Data Sufficiency

Data Sufficiency requires a basic knowledge of the principles of arithmetic, algebra, and geometry and other topics. Each Data Sufficiency question consists of a mathematical problem and two statements containing information relating to it. You must decide whether the problem can be solved by using information from: (A) the first statement alone, but not the second statement alone; (B) the second statement alone, but not the first statement alone; (C) both statements together, but neither alone; or (D) either of the statements alone. (E) if the problem cannot be solved, even by using both statements together.
Approaching Data Sufficiency problems properly will help you use this time wisely.

Care: Legends / options may vary from examination to examination. You are advised to go through the instructions carefully to select the right options.
Always keep in mind the fact that you are never asked to supply an answer for the problem; you need only determine if there is sufficient data available to find the answer. Therefore, don't waste time figuring out the exact answer. Once you know whether or not it is possible to find the answer with the given information you are through. If you spend too much time doing unnecessary work on one question you may not be able to finish the entire section.

Strategy For Data Sufficiency Questions
A systematic analysis can improve your score on Data Sufficiency sections. By answering three questions, you will always arrive at the correct place. In addition, if you can answer any one of the three questions, you can eliminate at least one of the possible choices so that you can make an intelligent guess.

The three questions are:
(i) Is the first statement alone sufficient to solve the problem?
(ii) Is the second statement alone sufficient to solve the problem?
(iii) Are both statements together sufficient to solve the problem?

As a general rule try to answer the questions in the order I, II, III, since in many cases you will not have to answer all three to get the correct choice.

Here is how to use the three questions:
(i) If the answer to I is YES, then the only possible choices are (A) OR (D). Now, if the answer to II is YES, the choice must be (D), and if the answer to II is NO, the choice must be (A) (ii) If the answer to I is NO then the only possible choices are (B), (C), or (E). Now, if the answer to II is YES, then the choice must be (B), and if the answer to II is NO, the only possible choices are (C) or (E) (iii) So, finally, if the answer to III is YES, the choice is ©, and if the answer to III is NO, the choice is (E)

A better way to see this is to use a decision tree.

Choice is (C) Choice is (E)

To use the tree simply start at the top and by answering YES or NO move down the tree until you arrive at the correct choice. For example, if the answer to I is YES and the answer to II is NO, then the correct choice is (A). (Notice that in this case you don't need to answer III to find the correct choice.)
The decision tree can also help you make intelligent guesses. If you can only answer one of the three questions, then you can eliminate the choices that follow from the wrong answer to the question.

BUT
Please don't conclude immediately;
Check all the possibilities before you conclude;
Never conclude midway until you are sure of results.

Tip 1: You know the answer to I is YES. You can eliminate choices (B), (c) and (E)
Tip 2: You know the answer to II is NO. You can eliminate choices (D) and (B) since they follow from YES for II
Tip 3 You know the answer to III is YES. You can eliminate choice (E) since it follows from NO for III
Tip 4: You know the answer to I is NO and the answer to III is YES. You can eliminate (E) since it follows from NO to III. You also can eliminate (A)k and (D) since they follow from YES to I

Since you get one raw score point for each correct choice and lose only one quarter of a point for an incorrect choice, you should guess whenever you can answer one of the three questions.
Read the following directions carefully and then try the sample Data Sufficiency questions below. Allow yourself 8 minutes total time. All numbers used are real numbers. A

ILLUSTRATIONS
DIRECTIONS: Each of the following problems have a question and two statements which are labeled (I) and (2). Use the data given in (I) and (2) together with other available information (such as the number of hours in a day, the definition of clockwise, mathematical facts, (etc.) to decide whether the statements are sufficient to answer the question. Then choose. (A) if you can get the answer from (1) alone but not from (2) alone; (B) if you can get the answer from (2) alone but not from (1) alone; (C) if you can get the answer from (1) and (2) together, although neither statement by itself suffices; (D) if statement (1) alone suffices and statement (2) alone suffices; (F) if you cannot get the answer from statements (1) and (2) together, but need even more data.
All numbers used are real numbers. A figure given for a problem is intended to provide information consistent with that in the question, but not necessarily consistent with the additional information contained in the statements.

1. A rectangular field is 40 yards long. Find the area of the field (1) A fence around the entire boundary of the field is 140 yards long (2) The width of the field is more than 20 yards.
2. Is X a number greater than zero? (1) X2 ? 1 = 0 (2) X3 + 1 = 0
3. An industrial plant produces bottles. In 1961 the number of bottles produced by the plant was twice the number' produced in 1960. How many bottles were produced altogether in the years 1960, 1961 and 1962? (1) In 1962 the number of bottles produced was 3 times the Number produced in 1960 (2) In 1963 the number of bottles produced was one half The total produced in the year 1960, 1961 and 1962
4. A man 6 feet tall is standing near a tube light fitted on the top of a Pole . What is the length of the shadow cast by the man? (1) The pole is 18 feet high. (2) The man is 12 feet from the pole.
5. Find the length of RS if z is 90 degree and PS = 6 (1) PR = 6 (2) X = 45 degree
6. Working at a constant rate it takes 'U' worker in all 3 hours to fill up a ditch with sand. How long would it take for 'V' workers to fill up the same ditch working without any changes. (1) Working together but at the same time U and V can fill in the ditch in 1 hour 52 ½ minutes. (2) In any length of time worker V files in only 60% as much as worker U does in the same time.
7. Did John go to the beach yesterday? (1) If John goes to the beach, he will be sunburned the next day. (2) John is sunburned today.

Analysis: (1) (A) The area of a rectangle is the length multiplied by the width. Since you know the length is 40 yards, you must find out the width in order to solve the problem. Since statement (2) simply says the width is greater than 20 yards you cannot find out the exact width using (2). So (2) alone is not sufficient. Statement (1) says the length of a fence around the entire boundary of the field is 140 yards. The length of this fence is the perimeter of the rectangle, the sum of twice the length and twice the width. If we replace the length by 40 in P = 2L + 2W we have 140 = 2 (40) + 2W and solving for W yields 2W ? 60 or W = 30 yards. Hence the area is (40)(30) = 1200 square yards. Thus (1) alone is sufficient but (2) alone is not. (2) (B) Statement (1) means X2 = 1, but there are two possible solutions to this equation, X = 1, X = -1. Thus using (1) alone you can not deduce whether X is positive or negative. Statement (2) means X3 = -1 but there is only one possible (real) solution to this, X = -1. Thus X is not greater than zero which answers the question. And (2) alone is sufficient. (3) (E) T, the total produced P0 + P1 + P2, where P0 is the number produced in 1960,P1 the number produced in 1961, andP2 the number produced in 1962. You are given that P1 = 2P0.Thus 2 = P0 + P1 + P2 = 2P0 + = 3P0 + P2. So we must find out P0 and P2 to answer the question. Statement (1) says P2 = 3P0; thus by using (1) if we can find the value of P0 we can find T. But (1) gives us no further information about P0 . Statement (2) says T equals the number produced in 1963, but it does not say what this number is. Since there are no relations given between production in 1963 and production in the individual year 1960, 1961, or 1962 you cannot use (2) to find out what P0 is. Thus even (1) and (2) together are not sufficient. (4) (C) Sometimes it may help to draw a picture. By proportions or by similar triangles the height of the pole, h, is to 6 feet as the length of shadow, s, + the distance to the pole, x, is to s. So h/6 = (s + x)/s. Thus hs = 6s + 6x by cross multiplication. Solving for s gives hs ? 6s = 6x. or s(h ? 6) = 6x, finally we have s = 6x/(h ? 6). Statement (1) says h = 18; thus s = 6x/12 = x/2, but using (1) alone we cannot deduce the value x. Thus (1) alone is not sufficient. Statement (2) says x equals 12; thus, using (1) and (2) together we deduce s = 6, but using (2) alone all we can deduce is that s = 72 / (h ? 6), which cannot be solved for s unless we know h. Thus using (1) and (2) together we can deduce the answer but (1) alone is not sufficient nor is (2) alone.
(5) (D) Since z is a right angle,, (RS)2= (PS)2 + (PR)2. Sp (RS)2 = (6)2 + (PR)2 , and RS will be the positive square root of 36 + (PR)2 . Thus if you can find the length of PR the problem is solved. Statement (1) says PR = 6, thus (RS)2 = 36 + 36, so RS = 6 . Thus (1) alone is sufficient. Statement (2) says x = 45º but since the sum of the angles in a triangle is 180º and z is 90º them y = 45º. So x and y are equal angles and that means the sides opposite x and opposite y must be equal or PS = PR. Thus PR = 6 and RS = 6 so (2) alone is also sufficient. (6) (D) (1) says U and V together can fill in the ditch in 1 7/8 hours. U would fill in (1/3)(15/8) = 5/8 of the ditch. So V fills in 3/8 of the ditch in 1 7/8 hours. Thus V would take (8/3)(15/8) = 5 hours to fill in the ditch working by himself. Therefore, statement (1) alone is sufficient. According to statement (2) since U fills the ditch in 3 hours, V will fill 3/5 of the ditch in 3 hours. Thus V will take 5 hours to fill in the ditch working by himself. (7) (E) Obviously, neither statement alone is sufficient. John could have gotten sunburned at the beach, but he might have gotten sunburned somewhere else. Therefore (1) and (2) together are not sufficient. This problem tests your grasp of an elementary rule of logic rather than your mathematical knowledge.