If the remainders when three consecutive integers are each divided by 5 are 2, 3, and 4 respectively, which of the following could be the three integers?
a.) 3, 4, 5
b.) 5, 6, 7
c.) 6, 7, 8
d.) 7, 8, 9
e.) 8, 9, 10
I don't understand please explain

Question

If the remainders when three consecutive integers are each divided by 5 are 2, 3, and 4 respectively, which of the following could be the three integers?
a.) 3, 4, 5
b.) 5, 6, 7
c.) 6, 7, 8
d.) 7, 8, 9
e.) 8, 9, 10
I don't understand please explain

anonymous · Answer

let the integers be x,x+1,x+2
x=5m+2
x+1=5m+3,x=5m+2
x+2=5m+4,x=5m+2
here m is an integer.
when m=1
x=5*1+2=7
x+1=5*1+3=8
x+2=5*1+4=9

radar · Answer

@surjithayer Thanks for such a straight-forward solution, I was really making it complicated.  Your logic is so clear.  Note.  It wasn't my problem, but I like to give em a try.