number theory problems

MBA CAT 2023
1

The squares of 3 consecutive terms of an arithmetic progression are a336, a and a+624. What is the value of a?

2

The squares of 3 consecutive terms of an arithmetic progression are a−336, a and a+624. What is the value of a?

3

Evaluate

(8^4+64)(16^4+64)(24^4+64)(32^4+64)(40^4+64)(48^4+64)(56^4+64)(64^4+64)/((4^4+64)(12^4+64)(20^4+64)(28^4+64)(36^4+64)(44^4+64)(52^4+64)(60^4+64))

4

All the digits of a 50 digit positive number are 4 except for the nth digit.If the number is divisible by 13 for some choice of that nth digit, then howmany possible values can n have?

5

All the digits of a 50 digit positive number are 4 except for the nth digit.If the number is divisible by 13 for some choice of that nth digit, then howmany possible values can n have?

6

The base 6 representation of 0.3333333............. is?

7

Find the remainder when 15! is divided by 17

  • 2
  • 3
  • 4
  • 1

0 voters

8

Find the last digit of 112^112^112^112.........

  • 8
  • 2
  • 6
  • 4

0 voters

9

What is the remainder when 167*234*99*347 by 77?

10

what is the highest value of x in the expression (167!)/(24!)^x to yield an integral answer?

a.7
b.8
c.9
d.6
correct ans is 7.plz give soln.....mg
11

can v apply remainder theorem for question:

what will be the remainder when 2^89 is divided by 89?

12

can someone please provide some basic funda material on number theory for CAT