Data Sufficiency - Sufficient or Not? (Updated)

(Note: Since my last posting on this topic, I have learnt new techniques on answering Data Sufficient questions. Please reread this section for the new knowledge)

The Quantitative (Quant) section is divided into two sub-categories: Problem Solving (PS) and Data Sufficiency (DS). Out of 37 quant questions, about 13/14 questions or 1/3 will be on Data Sufficiency. For most of us, Problem Solving should be easy to score. However, I find DS more challenging:

1. We have been taught to solve problems, not on whether the information is sufficient to solve a problem; thus, the tendency to spend time and solve it.


2. We learnt by rote. We memorize workings and through practice, perfect our speed in answering problem solving questions.

Data Sufficiency tests us on the quantitative concepts and principles; the foundation. You are to decide whether the statements — either individually or in combination — provide enough information to answer the question.

(A) If statement 1 alone is sufficient to answer the question, but statement 2 alone is not sufficient.
(B) If statement 2 alone is sufficient to answer the question, but statement 1 alone is not sufficient.
(C) If both statements together are needed to answer the question, but neither statement alone is sufficient.
(D) If either statement by itself is sufficient to answer the question.
(E) If not enough facts are given to answer the question.

Here is a tip that I find helpful and is represented by these two triangle (below)

Now, which to use - AD/BCE or BD/ACE?

A and B refer to Statement (1) only and Statement (2) only respective. Depending on the question stem, which statement is easier to understand? Let's take this example.

Class A and class B took the same test. The average (arithmetic mean) score for class A was 79.5. What was the average score for all the students in both classes?
(1) The average score for class B was 80.5.
(2) Class B had 25 fewer students than class A.

For this question, you need these variables to solve the question:
a. average of Class A (given)
b. average of Class B
c. no. of students of Class A and B or ratio of Class A and B.

Statement (1) only average of Class B is given. Not Sufficient; eliminate A and D.
Statement (2) only does not tell us how many students in Class A and what's the average of Class B. Not Sufficient; eliminate B.
Both Statement (1) and (2) also not sufficient because the missing part is still no. of students in Class A or the ratio of Class A and B students. Eliminate C.

The correct answer is "E" and I took less than 1 minute. By rephrasing the question stem and knowing what information you need, you can play the elimination game. I started with Statement (1); which alone is will not solve the question, thus, immediately eliminate answer A and D. You have increased your chances of finding the right answer from 20% (1 out of 5) to 33% (1 out of 3).

You can also tackle this question starting with Statement (2) as folllows:

Statement (2) does not tell us how many students in Class A and we do not know what is the average of Class B. Not Sufficient; eliminate B and D.
Statement (1) alone does not tell us about no. of students of Class A and B or their ratio. Eliminate A.
Both Statement (1) and (2) also not sufficient because the missing part is still no. of students in Class A or the ratio of Class A and B students. Eliminate C.

Whether you use AD/BCE or BD/ACE, you can still come to the right answer. Then does it matter which one? Well, whichever statement (1) or (2) is "easier" for you to start. If Statement (1) is "easier", then use AD/BCE, use BD/ACE. After some practice, you should be able to master this technique and shave 1 minute from "easy" data sufficiency questions. If half of data sufficiency questions, say 6 questions, are "easy" ones, you have saved 6 minutes which you could use to tackle 2-3 "difficult" questions.

Look at the triangle again and visualize how it works. After a few attempts, you should be able to master this triangle. Draw this triangle at the start of your test and use it whenever you come across DS questions.

Jimmy Low

P/S: As you noticed, I use the quote/unquote marks when I mentioned "easy/easier" and "difficult" questions. What is "easy" for me might be "difficult" for you. It is a question of relative difficulty. But, with a strong foundation and more practice, you can handle them.