vaibhav101 wrote:Find the greatest number that will divide 43,91 and 183 so as to leave the same remainder in each case :
A 4
B 7
C 9
D 13
E 41

This question lends itself to testing the answer choices
Since we're looking for the greatest number, we'll start at E and work our way to A

E) 41
43 divided by 41 equals 1 with remainder 2
91 divided by 41 equals 2 with remainder 9
We need the SAME remainder each time - ELIMINATE E

D) 13
43 divided by 13 equals 3 with remainder 4
91 divided by 13 equals 7 with remainder 0
We need the SAME remainder each time - ELIMINATE D

C) 9
43 divided by 9 equals 4 with remainder 7
91 divided by 9 equals 10 with remainder 1
We need the SAME remainder each time - ELIMINATE C

B) 7
43 divided by 7 equals 6 with remainder 1
91 divided by 7 equals 13 with remainder 0
We need the SAME remainder each time - ELIMINATE B

By the process of elimination, the correct answer is A

Cheers,
Brent