GMATPrepNow wrote:
Bunuel wrote:
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
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 1Possible values of the number are: 1, 5,
9, 13, 17, 21,...
A number when divided successively by 5 leaves a remainder 4Possible 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 9Answer: D
Cheers,
Brent
I think the keyword here is that the number is divided
successively .
Let x be the number which when successively divided by 4 and 5 gives 1 and 4 as remainder.
1. When we first divide the number by 4 .
x = 4y +1
where y is quotient from the first division
2. Now as the division is done successively , we divide the quotient from the first step by 5
y= 5z +4
where z is quotient from the second division
If Z=1 ,
y = 9
x= 9*4 + 1
= 37
Now , on dividing the by 20 , we get 17
Answer E
Alternatively , we can also proceed from the final quotient .
Let x be the quotient after dividing the original number by 5.
So , the number which we divided by 5 to yield a remainder of 4 = 5x+ 4
This number 5x+4 is the quotient from the first division of the original number by 4
Therefore , the number should be = 4(5x+4) + 1
= 20x +17
We can clearly see that when divided by 20 , we should get a remainder of 17
Answer E