Data Sufficiency Reasoning: Concepts & Tricks

Introduction
Data sufficiency questions test your knowledge of basic math facts and skills along with reasoning, analytical, and problem-solving abilities. Each data sufficiency item presents you with a question. You do not actually have to find the answer to the problem; instead, your challenge is to decide whether or not the information presented along with the question would be sufficient to allow you to answer the question. Five answer choices are provided, each of which categorizes the relationship between question and the information provided in a different way. You must select the answer choice that accurately describes this relationship.
Understanding Answer options
In Data sufficiency problems, a question consists of two statements labeled I and II, in which a certain information is given. You have to decide whether the information given in the statements is sufficient to answer the question or not. Using the information given in the statements plus your knowledge of mathematics and wellknown facts (such as Earth revolves around Sun or the meaning of counterclockwise), you must indicate whether.
  1.  The answer can be obtained from Statement I alone but statement II alone is not sufficient to answer the question asked;
  2.  The answer can be obtained from statement II alone but statement I alone is not sufficient to answer the question asked;
  3. The answer can be obtained from both statements I and II together; but neither statement I nor statement II alone  is sufficient to answer the question asked ;
  4. We can answer  the asked question from either statement I or statement  II;
  5. We can not answer the question asked  from Statement I and II together, and additional information is required to answer the question.
Note: In data sufficiency problems, the information given in the statements is sufficient only when it is possible to determine exactly one numerical value as answer for the problem.
Examples:
1.     Three packages have a combined weight of 48 pounds. What is the weight of the heaviest package?
A.    One package weighs 12 pounds.
B.    One package weighs 24 pounds.
1.    Statement A alone is sufficient to answer this question, but statement B alone is not sufficient.
2.    Statement B alone is sufficient to answer this question, but statement A alone is not sufficient.
3.    Both statements together are needed to answer this question, but neither statement alone is sufficient.
4.    Either statement by itself is sufficient to answer this question.
5.    Not enough facts are given to answer the question.
The correct answer is option 2. Statement A is not sufficient to determine the weight of the heaviest package. It implies only that the combined weight of the other two packages is 36 pounds. (Eliminate options 1 and 4). Statement B alone is sufficient for it implies that the combined weight of two of the packages is only 24 pounds. Since the weight of the 24 -pound packages is equal to the combined weight of the other two packages, the heaviest package must weigh 24 pounds. (Eliminate options 3 and 5). Since statement B alone is sufficient to answer the question but statement A alone is not, answer this question as option 2.
2.     How many books are there on a certain shelf?
A.     If four books are removed, the number of books remaining on the shelf will be less than 12.
B.     If three more books are placed on the shelf, the total          number of books on the shelf will be more than 17.
1.    Statement A alone is sufficient to answer the question, but statement B alone is not sufficient.
2.    Statement B alone is sufficient to answer the question, but statement A alone is not sufficient.
3.    Both statements together are needed to answer the question, but neither statement alone is sufficient.
4.    Either statement by itself is sufficient to answer the question.
5.    Not enough facts are given to answer the question.
The correct answer is option 3. Neither statement alone is sufficient to answer the question asked. Statement A alone implies only that the number of books on the shelf is 15 or fewer, and statement B alone implies only that the number of books on the shelf is 15 or more. (Eliminate options 1, 2 and 4). But the two statements taken together are sufficient to answer the question, for they imply that the number of books on the shelf is 15. (15 is the only integer that satisfies both statements A and B). Since neither statement alone is sufficient, but the two statements together are, answer this question as option 3.
Data sufficiency tricks
Step 1 – Examine the Question:
What is asked? Do we have to find a value or do we have to check a relationship?
Before looking at the two numbered statements, take twenty to thirty seconds to consider the question by itself. Figure out what is being asked. There are usually 2 possibilities a specific number may be sought (“What is the value of y?” "How many gallons of milk is in the tank?”), or a true/false answer may be needed (“Is it true that a >7?” “Is n a prime number?”) Make sure you understand what the question is asking.
Then consider what information would be needed to answer the question. This will depend on the type of question, of course. If it is a geometry question, the information needed will be based on rules you’ve learned about how one geometric fact can be deduced from another. 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.
On the other hand, if it is a percentage question, different rules will come into play. To determine what percentage X is of Y, for example, you need to know the value of X and the value of Y. When a change from one value to another is involved – the increase in value of an investment, for example – you need to know both the old value and the percentage by which it has increased if you want to calculate the new value.
As these examples suggest, the data sufficiency question format allows the test makers to measure your knowledge of a wide array of mathematical topics.
Step 2 – Consider each statement individually
Having figured out the nature of the question and decided, in a general way, what information is needed to answer it, look at each of the two numbered statements provided. Consider them one at a time, without reference to each other.
First look at statement A. 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: 1 and 4. If not, three answer choices are possible: 2, 3 and 5.
Then look at statement B. Does it provide, all by itself, enough information to answer the question? If so, only answers 2 and 4 are possible. If not, only answers 1, 3 and 5 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 1, 2 and 4, 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:
Step 3 – Combine the two statements
Third, if necessary, combine the two statements. If neither of the statements by itself is sufficient to answer the question, consider whether you can answer the question by combining the information given in both statements. If so, the answer is 3; if not, the answer is 5.
Flow Chart:
The following flow chart summarizes the questions you need to ask yourself as you use the three-stage system. It’s a handy way to review and refresh your understanding of this method.