soaringAlone wrote:
'a' and 'b' are positive integers such that their LCM is 20 and their HCF is 1. What is the difference between the maximum and minimum possible values of 'a + b'?
A. 0
B. 12
C. 13
D. 9
E. 11
ok, we can use the formula: a*b= GCF*LCM
we have the last 2. we know that a*b=20.
now, let's see what are the possible values for a and b
a=1 - b=20
a=2 - b=10 -> can't be, since GCF=1.
a=4 - b=5
as we see, only 2 options work. the values might be switched, yet still, only 2 options work. when a+b=21, and when a+b=9.
difference is 21-9=12.
B.