Question

a number N when divided by a divisor D leaves a remainder of 19. When 3N is divided by D, the remainder is 14. What is the value of D?(a.23 b.37 c.43 d.47)?

Answer 1

We will use this formula:

Dividend = Divisor * Quotient + Remainder

Answer 2

So, in first case...

We have:

\[N = D* Q_1 + 19\]

Answer 3

Any doubt so far?

Answer 4

Similarly for second case:

\[3N = D*Q_2 + 14\]

Answer 5

@debpriya any doubts so far?

Answer 6

nope got it :) ...what after that?

Answer 7

\[\implies 3*D*Q_1 + 57 = D*Q_2 + 14\]

\[\implies D*(Q_2 - 3*Q_1) = 43\]

Answer 8

Now can you guess what we can do after this?

Answer 9

Hint: 43 is a prime number...

Answer 10

hi need help

Answer 11

@kindaljoshconall can you tag me in the question you want help in?

Answer 12

sure

Answer 13

its on science

Answer 14

I can try :)

Answer 15

doesn't matter in what section your question is. you can tag anyone in any section.

Answer 16

kk ty i fanned u

Answer 17

@debpriya any guesses?

Answer 18

none so far :(

Answer 19

No problem, see, 43 is a prime number... thus it will have only two factors 1 and 43...

Also, we have from the equation that D*(Q2 - 3*Q1) = 43 that means D and (Q2 - 3*Q1) are also the factors of 43...

Now, there arise two cases... D = 1 or D = 43...Now, since every number is a multiple of itself, dividing N by 1 should not leave any remainder... Thus, only possibility is D = 43.

Answer 20

If you have any kind of query regarding this solution, please feel free to ask

Answer 21

oh I got it...thank you so much for your help :)

Answer 22

:) Glad to be of help

Answer 23

hes a morning helper lol