Page 309 - Start Up Mathematics_8 (Non CCE)

Example 6: Given that the number 1372x413 is divisible by 11, where x is a digit, find the value of x.
Solution: Given number = 1372x413

Sum of digits at odd places = 1 + 7 + x + 1 = 9 + x
Sum of digits at even places = 3 + 2 + 4 + 3 = 12
Difference = (x + 9) – 12 = x – 3
Given, 1372x413 is divisible by 11.

fi x – 3 is divisible by 11.
fi x – 3 = 0 or 11 or 22 or 33 and so on.
x – 3 = 0 fi x = 3 ; x – 3 = 11 fi x = 14
x – 3 = 22 fi x = 25 and so on.
Since x is a digit, so x = 3.

EXERCISE 19.2

1. Give three numbers which are divisible by 2 but not by 4. Is there any number which is divisible by
4 but not by 2?
2. Give two examples of a number which is divisible by: (a) 3 but not 9 (b) 2 but not 6 (c) 2 and 4
but not 8
3. Form all the possible 3-digit numbers using the digits 2, 3 and 4 which are divisible by (a) 2 (b) 3.
4. Which of the given numbers are divisible by (a) 5, (b) 10: 35, 142, 200, 750, 109, 625, 130
5. If 31z5 is a multiple of 3, where z is a digit, then what might be the value(s) of z? (NCERT)
6. If a number 43y is a multiple of 9, where y is a digit, then find the value of y.

Letters for Digits
Here we have number puzzles with letters instead of digits in an arithmetic sum and the aim is to find out
which letter represents which digit.
The two important rules for cracking the code of these puzzles are:
(1) Each digit is represented by just one letter. (2) The first digit of the number cannot be zero.
Example 7: Solve the following: (NCERT)

(a) 2 A B (b) A B
+ A B 1 ¥ 6
B 1 8 B B B

Solution: (a) Step 1: Step 2: A + 7 = 1
Starting from ones column, Now 7 + 4 = 11 (1 remains in ones place and

we have B + 1 = 8. 1 of tens place is carried forward)
fi B = 8 – 1 = 7 (as B is a digit) \ A = 4
1
\ 2 A 7
+ A 7 1 + 2 4 7
1
7
4
7 1 8
7 1 8
\ A = 4, B = 7
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