 82\), so we narrow down \(97t-83s =r -73\leq 9\)

Answer 15

in the second case, s=42

Answer 16

Now, start from 9
97t -83s =9,
and (97,83)=1
and then

\(97 = (1)83 +14\rightarrow 14= 97-83\\83=(5)14+13\rightarrow 13=83-(5)14\\14=13+1\rightarrow 1=14-13\)

Go backwark to get \(1=14-(83-(5)14=(6)14-83\\1=(6)(97-83)-83=(6)97-(7)83\)

Answer 17

multiple both sides by 9, you have \(9=(54)97-(63)83\)
Hence that gives you t = 54, s = 63 and r = 82

Answer 18

Take down 1 unit, that is multiple both sides by 8, you have
\(8= (48)97-(56)83\), that gives you t=48, s=56 and r = 81

Answer 19

if you down 2 more units, you have \(6= (36)97-(42)83\)
so t =36, s =42, r = 79 (one of your options)
Now test
n = 36* 97 +73= 3565

n = 42*83 +79= 3565
Bingo

Answer 20

hA ha ha ... great... :)

Answer 21

hehehe... not great at all. It took me so much time to work!!

Answer 22

n/97 =97q+73

n/83=83(42)+r

n/83 =97(35)+91+r

Now 91+r when divided by 97 must give remainder 73 and also r must be less than 83 which gives r=79