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Divisibility

Q.No: 1
Test Name : CAT 2018 Actual Paper Slot 1

The number of integers x such that 0.25 < 2x < 200, and 2x +2 is perfectly divisible by either 3 or 4, is

Solution:
Q.No: 2
Test Name : CAT Actual Paper 2020 Slot-3

How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?

A
41
B
42
C
43
D
40
Solution:
Q.No: 3
Test Name : CAT Actual Paper 2022 Slot-1

Let A be the largest positive integer that divides all the numbers of the form 3k + 4k + 5k, and B be the largest positive integer that divides all the numbers of the form 4k + 3(4k) + 4k+2, where k is any positive integer. Then (A + B) equals

Solution:
Q.No: 4
Test Name : CAT Actual Paper 2022 Slot-2

For some natural number n, assume that (15,000)! is divisible by (n!)!. The largest possible value of n is

A
4
B
6
C
7
D
5
Solution:
We need to find largest possible value of ‘n’ such
that (n!)! divides 15000! for that n! < 15000
Note: 7! = 5040 and 8! = 40320 > 15000
which implies 15000! is not divisible by 40320!
Therefore, maximum value n can take is 7.
Q.No: 5
Test Name : CAT Actual Paper 2023 Slot 2

For any natural numbers m, n, and k, such that k divides both m + 2n and 3m + 4n, k must be a common divisor of

A
m and n
B
m and 2n
C
2m and 3n
D
2m and n
Solution:
Solution:


Solution:


Solution:


Solution:
We need to find largest possible value of ‘n’ such
that (n!)! divides 15000! for that n! < 15000
Note: 7! = 5040 and 8! = 40320 > 15000
which implies 15000! is not divisible by 40320!
Therefore, maximum value n can take is 7.


Solution:


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