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5d. Introduction to Data Sufficiency

The mathematical knowledge and skill required solving Data Sufficiency problems is no greater than that required to solve standard math problems. What make Data Sufficiency problems appear more difficult at first is the complicated directions. But once you become familiar with the directions, you'll find these problems no harder than standard math problems. In fact, students usually become proficient more quickly on Data Sufficiency problems over time. Here are some tips:


Unwarranted Assumptions


• Be extra careful not to read any more into a statement than what is given.


• The main purpose of some difficult problems is to lure you into making an unwarranted assumption.


Elimination
Data Sufficiency questions provide fertile ground for elimination. In fact, it is rare that you won't be able to eliminate some answer-choices. Remember, if you can eliminate at least one answer choice, the odds of gaining points by guessing are in your favor.


Analysis
Ask yourself what specific information you need in order to answer the question posed. As you consider each of the two numbered statements independent of each other, ask yourself whether the statement provides any such information.


This problem involves the concept of proportion. Notice that no arithmetical calculations are required here. That's because Data Sufficiency problems are designed to test you primarily on concepts, not on your ability to solve a problem by working to a quantitative solution. (That's what Problem Solving questions are for.)


A good way to see this to use a decision tree.



DIRECTIONS for Data Sufficiency questions: Each of the data sufficiency problems below consists of a question and two statements, labeled I and II, in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you are to blacken space.


(A) if statement I BY ITSELF is sufficient;
(B) if statement II BY ITSELF is sufficient;
(C) if statements I and II TAKEN TOGETHER are sufficient;
(D) if EITHER statement by ITSELF is sufficient;
(E) if I and II TOGETHER are NOT SUFFICIENT.


Before starting with Data Sufficiency questions revise the directions.


ELIMINATION: GMAT Data Sufficiency questions provide fertile ground for elimination. In fact, it is rare that you won't be able to eliminate some answer-choices. Remember, if you can eliminate at least one answer choice, the odds of gaining points by guessing are in your favor. The following table summarizes how elimination functions with Data Sufficiency problems.


1. What are the two numbers x and y?


I. Sum of x and y is 528.
II. HCF of x and y is 33. 

Solution: Each statement alone is not sufficient.


Combining I and II: As HCF of x and y is 33.
Let the two numbers be 33a and 33b.
33a + 33b = 528 Therefore, a + b = 16.
Now, two co-primes with sum 16 are (1, 15), (3, 13), (5, 11) and (7, 9)
Thus, the numbers could be (33, 415) or (99, 429) and so on.
Thus, the value of x and y cannot be uniquely found out. Hence, the question cannot be answered. Hence, (E).








 
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