Data Sufficiency: Master the Numbers

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Data sufficiency is a subset of DI. DS questions can be asked in QA as well but I think it is more apt for us to discuss it here. In this section, you are not expected to solve and find the actual answer, but just figure out whether the answer can be found out. Let us try one question:

Question

The question below is followed by two statements X and Y. Answer using the following instructions:

Mark (A) if the question can be answered by using the statement X alone but not by using the statement Y alone.

Mark (B) if the question can be answered by using the statement Y alone but not by using the statement X alone.

Mark (C) if the question can be answered by using either of the statements alone.

Mark (D) if the question can be answered by using both the statements together but not by either of the statements alone.

Mark (E) if the question cannot be answered on the basis of the two statements.

What is the value of a and b?

X: b is an even number, a is an odd number and a>b

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Y: ab = 30

Let us try to solve this. Clearly, X alone is not enough to solve this since there can be many such combinations of a and b. Y alone also cannot be used to find the solution since there are innumerable possibilities for a and b (yes, innumerable since in Y alone, a/b can be fractions also). Options A, B and C are out now.

We just need to see if X and Y together can solve this. The only combinations of (a,b) where ab = 30 and a is odd while b is even, are (1,30), (3,10), (5,6) and (15,2). Only in one of these, is a>b. Hence, the answer is option D.

In this case, we had to figure out the solution to arrive at the answer, but there will be cases where that will not be required.

Pearl of Wisdom: It is very important to understand that when you are considering the statement X or Y individually, you don’t assume in your head the other one as well. As in the example above, Y doesn’t mention that a and b and whole/natural numbers while X does. While using only Y, it shouldn’t be assumed. This is the most important rule for DS questions; and if you get this right, you will usually score well in DS. In addition, beware that the answer using only X and the one using only Y, if both can be individually used to find an answer, need not be same.

Pearl of Wisdom: I used the ‘usually’ above because the 2nd trick is to figure out how a solution can be reached. A lot of examinees assume that a solution cannot be reached since usually you need 2 equations to find two variables. This is incorrect practice. You should think of only the particular case presented in the question and not think generically. If you do think generically, you would get DS questions wrong almost always.

There is no particular syllabus for DI. Practice different types from whatever source you can lay your hand on. Do not see the solution before you attempt all the questions. If you cannot answer a question in the set, refer the solution after you have attempted the whole set (do not see the answer of that question without trying to solve all the other questions in the set). After understanding the solution, you must try answering the question yourself. This will increase the chances of you remembering the solution.

It is a capital mistake to theorize before one has data. – Sir Arthur Conan Doyle

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