212 x 5 is a multiple of 3 and 11. Find the value of x.
Solution:
If a number is divisible by 3 the sum of its digits is divisible by 3
2 + 1 + 2 + x + 5 will be divisible by 3
10 + x will be divisible by 3 when
x = 2, or 5, or 8
But for the number to be divisible by 11 the difference of the sum of digits in odd places and even places is either zero or multiple of 1111
2 + 2 + 5 - (1 + x) = 0
x = 8
Or
1 - (2 + 2 + 5) = 11
x = 20
But x has to be a single digit.
Hence x = 8
✦ Try This: If a four digit number ABBA is divisible by only one two digit number 11 what is the value of A and B?
Since 11 is the only two digit number which can divide ABBA then multiply 11 by 11 till we get a four digit number.
11 × 11 = 121 which is a three digit number
11 × 121 = 1331
The four digit number is 1331 that is only divisible by only one two digit number i.e. 11.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 16
NCERT Exemplar Class 8 Maths Chapter 13 Problem 62
212 x 5 is a multiple of 3 and 11. Find the value of x.
Summary:
212 x 5 is a multiple of 3 and 11, the value of x is 8
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