Bunuel wrote:
Which of the following is the greatest possible common divisor of two different positive integers, both smaller than 124?
A. 123.
B. 122.
C. 63.
D. 62.
E. 61.
Given to find the greatest possible common divisor for two different positive number.
Let X be GCD and A and B are two different number.
We need to see the XA and XB has to be less than 124.
Now from options,
if we consider 62 * 2 = 124, which is equal to 124, we need to consider some number lesser than 124.
Consider 61 * 2 = 122 and 61 * 1 = 61 ( Both these numbers are lesser than 124 as requested ).
So GCD will be 61.
IMO E is correct option.
For clarity purpose let's check all the options.
A. 123 = ( 123 * 1 ) ( 123 * 0) can't be this. ( value = GCD * some number) . Apart from 0 and 1 , we'll get more result which is > 124 ( for ex 123 * 2 = 246 )
B. 122 = ( 122 * 1 ) ( 122 * 0 )
C. 63 = ( 63 * 1 ) ( 63 * 0 )
OA please...will correct if I missed anything.