IMO, E.

It's a bit tricky to understand "divided successively". IMO, it means that, number x is divided by 4 first, quotient is n, remainder is 1. Then n is divided by 5, quotient is m, remainder is 4. (m and n are positive ingeters.)

If my understanding is correct, number x
= (5m+4)4n+1
= 20mn+16n+1
= (20mn+15n+5)+(n-4)

When above number is divided by 5, remainder is n-4. Since we don't know value of n, data is not sufficient.

Another way is to use real numbers for (5m+4)4n+1.
When m=1, n=1, x=37, divided by 5, quotient is 7, remainder is 2; 7 divided by 4, remainder is 3.
When m=2, n=2, x=113, divided by 5, quotient 22, remainder 3; 22 divided by 4, remainder 2.
So data not sufficient.

The answer is B

Take a Look:

d1=4 and d2 =5
r1 =1 and r2 =4

so the number is d1*r2+r1 where d1 and d2 are the divisors arranged in increasing order

so number = 4*4 +1 = 17

now question says, this number, 17 divided by 5 remainder =2

and then further divided by 4,so we here divide the quotient left from previous division ie.3

so 3 divided by 4,remainder = 3

answer B

Hope this helps

Thanks Karan GMAT740: here is another way to klook at it:

4|x
-----------
5| y -1
-----------
|1 - 4
-----------

SO Y = 5*1 + 4 = 9
X = 4y + 1 = 37
So the number was 37, if we go for reverse division:
5 divides 37 to give quotient of 7 remainder 2
4 divides 7 to give quotient 1 and remainder 3

So 2,3 will be ans