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# 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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