Examveda
Examveda

Find the remainder when 73 × 75 × 78 × 57 × 197 × 37 is divided by 34.

A. 32

B. 30

C. 15

D. 28

Answer: Option A

Solution(By Examveda Team)

Remainder,
$$\frac{{73 \times 75 \times 78 \times 57 \times 197 \times 37}}{{34}}$$
$$ = \frac{{5 \times 7 \times 10 \times 23 \times 27 \times 3}}{{34}}$$
[We have taken individual remainder, which means if 73 is divided by 34 individually, it will give remainder 5, 75 divided 34 gives remainder 7 and so on.]

$$\eqalign{ & \frac{{5 \times 7 \times 10 \times 23 \times 27 \times 3}}{{34}} \cr & = \frac{{35 \times 30 \times 23 \times 27}}{{34}} \cr & = \frac{{1 \times - 4 \times - 11 \times - 7}}{{34}} \cr} $$

[We have taken here negative as well as positive remainder at the same time. When 30 divided by 34 it will give either positive remainder 30 or negative remainder -4. We can use any one of negative or positive remainder at any time.]

$$\eqalign{ & \frac{{1 \times - 4 \times - 11 \times - 7}}{{34}} \cr & = \frac{{28 \times - 11}}{{34}} \cr & = \frac{{ - 6 \times - 11}}{{34}} \cr & = \frac{{66}}{{34}} \cr & {\text{R}} = 32 \cr} $$
Required remainder = 32

This Question Belongs to Arithmetic Ability >> Number System

Join The Discussion

Comments ( 17 )

  1. Sazzad Hossain
    Sazzad Hossain :
    6 months ago

    Today me and my friend shafiq solve this problem very easily.

  2. Fred Hahn
    Fred Hahn :
    2 years ago

    Kiyara, 3x10 =30

  3. J
    J :
    2 years ago

    I got it.. 32.
    Divide each number by 34.. e.g., 73/34, R(reminder)=5.. like that, u will get... (5*7*10*23*27*3)/34 = 35*23*27*30 / 34. Now 35/34, R=1 and {{23/34 (or) also = - (34/23)=R= - 11}} & -(34/27)=R= -(7).
    (1*(-4)*(-11)*(-7)) / 34 = -(-28)*(-11) /34= [28*(-11)] / 34=
    [(-6)*(-11)]/34 (since, -[(34/28)]=-6) so, finally 66/34= R=32, Q=1._ _

  4. Imran Immu
    Imran Immu :
    2 years ago

    how did 28 came ?

  5. Pijus U
    Pijus U :
    2 years ago

    In this working method, if we take arbitrary combination of the factors from the second step of the above calculation the result varies. So there must be some definite rule for combining the factors. Need the explanation.

  6. Kiyara's World
    Kiyara's World :
    2 years ago

    35×30×23×27
    I don't understood how 30 came here?

  7. Jaglul Kabir
    Jaglul Kabir :
    2 years ago

    Thanks...

  8. Biswajit KUMAR
    Biswajit KUMAR :
    3 years ago

    Nice

  9. K Kùnñål
    K Kùnñål :
    3 years ago

    It's deeply understand this type of math n trick

  10. Bishal Saren
    Bishal Saren :
    5 years ago

    Understood the math

  11. Sukhdev Chandrahas
    Sukhdev Chandrahas :
    5 years ago

    Sir please shoot your video then it would be easy to understand

  12. Phernaki Mawlong
    Phernaki Mawlong :
    5 years ago

    First divide all the number by 34 after getting the remainder multiplying all the remainder and then divide that by 34

  13. Anju Napit
    Anju Napit :
    5 years ago

    nice

  14. Maha Lakshmi
    Maha Lakshmi :
    5 years ago

    Pls explain easily...&how to come answr with minus in this solution...

  15. Raj Kumar
    Raj Kumar :
    6 years ago

    we have to multipy the unit digits of all the given numbers. we got 0 as the unit digit. And we have to divide with the unit digit of 34 i.e. 4 and obviously, we will get the reminder as 2.The only option having unit digit as 2 is option A.

  16. SONALI CHOUHAN
    SONALI CHOUHAN :
    6 years ago

    Can you explain short trick for such type of questions

  17. Ami Raheja
    Ami Raheja :
    6 years ago

    kindly someone pls explain me why minus came into picture

Related Questions on Number System