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Quantitative Aptitude > Mensuration > Data Sufficiency
Mensuration

Data Sufficiency

In Coding Data sufficiency, it is important that you know your basics well. Because it is very easy to make mistakes in Coding Data sufficiency. You may think that one of the options is correct although the correct answer is something else. And that is why we have decided to help you get the basics right. Today, in Coding Data sufficiency we will focus on mensuration part. Thus the questions will be related to Area and volume, geometry, etc.

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Coding Data Sufficiency

Data sufficiency is tricky because you are not required to actually solve the question, rather you are asked to mention whether the questions can be solved with the given data or not. Generally, it aims to check the keen-minded ability of the candidate. Usually, data sufficiency consists of the following things:

1. Test of Sufficiency

In this type of questions, an aspirant is required to identify which sets of data together or alone are required to answer the question. Thus, it is just a test of sufficiency and you are not required to calculate the actual answer.

Data sufficiency

2. Problem Statement

This gives you the basic data and the question. It is advisable that you understand the question (problem statement) properly before jumping to any conclusion.

3. Additional Dataset

Along with the problem statement, there can be multiple additional data which can be capable of solving the question and supporting the data.

Browse more Topics under Mensuration

Steps to Solve Data Sufficiency

  1. It is better that you read the data carefully and comprehend it. One of the most important things you need to know in data sufficiency is that never assume any extra information that is not given in the question.
  2. Now, combine the data that is available to you in the question and see whether you can arrive at any solution or not. It is not necessary to solve the question, just get a hint whether the question is solvable or not!
  3. If you are not able to get the solution from statement 1 then move on to the statement 2 and check the same for statement 2. Remember not to use the data available in statement 1.
  4. If you are not able to get any solution from either of the statements that combine the data available in both the statements and try and find the solution.
  5. Choose the correct answer.

Now, we will look into some types of questions that can be expected in data sufficiency.

Example Based on Triangle

Q. Are the two triangles congruent?

Statement I: They both have equal bases and equal heights.

Statement II: They are both equal equilateral triangle.

  1. Data in statement 1 is sufficient alone to determine the answer.
  2. Data in statement 2 is sufficient alone to determine the answer.
  3. Data in either of the statements is sufficient to determine the answer.
  4. Data provided in both the statements together are not sufficient to determine the answer.
  5. Data from both the statements are necessary to determine the answer.

Now, in this question, we just need to determine whether the two triangles are congruent or not. We don’t need to actually solve the question. We will start by solving the statements individually and then if we are not able to find the answer we will combine the data given in both the statements.

The statement I implies that both the triangles have equal heights and bases. But, the rule of congruency states that the two triangles that have the same base and equal height may or may not be congruent. So, from the statement I, we cannot determine the answer.

Statement II implies that both are equal equilateral triangles. As both the triangles are equilateral it does not mean that they are congruent. The necessary conditions for two equilateral triangles to be congruent is to have both the sides of the triangles as equal. But, this is not mentioned in the above statement. So statement II is also detrimental to find the answer.

Now, on combining we get the data that both the triangles are equilateral and both have the same base. This condition satisfies the congruency of the triangles. So the correct answer is (5).

Example Based on the Circle

Q. In the given figure, what will the measure of inscribed ∟PQR?

Data sufficiency

Statement I: PQ is the diameter of the circle.

Statement II: Inscribed ∟PQR = 60°

  1. Data in statement 1 is sufficient alone to determine the answer.
  2. Data in statement 2 is sufficient alone to determine the answer.
  3. Data in either of the statements is sufficient to determine the answer.
  4. Data provided in both the statements together are not sufficient to determine the answer.
  5. Data from both the statements are necessary to determine the answer.

From statement I, it is given that PQ is the diameter of the circle. So, the circle is divided into two parts and it becomes a semi-circle. Angle in the semi-circle always forms a right angle. PQ is the diameter. Therefore ∟PRQ =90°. Therefore we have found our required answer. But we also need to check the other statement.

For statement II it implies that ∟PQR = 60°, but we can’t be sure whether PR = RQ. So, we cannot determine the angle of PRQ.

Thus, in this question, we can find the answer only through statement 1. So, the correct answer is (1).

Practice Questions

The options for all the questions will be following:

  1. Data in statement 1 is sufficient alone to determine the answer.
  2. Data in statement 2 is sufficient alone to determine the answer.
  3. Data in either of the statements is sufficient to determine the answer.
  4. Data provided in both the statements together are not sufficient to determine the answer.
  5. Data from both the statements are necessary to determine the answer.

Q. What are the dimensions of a certain rectangle?

Statement I: The perimeter of the rectangle is 14.

Statement II: The diagonal of the rectangle is 5.

A. 1         B. 2          C. 3             D.4              E.5

The correct answer is C.

Q. How many different triangles can be formed?

Statement I: There are 16 coplanar, straight lines in a.

Statement II: No two lines are parallel.

A. 1         B. 2          C. 3             D.4              E.5

The correct answer is D.

Q. How many bricks of length 6″ and width 4″ are required to build a rectangle wall?

Statement I: The wall is 1/10th of its height thick.

Statement II: The wall is 10″ high and 20″ long.

A. 1         B. 2          C. 3             D.4              E.5

The correct answer is D.

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