Data Sufficiency questions test a combination of skills: your knowledge of basic mathematics coupled with reasoning, analytical and problem-solving abilities. Each data sufficiency question presents you with a prompt where you need to decide whether or not the information given is sufficient to answer the question. Remember, these questions do not ask you to arrive at the exact answer but probe you on the sufficiency of information given. Considering the nature of these questions, there are scenarios wherein you actually don’t need to solve the given questions and can arrive at answers using logic and tricks.
Before we actually begin with this question type and its analysis, lets cover the groundwork. This includes the syllabus for this topic, which, to be honest is fairly vast. Since these questions are based on the sufficiency of information, you can expect questions from any area in mathematics. With relation to CAT, Data Sufficiency questions most commonly appear from Number System. But this does not mean you ignore topics such as Algebra, Geometry, Mensuration and Time, Speed & Distance. The following is an exhaustive list from where the Data Sufficiency Questions may appear in CAT:
This is the most relevant part of the article, isn't it? The following points can help you perform better in data sufficiency in CAT.
Do remember that Data Sufficiency questions are relatively less time consuming as compared to the other CAT Quantitative Aptitude questions. So, if you are able to crack them, it might prove to be a blessing in disguise in CAT.
Before learning the typical way to answer a Data Sufficiency question, let us have a look at the 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.
The above given statements are generic instructions that accompany Data Sufficiency questions. Obviously, it is advisable that you go through these directions every time and do not assume anything. The examiner might change the typical order of direction statements and this might lead you to select an incorrect answer choice.
(i) Understanding the question
First of all, before going through the two numbered statements, take twenty to thirty seconds to consider the question by itself. Figure out what is being asked. There are generally two possibilities- a specific number may be sought i.e. "What is the value of p?”,"In how many days the work will be done, or a true/false answer may be needed i.e. "Is Z a natural number". Make sure you understand exactly what the question is asking. Then consider what information would be needed to answer the question. This will depend on the type of question. For example, to determine the area of a circle, you need to know its radius, its diameter, or its circumference. To determine the length of the hypotenuse of a right triangle, you need to know the length of the other two sides and so on.
(ii) Consider each statement individually
After understanding the question and the information needed to answer the question, you should look at both the statements individually, without reference to each other.
First look at statement I. Does it provide, all by itself, enough information to answer the question? If so, you've already narrowed the possible answer choices to just two: A and C. If not, three answer choices are possible: B, D and E.
Then look at statement B. Does it provide, all by itself, enough information to answer the question? If so, only answers B and C are possible. If not, only answers A, D and E are possible.
Having gotten this far, you may already be able to pick the right answer. If either statement by itself provides enough information to answer the question, you can pick from answers A, B and C, depending on which statement is sufficient or whether either statement will do.
If neither statement by itself is sufficient to answer the question, go on to the third stage as follows:
(iii) Combine the two statements
If neither statement by itself is sufficient to answer the question, check whether you can answer the question by combining the information given in both the statements. If so, the answer is E; else, the answer is D.
Solved Examples:
Example 1: Is the product of two numbers greater than 400?
A. The sum of the two numbers is greater than 100.
B. Each of the numbers is greater than 20.
Solution: Statement A alone is not sufficient to answer the question and this can be proved with the help of examples. If the two numbers are 50 and 51, their sum is greater than 100 and their product is greater than 400; but if the two numbers are 100 and 1- though their sum is greater than 100, their product is only 100, which is less than 400. Statement B is sufficient. If both of the numbers are greater than 20, then their product must be greater than 20 x 20, or greater than 400.
Hence, only the second statement is sufficient to solve the question.
Example 2: Is x a prime number?
A. 114 < x < 126
B. x is a factor of 169
Solution: Here, the first statement is sufficient to answer the question as we see that there is no prime number between 114 <x< 126. Hence, 'x' is not a prime number.
What do we learn from this question? Remember, even if a question has an answer as 'no', even then it is a valid answer. In second statement, the factors of 169 are 1, 13 and 169. Here, 1 and 169 are not prime numbers whereas 13 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.
Example 3: Is x = - 11?
A. x2 = 144
B. x is a natural number.
Solution: Here, the question directly asks whether x is equal to – 11 or not. From statement A, we have x = 12 or – 12. In both the cases, x is not equal to – 11. Hence, the 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 – 11. So, the second statement is also sufficient to solve the question.
Hence, both statements are independently sufficient to answer the question.
Example 4: What is the value of 'x'?
A. x<10
B. x>8
Solution: By combining both statements, we can say that x lies between 8 and 10. The only integer between 8 and 10 is 9. So our answer should be Option E. But this approach is actually incorrect.
Remember, nowhere in the question is it mentioned that x is an integer / natural number. Until and unless that is specified, we cannot uniquely determine the value of 'x'. It can take any value from 8 to 10 {e.g.: 8.1, 8.2, 9.999, etc.}
So, the correct answer is option D i.e. the answer cannot be determined even with the help of both the statements.
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.
As a parting note, do keep in mind that 'NO' is also an answer for Data Sufficiency questions.