The numerator of a fraction is multiple of two numbers. One of the numbers is greater than the other by 2. The greater number is smaller than the denominator by 4. If the denominator 7 + C (C > -7) is a constant, then the minimum value of the fraction is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. -1/5
Let numerator = a × b, [where a = b + 2]
Denominator = c + 7
Now,
a = Denominator - 4 = c + 7 - 4 = c + 3
Also, b = a - 2
b = c + 1
Fraction = [(c + 3)(c + 1)]/(c + 7) = (c2 + 4c + 3)/(c + 7) = [(c + 2)2 - 1]/(c + 7)
Since c + 7 is constant, the fraction will be minimum when the numerator is minimum.
Numerator will be minimum, when c + 2 = 0, i.e. c = -2
Fraction minimum value = [(-2 + 2) - 1]/(-2 + 7) = -1/5