Question

If 35x is a multiple of 3, where x is a digit, what is the value of x?​

Answer 1

Answer:

x value is 1

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Answer 2

Answer:

x = 1, 4, 7, 10

Step-by-step explanation:

Given,

35x is a multiple of 3

To find,

What is the value of x

Solution,

We know that the divisibility rule for 3 is that if sum of all the digits of that number is divisible by 3 then that number will be divisible by 3.

As 35x is a multiple of 3,

Then,

3 + 5 + x = 3n [As the sum is divisible by 3, hence we have to equate the sum to 3n where n is a number and not to 3 itself]

As there are two variables, we need two equations to slove them both but we have only one equation so we will slove using trial and error method.

Let n = 1

3 + 5 + x = 3

x = 3 - 8

x = -5

As x is a digit so it can't be negative,

Therefore,

x ≠ -5

Let n = 2

3 + 5 + x = 6

x = 6 - 8

x = -2

As x is a digit so it can't be negative,

Therefore,

x ≠ -2

Let n = 3

3 + 5 + x = 9

x = 9 - 8

x = 1

Hence, one of the solution of x is -1

Let n = 4

3 + 5 + x = 12

x = 4

Hence, other solution of x is 4

Let n = 5

3 + 5 + x = 15

x = 7

Hence, other solution of x is 7

Let n = 6

3 + 5 + x = 18

x = 10

As x is digit in the units digit and a digit is a number with only one digit in the units place

Hence,

x ≠ 10

Also,

n ≥ 6 the x values comes out as a two digit number

Therefore,

$\boxed{\rm The \: solutions \: of \: x \: are \: 1,4,7}$