Is (50 + 5n)/n
^2 an integer?
Assumption in RED.
(1) n/5 is a positive integer.
So, n = 5k where k is a positive integer
(50 + 5n)/n^2
= (50 + 5*5k)/(5k)^2
= (25*(2+k))/(25*(k^2))
= (2+k)/(k^2)
If k = 1 then the value of (2+k)/(k^2) = 3, an integer.
If k = 4 then the value of (2+k)/(k^2) = 3/8, not an integer.
Two different answers. So, statement 1 is insufficient to answer the question.
(2) n/10 is a positive integer
So, n = 10k where k is a positive integer
(50 + 5n)/n^2
= (50 + 5*10k)/(10k)^2
= 50(1+k)/(100*(k^2))
= (1+k)/(2*k*k)
If k = 1 then the value of (1+k)/(2*k*k) = 1, an integer.
If k = 4 then the value of (1+k)/(2*k*k) = 5/32, not an integer.
Two different answers. So, statement 2 is insufficient to answer the question.
From 1 and 2
If n = 10, then (50 + 5n)/n
^2 = (50+50)/100 = 1, an integer.
If n = 40, then (50 + 5n)/n
^2 = (50+200)/1600 = 5/32, not an integer.
Two different answers. So, statement 1+2 combined is insufficient to answer the question.
IMO
E