12) B

Since 6 out of the 7 options mention ‘all values of X’ we can use X = 1 to make everything simpler.

a = __ 3
__ 5 + X

b = __ 3 + X
__ 5

c = __ 3 + X
__ 5 + X

Substituting X = 1,

a = __ 3 __ = 3/6 = 1/2

5 + 1

b = __ 3 + 1 __ = 4/5

5

c = __ 3 + 1 __ = 4/6 = 2/3

5 + 1

The order of inequalities: a < c < b

However, option G states that the order of fractions depend on the value of X. In order to proves this wrong, we need to use a different value for X. Let us say X = 2.

a = __ 3 __ = 3/7

5 + 2

b = __ 3 + 2 __ = 5/5 = 1

5

c = __ 3 + 2 __ = 5/7

5 + 2

The order still remains the same: a < c < b