Question

For positive integers x, let ♮x be defined as the remainder when x is divided by 3. Which of the following is equal to ♮11?

a. ♮16-♮5
b. ♮15-♮4
c. ♮14-♮3
d. ♮13-♮2
e. ♮12-♮1

Answer 1

what kind of symbol is that?

Answer 2

if you divide 11 by 3 the remainder is 2

Answer 3

its a natural note symbol. the SAT question just had it ;_;

Answer 4

so you have a bunch of work to do to see which of the above is equal 2

Answer 5

for example
\[ ♮16-♮5\] is the same as \(1-2=-1\)

Answer 6

wait, why does ♮16 = 1

Answer 7

which is in fact equal to 2 mod 3, but i am not exactly sure if that is what you want

Answer 8

\(♮16 = 1\) because if you divide 16 by 3, the remainder is 1

Answer 9

i.e. 3 goes in to 16 five times, with a remainder of 1

Answer 10

so ♮x isn't the remainder?

Answer 11

it is the remainder, yes

Answer 12

that is why \( ♮16=1\)

Answer 13

oh, okay. i think i get it xD

Answer 14

the next one is
\[ ♮15-♮4=0-1=-1\]

Answer 15

ohhh.

Answer 16

ty :)

Answer 17

\[ ♮14-♮3=2-0=2\] that is probably the one you want

Answer 18

thx again. :]

Answer 19

yw