Question

Study the question 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

Hint:

Show algebraically that the new fraction is smaller exactly when a is greater than b, then check which statements establish that relation directly.

Answer 1

The Correct Option is B

Step 1: Test with examples. a=4,b=10 (a<b): fraction grows. a=10,b=4 (a>b): fraction shrinks. Confirms rule: shrinks iff a>b.

Step 2: Check statements. II gives a<b directly. III gives a>b directly. I gives specific numbers 73<103, just a special case already implied by II's general relation, hence redundant.

Final Answer: Only II or III.