Divisibility Rule for Composite Numbers

Q. The L.C.M of two numbers is 120 and their H.C.F. is 10. Which of the following can be the sum of those two numbers?

1. 224
2. 140
3. 80
4. 70
5. 60

Q. If a number 774958A96B is to be divisible by 8 and 9, the respective values of A and B will be :

(CAT 1996)

1. 5 and 8
2. None of these
3. 7 and 8
4. 8 and 0

Q. Digit sum of a number is defined as the sum of the digit till a single digit number is obtained.N = 2! +3! +4! + 5! +……………….10 !. Find the digit sum of N ?

1. 8
2. 9
3. 1
4. 5

Q.

If m and n are whole numbers such that n>1 and m${}^n$ = 121, then the value of (m - 1)${}^{n+1}$ is :

1. 1

2. 10

3. 121

4. 1000

5. 14400

Q. Let A and B be digits (that is, A and B are integers between 0 and 9 inclusive). If the product of the three-digit integers 2A5 and 13B is divisible by 36, determine the number of possible ordered pairs (A, B).

1. 3
2. 4
3. 1
4. 0
5. none of these

Q. 100 - Sum of first 9 odd natural numbers = ___ .

Q.

In a two-digit number, if two is added to the digit in ten's place, the number formed will have ten's place digit which is 0.6 times the original one and unit's digit which is four times more than the initial digit in unit's place. The difference between the digits in ten's place and that in unit's place is

1. 0.

2. Positive and divisible by 4

3. Negative and divisible by 4

4. Positive and divisible by 5

5. None of these

Q.

If $3m-5m=-1$ and $2m=n-3$ find the value of $(3m+5n)$ and $(m+2n)$.

1. 11, 4

2. -11, -4

3. -1, -2

4. 2, 11

5. -1, 2

Q.

What is the difference between any $2$ consecutive multiples of $17$?

Q.

If m and n are whole numbers such that n>1 and m${}^n$ = 121, then the value of (m - 1)${}^{n+1}$ is :

1. 10

2. 121

3. 1000

4. 14400

Q. Remainder when 9999999 is divided by 11 is ______________.
___

Q.

Find the number of five digit positive integers divisible by 3 that can be formed using the digits 0, 1, 2, 3, 4 and 5, without repeating any of the digits.

1. 216

2. 240

3. 96

4. 120

5. 186

Q. If n is an integer, how many values of n will give an integral value of$\frac{(16n^z+7n+6)}{n}?$ (CAT 1997)

1. 2
2. 3
3. 4
4. None of these

Q. What is the remainder when $4^{96}$ is divided by 6? (CAT 2003)

1. 0
2. 2
3. 3
4. 4

Q. What is remainder when $7^{84}$ is divided by 2402?

1. 6
2. 2401
3. None of these
4. 1

Q. If $x=({16}^3+{17}^3+{18}^3+{19}^3)$, then $x$ divided by $70$ leaves a reminder of? (CAT 2005)

1. 0
2. 1
3. 69
4. 35

Q.

The number of two digit numbers which are divisible by 2 or 3 is

1. 60

2. 68

3. 62

4. 65

Q.

If $A=3^{46},B=3^0+3^1+3^2+3^3+3^4+3^5+3^6+.........+3^{46},$ then A-B =

1. 3

2. 1

3. None of these

4. 0

Q.

If $A=2^{46},B=2^0+2^1+2^2+2^3+2^4+2^5+2^6+.........+2^{45}$, then which of the following is true?

1. A>B

2. Both B and C

3. A < B

4. A-B =2

Q.

Find the number of two digit numbers which are divisible by 2 and 3?

1. 16

2. 15

3. 19

4. 17

Q. A 32-digit number has all 9’s. Find the remainder when the number is divided by 111.

1. 11
2. none of these
3. 1
4. 99
5. 9

Q.

The remainder when 513513 is divided by 13 is _____________.

Q. N=9876543298765432.........82 digits. Find the remainder when N is divided by 34?

1. 0
2. 1
3. 15
4. 30
5. -1

Q.

The value of a two digit number remains same even if it is reversed. The remainder left when the number is divided 11?

1. 4

2. 0

3. 1

4. 2

5. 3

Q.

What is the remainder obtained when 96! + 97! Is divided by 9506 is

1. 1

2. 96

3. 97

4. 0

Q.

The remainder when 124124 is divided by 11 is _____________.

Q. Show that the function defined by $g\left(x\right)=x-\left[x\right]$ is discontinuous at all integral point. Here $\left[x\right]$ denotes the greatest integer less than or equal to $x$.

Q.

The remainder obtained when the denominator of a fraction is divided by the numerator is zero. If 2 is added to the numerator the fraction becomes $\frac{1}{2}$. The original fraction is

1. 1/2

2. 3/4

3. 1/4

4. 1/6

5. 7/30

Q. Remainder when 15742386 is divided by 9 is ___.

Q.

The remainder obtained when the denominator of a fraction is divided by the numerator is zero. If 2 is added to the numerator the fraction becomes $\frac{1}{2}$. The original fraction is

1. 

2. 

3. 

4.