# PLAYING WITH NUMBERS

## EXERCISE 5 (A)

1.The sum of the digits of a 2 digit number is 9.The numbers is 6 times the unit digit.Find the number.

2.The sum of the digits of a 2 digit number is 7.If the digits are reserved, the new number increased by 3 less than 4 times the original number. Find the original number.

3.The sum of a number of 2 digits and of the number formed by reversing the digits is 110; and the difference of the digits is 6. Find the number.

4.A certain number between 10 and 100 is 8 times the sum of its digits, and if 45 be subtracted from it the digits will be reserved. Find the number.

5.A number consists of three digits, the right-hand digit being zero. If the left hand and the middle digits be interchanged the number is diminished by 180.If the left hand digit be halved and the middle and right hand digits be interchanged the number is diminished by 454.Find the number.

Hint: let the original number be 100a + 10a + 0, i.e., 100a +10b, then ,by the first condition (100a+10b)-(100b-10a)=a-b=2

By the second condition, new number = 100​$$\times$$​​$$\dfrac{a}{2}+0+b=50a+b$$​ and so ​$$(100a+10a)-(50a+b)=454\Rightarrow 50a+9b = 454$$

## EXERCISE 5 (B)

1.Which of the following numbers are divisible by 2 ?

57, 4, 60, 93, 126, 365, 80, 992

2.Which of the following numbers are divisible by 3 ?

42, 73, 84, 105, 314, 726, 814, 915

3.Which of the following numbers are divisible by 5 ?

30, 49, 75, 210, 305, 640, 704, 985

4.Which of the following numbers are divisible by 9 ?

36, 90, 157, 243, 514, 810, 719, 936

5.Which of the following numbers are divisible by 10 ?

75, 80, 140, 400, 670, 895, 985, 990

## EXERCISE 6 (A)

1.State which of the following sets are finite and which are infinite.

(i) {The men who have orbited the Earth}.

(ii) {The men who have landed on the moon}.

(iii) {The integers between -5 and +5}

(iv) {}

(v) {The infants in your class}.

(vi)

(vii) {The sets of atoms in Earth}

(viii) {The set of multiples of ten}

(ix) {The set of points on a line segment}.

(x) {The set of grains of sand in a small bottle}.

2.Which of the following are singleton sets?

(i) {Capital of India}

(ii) {Mountain peaks more than 800 m high}.

(iii) {}

(iv) {}

3.State which of the following are empty sets ?

(i) {Odd numbers divisible by 2}

(ii) {Prime numbers which are even}.

(iii) {Cubes with 8 faces}.

(iv) {}

(v) {Days with 1440 minutes}.

4.State the cardinal number of the following sets.

(i) P={Planets of our solar system}.

(ii)C={Consonants of the English alphabet}

(iii) K={Letters in the word ‘MADAM’}

(iv)A={}

(v) B={Set of numbers whose square is 16}.

(vi)M={}

5.Determine whether the two sets specified below are equivalent.

(i) {a,b,c,d} and {-3, -7, -8, 0}

(ii) {}

(iii) {}

(iv) A={The even integers x between 1 and 9} and B={The negative integers between -8 and -2}

6.State whether the following pairs of sets are equal or not .

(i)

(ii)

(iii)

(iv)

7.From the following pairs of sets, identify the disjoint and overlapping sets.

(i)

(ii)

(iii)

(iv)

8.Tell whether set A is a subset of set B.

(i)

(ii)

(iii)

(iv)