Question

how many positive integars less than 50 have remainder 2 when divided by 13

Answer 1

what do you think

Answer 2

just type in 13 s table n add 2 to it
13+2,
26+2
39+2
hence 3

Answer 3

Basically this is a counting problem that is asking for positive integers that satisfy the following inequality:\[\bf \frac{ x }{ 13 }=k + \frac{2}{13} < \frac{ 50 }{ 13 }, \ k \in \mathbb{Z^+} \]\[\bf \implies x = 13k+2 < 50\]\[\bf \implies x = 13k < 48\]How many positive integers ''k" do there exist such that 13 times k is smaller than 48? You can either do that by hand similar to how @chandanjha did it or observe that:\[\bf k < \frac{ 48 }{ 13 } = 3.692\]Since \(\bf k\) is a positive integer less than 3.692, there is only 3 positive integers that would satisfy the inequality: 1, 2, 3.

Doing it the way @chandanjha is easier in the sense that its more obvious to see what the question is asking and how the answer is to be arrived at.

@helpsat

Answer 4

maybe u took the long route @genius12

Answer 5

@chandanjha I only posted this way to have more than 1 way posted here of doing it lol.

Answer 6

obviously 13*4=52 the only answers we can get are less than 4

Answer 7

ya ok lol i get it...