Data Sufficiency - Quant/Math -

Question 4 the day: October 28, 2002
The question for the day is a data sufficiency question. One important thing about Data Sufficiency questions is that more often than not these questions take you about 30 seconds to crack them. And it generally does not involve any difficult calculations which tend to take most of the time when you solve a problem. Here the question is about whether you can solve the problem with the information given and NOT about actually solving the problem.

In this question, there is a question statement which is followed by two statements. You have to decide whether the information provided in the two statements is sufficient for answering the question.

Mark 1

If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.

Mark 2

If the question can be answered by using either statement alone.

Mark 3

If the question can be answered by using both statements together, but cannot be answered by using either statement alone.

Mark 4

If the question cannot be answered even by using both the statements together.

Question

The values of x and y can be determined uniquely if

1. 4x + 7y = 30
2. 10x + 17.5y = 75

Solution:

You need two distinct equations to solve for unique values of two variables x and y.

Statement A is an equation involving x and y. Statement B is another equation involving x and y.

However, the equation in Statement B can be reduced to that in Statement A, by dividing both sides of the equation in Statement B by 2.5. Therefore, both Statements A and B alone or together cannot solve for the variables x and y.