Question

Study the questions and the statements given below. Decide whether any information provided in the statement(s) is redundant and/or can be dispensed with, to answer it.
If 7 is added to numerator and denominator each of fraction a/b, will the new fraction be less than the original one?
Statement I: a = 73, b = 103
Statement II: The average of a and b is less than b
Statement III: a − 5 is greater than b − 5

• A. II and either I or III
• B. Only II or III
• C. Any two of them
• D. Any one of them

Answer 1

The Correct Option is B

To determine if the new fraction is less than the original one when 7 is added to both numerator and denominator of the fraction a/b, we need to compare the fractions:

Original fraction: a/b
New fraction: (a + 7) / (b + 7)

We need to check if:

(a + 7) / (b + 7) < a/b

This simplifies to the inequality:
(a + 7) * b < a * (b + 7)
Expanding both sides:

a * b + 7b < a * b + 7a
Cancel out a * b on both sides:

7b < 7a
Divide by 7:
b < a
The inequality requires a to be greater than b for the new fraction to be less than the original. Now, let's analyze the statements:

• Statement I: a = 73 and b = 103. Thus, b is greater than a, so this cannot be used to confirm b < a.
• Statement II: The average of a and b is less than b. This implies:
  
  (a + b)/2 < b
  Multiply by 2:
  a + b < 2b
  This reduces to:
  a < b
  Since this confirms a < b, it is redundant for checking b < a, so this statement alone can not be used.
• Statement III: a − 5 is greater than b − 5. This directly simplifies to:
  
  a > b
  Which confirms b < a.

Given the analysis, only Statement II or Statement III can individually be useful to confirm the required condition.

Therefore, the correct answer is: Only II or III