Find this digit

Number Theory Level 2

Let $y$ denote a single-digit integer. The tens digit in the product of $\overline{2y7}$ and $39$ is $9$ . Find $y$ .

The answer is 8.

3 solutions

Chew-Seong Cheong
Mar 22, 2020

$\overline{2y7} \times 39 = 39(207+10y) = 8073+390y$

For the tens digit to be $9$ , we have $7+9y \equiv 9 \text{ (mod 10)}$ . $\implies 9y \equiv 2 \text{ (mod 10)}$ and $y = \boxed 8$ .

tens digit to be * $9$ .

Vilakshan Gupta - 1 year, 2 months ago

Thanks. Why don't you learn to use LaTex. I have been editing your problems. Members will read your problems and solutions if they are in LaTex.

Chew-Seong Cheong - 1 year, 2 months ago

I use LaTex already. You just modify my problems slightly in a different format...and that's all ! You know sometimes I feel that I also could modify other's problems when they are badly written...lol.

Vilakshan Gupta - 1 year, 2 months ago

Chris Lewis
Mar 22, 2020

$(207+10y) \times 39 = 8073+390y$

The tens digit of this is the units digit of $7+9y$ . Since we want this to be $9$ , we want the units digit of $9y$ to be $2$ ; this happens when $y=\boxed8$ .

Srinivasa Gopal
Mar 22, 2020

(200 + 10y + 7)* 39 = 7800 + 390y + 273 = 8073 + 390y as 0<=y<=9 the different possible values of (8073 + 390y) for y =0,1,...9 are 8463,8853,9243,9633,10023,10413, 10803,11193 and 11583. This implies that y = 8

Find this digit

The answer is 8.

3 solutions

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