A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. What will be the remainder when th

[BTGModeratorVI]

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: Veritas Prep

[Scott@TargetTestPrep]

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

Solution:

We need to find a number that, when divided by 4, leaves a remainder of 1, and when the quotient from this division is divided by 5, a remainder of 4 remains. Let’s represent this number by n.

Since our number produces a remainder of 1 when divided by 4, it must be true that n = 4p + 1 for some integer p.

Since the quotient from the previous division, which is p, produces a remainder of 4 when divided by 5, we have p = 5q + 4. Let’s substitute this expression for p into the previous equation:

n = 4p + 1

n = 4(5q + 4) + 1

n = 20q + 16 + 1

n = 20q + 17

Finally, since 20q is divisible by 20, the remainder from the division of n by 20 is 17.

Answer: E