08-08-2014, 11:55 PM
A 4 digit prime no when divided by 24 leaves a remainder r. how many possible values can r take ?
a)7
b)8
c)9
d)10
answer choice b
solution
24k+r=prime
r is not equal to 0
r can be 1
if r=2 then 24k+r will multiple of 2
24k+3=3(8k+1)
r has to be coprime with 24
r can be 1,5,7,11,13,17,19,23
8 values totally nothing pi (24)
a)7
b)8
c)9
d)10
answer choice b
solution
24k+r=prime
r is not equal to 0
r can be 1
if r=2 then 24k+r will multiple of 2
24k+3=3(8k+1)
r has to be coprime with 24
r can be 1,5,7,11,13,17,19,23
8 values totally nothing pi (24)