A four-digit hexadecimal integer is written on a napkin such that the units digit is illegible. The first three digits are 4, A, and 7. If the integer is a multiple of 17_{10}, what is the units digit?

Question

ganeshie8 · Answer

say the units digit is x : 
$$4A7x$$

notice that 17 = 11 in hexadecimal, so the same divisibility rule for 11 works in hexadecimal too : 

$$(4 + 7) - (A+x)$$ must be divisible by 17

ikram002p · Answer

Hi :)

ganeshie8 · Answer

Hello

ganeshie8 · Answer

$$(4A7x)_{16} \equiv   0 \pmod{17}$$

$$4\times 16^3 + A\times 16^2 +7\times 16^1 + x\times 16^0 \equiv   0 \pmod{17}$$
$16\equiv -1 \pmod{17}$ so 

$$4\times (-1)^3 + A\times (-1)^2 +7\times (-1)^1 + x\times (-1)^0 \equiv   0 \pmod{17}$$

$$-4+ A-7+x \equiv   0 \pmod{17}$$

anonymous · Answer

thanks a ton, gneshie8;  so x= 1, this was easy.. as all ques. are after you solve them

ganeshie8 · Answer

yes x=1 :)