Question

I + f - f' is an even integer, where I is an integer, f and f' are proper positive

fractions (0 < f, f' < 1). Then the integer I is an odd number.

• A. True
• B. False

Answer 1

The correct option is B

False

let us consider f - f' separately,

0 < f < 1 and 0 < f' < 1

f - f' will attain its maximum value when f = 1 and f' = 0 and it will attain its

minimum value when f = 0 and f' = 1.

⇒ -1 < f - f' < 1

I + f - f' is an even integer.

I is also an integer. For I + f - f' to be an integer, f - f' should also be an integer.

The only integer value it can take is 0, because -1 < f - f' < 1.

⇒ f - f' = 0

⇒ f = f'

⇒ I + f - f' = I = an even integer