CAT 1993 — QA Question 1
Each of these questions is followed by two statements. As the answer,
Mark (a), If the question can be answered with the help of statement I alone,
Mark (b), If the question can be answered with the help of statement II, alone,
Mark (c), If both, statement I and statement II are needed to answer the question, and
Mark (d), If the question cannot be answered even with the help of both the statements.
Given that X and Y are non-negative. What is the value of X?
I. 2X + 2Y ≤ 40
II. X − 2Y ≥ 20
Answer & solution
Answer: 3
From statement I: 2X + 2Y ≤ 40 or X + Y ≤ 20
This statement alone cannot give the value of X.
From statement II: X − 2Y ≥ 20
This statement also alone cannot give the value of X.
On combining statements I and II:
Multiplying the second statement by –1 and adding
both the statements, we get
3Y ≤ 0 i.e., Y ≤ 0, but it is given that Y is non negative.
∴Y = 0 and X = 20
Hence, the answer is (c).