Divisibility Problem

Number Theory Level 1

If the five digit number $\overline{8X357}$ is divisible by 11, what is the value of $X$ ?

2 4 1 3

1 solution

Animesh Basak
Oct 22, 2015

It is a simple problem about divisibility testing by 11. The rule for divisibility by 11 is ADD all ODD position numbers and then SUBTRACT remaining numbers. Then the value you got must be (zero) 0 or divisible by 11. For 8x357; 8+3+7=18; 18-5=13; (13-x) must be divisible by 11 so 13-x=11 , becoz logical nearest recurred number is 11. x=2

Plzz solve it again

Honey Tayyaba - 5 years, 7 months ago

I didn't get this solution

Honey Tayyaba - 5 years, 7 months ago

By Divisibility Rules of 11, if the alternating sum of digits of an integer is divisible by 11, then the integer itself is divisible by 11.

In this case, the number is $8X357$ , so the alternating sum of its digits is $8 - X + 3 - 5 + 7 = 13 - X$ . For $13-X$ to be divisible by 11, then $13-X = 0, 11, 22, \ldots$ . But because $X$ is a single digit integer, then $X=2$ only.

Pi Han Goh - 5 years, 7 months ago

But following that rule you would get 2 single-digit integers, i.e. in 13 - x = 11, x = 2 (single-digit integer) but also in 13 - x = 22 (another multiple of 11, and the 3rd one you put in the parenthesis), x = -9 (a single-digit integer, but negative instead of positive).

I didn't get quite clear that method, and correct me if I'm wrong at any step.

Carlos Mayers - 5 years, 7 months ago

Divisibility Problem

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