Data Sufficiency in Logical Reasoning

Data Sufficiency in Logical Reasoning is an important topic to prepare for competitive exams in India. It tests the logical, analytical and thinking capacity or ability of a candidate. Candidates need to practice the questions for scoring well in the examination

The following article contains various kinds of Data Sufficiency Questions. Candidates must go through the article to practice all the important questions of the topic.

Tips and Tricks to Solve Data Sufficiency Questions

1. Read the entire question carefully before attempting it. Then go through the options to find the correct answer.

2. Use the information given in the question and avoid making any assumptions.

3. Both the statements must be carefully read and then a make a conclusion.

4. Avoid any kind of confusion and answer the question.

Data Sufficiency Questions and Answers

Given below is a question and a set of statements. We have to find which of the given statements is required to reach the conclusion.

Q1. Who is the tallest among the brothers A, B, C, and D?

Statements:

1. C is shorter than only B.

2. D is taller than only A.

Options:

I) Statement 1 alone is sufficient

II) Statement 2 alone is sufficient

III) Both Statement 1 and Statement 2 together are sufficient

IV) Both Statement 1 and Statement 2 even together are not sufficient

Solution:

Considering Statement 1:

"C is shorter than only B" means that B is taller than C and all other brothers, making B the tallest. Therefore, Statement 1 alone is sufficient to determine the tallest brother.

Considering Statement 2:

"D is taller than only A" implies that D is the second shortest, and A is the shortest of all the brothers. However, this statement alone does not provide enough information about who the tallest is among B and C, so Statement 2 alone is not sufficient.

Conclusion:

Statement 1 alone is sufficient to answer the question, so the correct answer is I) Statement 1 alone is sufficient

Q2. What is the value of 'x' 
Statement 1 : x² + x - 6 = 0 
Statement 2 : x ≥ 0 

I) Statement 1 alone is sufficient 
II) Statement 2 alone is sufficient 
III) Both statement 1 and statement 2 together are sufficient 
IV) Both statement 1 and statement 2 even together are not sufficient 

Solution : If we consider statement 1 alone, we have x² + x - 6 = 0 => x² + 3x - 2x - 6 = 0 => (x + 3) (x - 2) = 0 => x = -3, 2 If we consider statement 2 alone, we have x ≥ 0 Combining the two statements, we can safely say that x = 2 Therefore, both statement 1 and statement 2 together are sufficient but neither alone is sufficient.   

Q3. What is the sum of the ages of John and Peter? 
Statement 1: John is 5 years older than Peter. 
Statement 2: The average of their ages is 25.

I) Statement 1 alone is sufficient 
II) Statement 2 alone is sufficient 
III) Both statement 1 and statement 2 together are sufficient 
IV) Both statement 1 and statement 2 even together are not sufficient

Answer: II) Statement 2 alone is sufficient 

Q4. What is the value of x in the equation x^2 + 6x + 9 = 0? 
Statement 1: x = -3 
Statement 2: The discriminant of the equation is zero.

I) Statement 1 alone is sufficient 
II) Statement 2 alone is sufficient 
III) Both statement 1 and statement 2 together are sufficient 
IV) Both statement 1 and statement 2 even together are not sufficient

Answer: III) Both statement 1 and statement 2 together are sufficient

Q5. Is triangle ABC an equilateral triangle? 
Statement 1: The length of AB is equal to the length of AC. 
Statement 2: The length of BC is equal to twice the length of AB.

I) Statement 1 alone is sufficient 
II) Statement 2 alone is sufficient 
III) Both statement 1 and statement 2 together are sufficient
IV) Both statement 1 and statement 2 even together are not sufficient

Answer: IV) Both statement 1 and statement 2 even together are not sufficient

Q6. What is the value of x in the equation 2x + 5 = 11? 
Statement 1: x = 3 
Statement 2: x is a prime number.

I) Statement 1 alone is sufficient 
II) Statement 2 alone is sufficient 
III) Both statement 1 and statement 2 together are sufficient 
IV) Both statement 1 and statement 2 even together are not sufficient

Answer: I) Statement 1 alone is sufficient

Q7. How much did Mr. Smith spend on his vacation? 
Statement 1: Mr. Smith spent $500 on his flight ticket. 
Statement 2: Mr. Smith spent $800 on his hotel stay.

I) Statement 1 alone is sufficient 
II) Statement 2 alone is sufficient 
III) Both statement 1 and statement 2 together are sufficient 
IV) Both statement 1 and statement 2 even together are not sufficient

Answer: III) Both statement 1 and statement 2 together are sufficient

Q8. Is the given rectangle a square? 
Statement 1: The length of each side of the rectangle is 8 cm
Statement 2: The diagonals of the rectangle are equal in length.

I) Statement 1 alone is sufficient 
II) Statement 2 alone is sufficient 
III) Both statement 1 and statement 2 together are sufficient 
IV) Both statement 1 and statement 2 even together are not sufficient

Answer: III) Both statement 1 and statement 2 together are sufficient

Q9. What is the sum of the angles of a triangle? 
Statement 1: One of the angles of the triangle is 60 degrees. 
Statement 2: The triangle is an equilateral triangle.

I) Statement 1 alone is sufficient 
II) Statement 2 alone is sufficient 
III) Both statement 1 and statement 2 together are sufficient 
IV) Both statement 1 and statement 2 even together are not sufficient

Answer: II) Statement 2 alone is sufficient

Q10. What is the total number of students in a class? 
Statement 1: There are 20 boys in the class. 
Statement 2: The ratio of girls to boys in the class is 2:5.

I) Statement 1 alone is sufficient 
II) Statement 2 alone is sufficient 
III) Both statement 1 and statement 2 together are sufficient 
IV) Both statement 1 and statement 2 even together are not sufficient

Answer: III) Both statement 1 and statement 2 together are sufficient

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