Taking All the Combinations of 3 Digit Numbers and Adding Them

Q.

The largest four digit number having distinct digits is:

1. $9000$

2. $9786$

3. $9867$

4. $9876$

Q. abc is a three digit number such that sum of its digits is 3.
abc + bca + cab = ?

1. 111
2. 333
3. 222
4. 555

Q.

If sum of the number 985 and two other numbers obtaind by arranging the digits of 985 in cyclic order is divided by 111 , 22 and 37 respectively.

Find the quotient in each case.

Q.

$\text{Show that}527+752+275\text{is exactly divisible by 14.}$

Q.

Soham took a 3 digit number and formed two other 3 digit numbers using the digits of the original number. He then added the three resulting numbers and divided their sum by 37 . He concluded that the result was exactly divisible by 37, no matter what number he chose. Is Soham's statement true or false?

1. True

2. False

Q.

Let $abc$ be a three digit number. Then $abc-cba$ is not divisible by

1. $9$

2. $11$

3. $18$

4. $33$

Q.

Let pqrbe a three digit number. Then, pqr + qrp + rpq will not be always divisible by

1. 9

2. 37

3. 3

4. p + q + r

Q.

Circle the numbers which are divisible by $3$.

$81748060720135082$

Q.

If pqr is a three digit number, then pqr + qrp + rpq is not always divisible by .

1. 37
2. 3
3. 9
4. p+q+r

Q.

The sum of 437, 374 and 743 is divisible by 14.

1. False

2. True

Q. If a, b, c are digits and abc + bca + cab = x, then the remainder when x is divided by 111 is 0.

1. False
2. True

Q.

If pqr is a three digit number, then pqr + qrp + rpq is not always divisible by .

1. 37
2. 3
3. 9
4. p+q+r

Q.

The sum of a three digit number and the number formed by the reversal of its digits (if for both the numbers middle digit is 0) is always divisible by 101

1. True

2. False

Q.

Let pqrbe a three digit number. Then, pqr + qrp + rpq is not divisible by:

1. 9

2. 37

3. p + q + r

4. 3

Q.

Write true or false for the given statement:

The number of factors for the given number is finite.

1. True
2. False

Q.

Which of the following numbers have $56$ as a multiple.

$9$

Q.

Take a 3 digit number 'abc'. If we add abc, cab, and bca together then the resulting sum is divisible by:

1. 11 and 3

2. 101 and 3

3. 37 and 7

4. 111, 37, and 3

Q.

Which of the following numbers have $56$ as a multiple.

$8$

Q.

Let pqrbe a three digit number. Then, pqr + qrp + rpq will not be always divisible by

1. 9

2. 37

3. 3

4. p + q + r

Q.

State whether the following statement is True or False

The product of two even numbers is always even.

1. True
2. False

Q.

Let pqrbe a three digit number. Then, pqr + qrp + rpq is not divisible by

1. 9

2. 37

3. 3

4. p + q + r

Q.

The smallest $2$digit number

Q. The sum of all two digit numbers which are not divisible by $2$ or $3$ is

1. $1734$
2. $1482$
3. $1620$
4. none of these

Q.

If pqr is a three digit number, then pqr + qrp + rpq is not always divisible by .

1. 37
2. 3
3. 9
4. p+q+r

Q. The number 19 + 91 is divisble by:

Q.

Take a 3 digit number 'abc'. If we add abc, cab and bca together then the resulting sum is divisible by:

1. 11

2. 111

3. 37

4. 111 and 37

Q. The difference between a 3 digit number and the number formed by reversing its digits is not always divisible by

1. 99
2. 5
3. 9
4. 11

Q. abc, bca and cab are the three numbers formed using three digits a, b and c. Addition of all the three numbers gives a new number. The new number is divisible by _____.

1. 29
2. 41
3. 14
4. 37

Q.

If pqr is a three digit number, then pqr + qrp + rpq is not always divisible by .

1. 37
2. 3
3. 9
4. p+q+r

Q. The sum of the numbers 123, 231 and 312 is divisible by 37.

1. True
2. False