Data Sufficiency - Quant/Math - CAT 2013
Question 4 the day:
March 28, 2002
The question for the day is a data sufficiency question.
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:
- Is the triangle ABC an isosceles triangle?
- One of the angles of the triangle ABC which is right angled is 45.
- The ratio of the sides of the triangle are 1 : 3(1/2) : 2.
Correct Answer - (2)
Solution:
We need to find out if the triangle ABC is an isosceles triangle.
An isosceles triangle is a triangle whose two sides and two angles are equal.
Information from Statement A: The triangle is a right angled triangle. So one of its angles (Let us say angle A) is 90 degrees. And the problem also states that one other angle (Let us say angle B) is 45 degrees. Let the third angle be C. We know that the sum of the angles of a triangle is 180 degrees.
Therefore, A + B + C = 180. i.e. 90 + 45 + C = 180. ==> C = 180 - 135 = 45 degrees.
Angle C = Angle B = 45o. As Angle B and Angle C are equal, the triangle is an isosceles triangle.
Therefore, Statement A alone is sufficient to answer the question.
The answer, therefore has to be either (1) or (2). It cannot be (3) or (4) as A alone has answered the question. You have improved your chances of success from 25% (1 in 4 choices) to 50% (1 in 2 choices) at this stage.
Now let us examine Statement B: The sides of the triangle are in the ratio of 1 : 3(1/2) : 2.
That is all three sides are different. This means that the triangle is not an isosceles triangle. Therefore, Statement B alone has also answered the question. Therefore, the answer is (2)
Note: Statement A gave the answer that the triangle is an isosceles triangle. It has conclusively given us the answer. Statement B led us to the answer that the triangle is not isosceles. This statement has again conclusively given us the answer. Therefore, even though the two statements might provide contradicting answers, as long as they provide conclusive answers, they are sufficient.
It is important to keep in mind that the question is to find out whether the data provided in the two statements are sufficient - not whether the answers are tallying. Be careful about such traps.
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