This article will cover the A-Z of Data Sufficiency, covering the type and pattern of Data Sufficiency questions followed by few solved examples.
What is Data Sufficiency?
Data Sufficiency questions test your knowledge of basic math facts and skills coupled with reasoning, analytical and problem solving abilities. Each Data Sufficiency item presents you with a question where you need to decide whether or not the information presented along with the question would be sufficient to answer the question.
What makes Data Sufficiency questions different?
The challenge in DS questions, as they are popularly called, is not question solving but rather establishing whether the question has a solution or not. A special array of five answer choices is provided, each of which categorizes the relationship between the question and the information provided in a different way. You must select the answer choice that describes this relationship accurately.
Let's have a cursory look at these answer options which generally feature in this question type
Give answer (A) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
Give answer (B) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question.
Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.
Give answer (E) if the data in both Statements I and II together are necessary to answer the question.
- Students often confuse the different answer options, and end up marking the incorrect choice. Always double check whether you are marking the correct option, and do not assume that the examiner would always present the options in a default order.
- Go through the answer options to check whether the order of statements is as expected.
Solved Data Sufficiency Questions
Example 1: Is the product of two numbers greater than 100?
- The sum of the two numbers is greater than 50.
- Each of the numbers is greater than 10.
Solution: Let us analyse the individual statements first and then take them together.
- Statement I alone is not sufficient to answer the question and this can be proved by examples. If the two numbers are 30 and 31, their sum is greater than 50 and their product is greater than 100; but if the two numbers are 50 and 1, though their sum is greater than 50, their product is only 50, and less than 100.
- Statement II is sufficient. If both of the numbers are greater than 10, then their product must be greater than 10 x 10, or greater than 100.
Hence only second statement is sufficient to solve the question. Option B is the answer.
Example 2: Is x a prime number?
- 91 <x< 97
- x is a factor of 121
Solution: Here the first statement is sufficient to answer the question as we see that there is no prime number between 91 <x< 97. Hence 'x' is not a prime number.
In second statement, the factors of 121 are 1, 11 and 121. Here 1 and 121 are not prime numbers whereas 11 is a prime number. Hence in this case 'x' may or may not be a prime number.
Hence, only the first statement is sufficient to solve the question. Option A is the answer.
- Remember, even if a question has an answer as 'no', even then it is a valid answer.
Example 3: Is x = - 5?
- x2 = 36
- x is a natural number.
Solution: Here the question directly asks whether x is equal to - 5 or not.
- From statement A, we have x = 6 or - 6. In both the cases x is not equal to - 5. Hence first statement is sufficient to get the answer.
- Statement B says that x is a natural number. Since x is a natural number, it cannot be negative. Hence it is not equal to - 5. So, the second statement is also sufficient to solve the question.
Hence, both statements are independently sufficient to answer the question.
Option C is the answer.
Data Sufficiency: Key Learning
- To conclude, it is very important to read the question carefully in the case of Data Sufficiency questions.
- One major mistake committed by a number of students is that when the answer has to be yes/no and normally whenever you get the answer as no, you mark the answer as insufficient.
- Remember: 'NO' is also an answer for Data Sufficiency questions.