BTGModeratorVI wrote: ↑Wed Dec 16, 2020 12:35 pm
A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. What will be the remainder when this number is divided by 20?
(A) 0
(B) 3
(C) 4
(D) 9
(E) 17
Answer:
E
Source: Manhattan prep
When it comes to remainders, we have a nice rule that says:
If N divided by D, leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
A number when divided successively by 4 leaves a remainder 1
Possible values of the number are: 1, 5,
9, 13, 17, 21,...
A number when divided successively by 5 leaves a remainder 4
Possible values of the number are: 4,
9...STOP!
Both lists contain
9, so this could be the number.
What will be the remainder when this number is divided by 20?
9 divided by 20 = 0 with
remainder 9
Answer: D
Cheers,
Brent
