CAT 1997 — QA Question 49
Answer the next 2 questions based on the following information.
A thief, after committing the burglary, started fleeing at 12 noon, at a speed of 60 km/hr. He was then chased by a policeman X. X started the chase, 15 min after the thief had started, at a speed of 65 km/hr.
Direction: Each of these items has a question followed by two statements, I and II. Mark the answer
1. if the question can be answered with the help of one statement alone.
2. if the question can be answered with the help of any one statement independently.
3. if the question can be answered with the help of both statements together.
4. if the question cannot be answered even with the help of both statements together.
What is the value of x and y?
I. 3x + 2y = 45
II. 10.5x + 7y = 157.5
Answer & solution
Answer: 4
Students! be careful. Generally, as we see two unknowns (i.e. x and y in this case) and two equations, we tempt to mark the answer as c, i.e. combining two statements, we can easily find the values of x and y. But have a look at the equations 3x + 2y = 45 and 10.5x + 7y = 157.5. Multiplying 1st equation by 3.5, we get 2nd equation. Hence, these are not really two different equations. Hence, data is insufficient to answer the question. In general, remember the following rule. If we have two equations Ax + By = k1 and Cx + Dy = k2, and A × D = B × C, then the equations cannot be solved.