playing with numbers

1. B.J.P
.S Samiti’s
M.V.HERWADKAR ENGLISH MEDIUM HIGH SCHOOL
Playing with numbers
Program:
Semester:
Course: NAME OF THE COURSE
Mahalakshmi uppin

2. PLAYING WITH NUMBERS
•Numbers in general form
•Letters for digits
•Tests of divisibility
2

3. NUMBERS IN GENERAL FORM
1. The General Form of a Two Digit Number
ab = a × 10 + b = 10a + b
Example
93 =
2. The General Form of a Three Digit Number
abc = 100 × a + 10 × b + c = 100a + 10b + c
Example
256 =
=
Remark: ab doesn’t mean a × b as we generally use it like this.ab
means digits
3

4. LETTERS FOR DIGITS
In this type of puzzles, the letter represents the digits and
we have to crack the code. Generally, it has puzzles
related to addition and multiplication.
Some important rules related to such types of puzzles:
•Every letter can represent only one digit and the vice-
versa.
•The first digit cannot be zero Like 25 cannot be written
as 025 and 0025.
•Every puzzle must have only one solution.
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5. EXAMPLE:
5

6. EXERCISE 1.1
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7. TESTS OF DIVISIBILITY
Divisibility by 2:
If the number ends with an even number
i.e. 0, 2, 4, 6 and 8 then it will always be divisible
by 2.
Example :Check the number 23 and 630 are divisible by 2 or
not.
Solution:
7

8. DIVISIBILITY BY 3 AND 9
If the sum of all the digits of the given number is
divisible by 3, then that number will also be divisible
by 3 and 9.
Example
Check the number 232 and 6300 are divisible by 3 and 9 or
not.
Solution:
•232 is not divisible by 3 as its sum of the digits i.e. 2 + 3 + 2
= 7 is not divisible by 3 and 9.
•630 is divisible by 3 as its sum of the digits i.e 6 + 3 + 0 = 9
is divisible by 3 and 9. 8

9. DIVISIBILITY BY 4:
If the last two digits of the number are divisible by 4
then that number will also be divisible by 4.
Example
Check the number 1748 and 258 are divisible by 4 or not.
Solution:
• 1748 is divisible by 4 as the last two digits 48 is divisible by 4.
• 258 is not divisible by 4 as the last two digits 58 is not
divisible by 4.
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10. DIVISIBILITY BY 5
If the number ends with ‘0’ or ‘5’ then it will
always be divisible by 5.
Example
Check the number 23 and 630 are divisible by 5 or not.
Solution:
•23 is not divisible by 5 as its one’s digit is 3.
•630 is divisible by 5 as its one’s digit is 0.
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11. EXERCISE 1.2
1. If 21y5 is a multiple of 9, where y is a digit, what is the
value of y?
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12. 2. If 31z5 is a multiple of 9, where z is a digit, what is
the value of z?
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13. 3. If 24x is a multiple of 3, where x is a digit, what is
the value of x?
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14. 4. If 31z5 is a multiple of 3, where z is a digit, what
might be the values of z?
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