35 tough questions on remainder

Q1. The unit digit of 23 4 x 34 5 x 45 6 x 67 8 x 78 9 is

A1: Unit digits of respective numbers is 4*3*6*6*7 will have unit digit 4.

Answer is 4.

Q2. If 2 n can exactly divide p! then the value of n which is not possible :a. 43              b. 44                  c. 45              d. None of these

A2: We don’t know what’s p!.

Answer is 4.

 Find  the reminders when

Q3. 6 6 6 . . . . . . Infinity is divided by 10.

A3: Answer is 6

Q4. 888222888222. . . . . up to 9235 digits divided by 53

Q5. 1 x 2 + 3 x 4 + 5 x 6 +  7 x 8 + . . . 10 terms divided by 19

Q6.  11 3 + 9 3 is divided by 7 3

A6: Please share shortcut method; however easy calculation, so would have attempted it.

Q7. 4 4 n + 3 is divided by 7a. 0               b. 1                  c. 5                    d. None of these

A7: n=1 gives answer 5.

N=2 gives answer 0.

I am assuming ((44^n)+3). Did I interpret something wrong?

Q8. 3 0 + 3 1 + 3 2 + . . . . .201 terms is divided by 13a. 0              b. 12                  c. 3                   d. None of these

A8: 0, option a.

1+3+9 form a group.

Q9. 1 3 + 2 3 + 3 3 +           1000 3 is divide by 13

A9: Answer is 0.

1000^2 * 1001^2/4 and 1001 is divisible by 13.

Q10. 10 2 + 11 2 + 12 2 +  . . . .  28 2 is divided by 19

A10: Answer is 0.

29*57/2 – 10*19/2

Q11.  21 12 – 12 21 is divided by 7

A11: Answer is 1. Check for (3*4) 21

Q12. 23 32 – 9 is divided by 16

A12: 8

232 = 529

529 mod 16 = 1

Q13. 1 3 + 2 3 + 3 3 + 4 3 +. . 10 terms is divided by 1 2 + 2 2 + 3 2 + 4 2 + . . .10 terms

A13: Answer is 4.

100*121*2 / 4*11*21

Q14. 3 37 + 4 37 is divided by 7

A14: Answer is 0

(3+4) mod 7 = (27+64) mod 7 = (243+1024) mod 7

And so on.

Q15. 10 3 + 9 3 is divided by 12 3?

A15: Please share shortcut method; however easy calculation, so would have attempted it.

Q16. 10 11 12 is divided by 13

A16: Answer is 1.

10^2 gives -4 => 10^8 is -1

Q17.  999 9  is divided by 99 9

Q18. 999 9  is divided by 99 9 an then by 9 9

Q19. 12121212. . .  300 times is divided by 99

Q20.  12233344455555…100 terms divided by  7

Q21.   (10 3 + 9 3)752 is divided 12 12

Q22.  44444 + 3333 is divided by 7

A22: Answer is 1.

Finding individual reminders. (3 ^ 330) will give reminder 1.

Q23. 1! + 2! + 3! +  . . . .70! divided by 100

A23: 1! to 6! Divided by 100;

1+2+6+24+20+20 = 73

Q24.  3456 is divided by 108?

Q25. 1 1 + 2 2 + 3 3 + . . . .100 100 is divided by 4?

A25: 0.

Calculate initial ones, you will see pattern.

Q26. 3 3 3 3 3 3 3 3 3. . .1001 digits. . . . divided by 1001

Q27. 4 + 44 + 444 +. . .100 terms. . divided by  7

Q28. 4 44 is divided by 15.

A28: Answer is 1.

(16 mod 15) is 1.

Q29.  37! 37! Divided by 100

Q30.  17 x 18 x 19 x . . . .  37     divided by 100

A30:Answer is 67

{(37*38/2) – (16*17/2)}/100

Q31.  4 101 is divided by  5

A31: Answer is 4.

4 and 1 is pattern.

Q32.  1 3 + 2 3 +  3 3 + . . . . .99 3  is divided by 10

A32: Answer is 0.

99^2 * 100 ^ 2 / 4

Q33. 2222 5555 + 5555 2222 is divided by 7

Q34. Find the sum of all two-digit numbers that give a reminder 4 when they are divided by 5a. 98,270                  b. 99,270                  c. 1,02, 090

A34: Looks like wrong options. Answer will be

9 * (28 + 17 * 5)

Q35. When 7179 and 9699 are divided by another natural number N, remainder obtained is same. How many values of N will be ending with one or more than zeroes?a. 24               b. 124                   c. 46                       d. None of these