# Data sufficiency

GMAT Study Guide - a prep wikibook

## General information

Data sufficiency has a unique question format developed especially for the GMAT. Nobody knows why data sufficiency and not data deficiency or something else; perhaps, cause ETS wanted to check decision making skills or ability to act promptly with unfamiliar questions. We don't know.

What we know, however, are a few traps that DS poses to a test taker. You will learn most of them when you practice, but we feel we need to warn you about them.

## Data sufficiency traps

The way answer choices work is the first trap of DS. They seem clear at first, but that's only the tip of the iceberg. What often confuses people is when enough or not. Thus, an answer choice is enough only and only if using the information provided in it, you can get an exact numerical value such as 4, $\frac{162}{3}$, or similar. However, it is not enough to say that b=a, or to have two values (for example if you have $x^2 = 16$, then $x$ is 4 and -4) this is not sufficient, there must be only one value. When one of the statements produces several possible answers (such as 9 and 5 or 3 and -3), the result is undefined.

There are several theories whether the two statements given with the DS question should result in the same numerical answer if either is sufficient. This controversy is illustrated below:

{{#x:box| Example 1. Triangle ABC has one angle equal to 90 degrees and AB equal to 5 inches, what is the area of ABC?

i. BC = 4

ii. AC = 12 }}

Apparently both answer choices are sufficient to answer the question, but in two cases, the numeric answer differs. In the first case we get a 3-4-5 triangle and in the second 5-12-13, thus area of ABC1 is 6 and ABC2 is 30. It is still unknown whether this is possible under ETS's regulations or not. I know for sure that some companies ignore this rule, such as Princeton for example. If we are able to say that ETS does not support the idea of getting two different numeric answers on the same DS question, it will become easier to eliminate some answer choices. Please, respond if you encounter an example of this sort.

To solve or not to solve? Every test taker moves through DS cycles. First, when one encounters GMAT, DS seem to be fairly simple and easy to solve. Then, we realize that we don't need to solve and DS becomes the easiest thing in the world. The third step happens when Problem Solving score goes up, and DS stays the same or falls down. Then we get back to solving DS, so the pattern goes like this: solve >> not solve >> solve.

There is a general belief that one should not solve DS since all it asks is enough or not enough to answer. In fact, many textbooks tell not to solve. However, under “do not solve” is implied to do the job of compiling an equation, get it to the final form and stop only when all you have to do is calculations. To get the majority of DS right, you need to solve, but you don't need to calculate. Don't try to solve in your head, use paper, don't stare at the problem trying to hypnotize it. See example below:

{{#x:box| Example 2. What is the volume of a box with dimensions $a$, $b$, and $c$?

i. $a = \frac{18}{bc}$

ii. $b = 2$, $c = 4$ }}

At the first glance both statements are needed to answer the question, but when actually attempted, the problem appears solvable. If you did not compile an equation, you did not see that the volume of a body is ; the first statement is enough to answer. Often, ETS will use fractions and they will cancel out, providing you with an answer; always make sure you write down the formula/equation.

{{#x:box| Example 3. What is the value of $x$?

i. $x + 2y = 6$

ii. $4y + 2x = 12$ }}

If you solve without a careful look, you will think that since there are two equations and two variables, you will find the solution. Nope. Both statements are masked and appear identical. According to our members, such problems are very common on the real GMAT.

{{#x:box| Example 4. How many miles is it from George's house to the groceries store?

i. If George did not visit a gas station on his way to the groceries store, he would have driven 4 miles less.

ii. The gas station is 8 miles from George's house }}

{{#x:box| Example 5. How many children are there in Nancy's class?

i. Yesterday there were 14 kids in the class besides Nancy

ii. Usually there are 2 kids who are sick and not present in the class }}

Do not assume anything on data sufficiency. Some questions ask you to give them a little of something - Don't. For Example 4, we don't know how George's house is situated on the map related to the gas station or the groceries store; it can be a straight line or a triangle, therefore we don't have enough information to give an answer, E.

In the Example 5, we cannot say how many children are in Nancy's class since we may not assume that yesterday there was a normal situation and only 2 children were not present. It may have been a big School Play day, so even the sick children came to see it. We don't know, therefore E.

{{#x:box| Example 6. Is the sum of six consecutive integers even?

i. The first integer is odd

ii. The average of six integers is odd }}

{{#x:box| Example 7. Does $x$ equal 3?

i. $x^2 = 9$

ii. $x$ minus three is negative 6 }} Watch out for Yes/No data sufficiency questions; they are the hardest and the most misleading.

Example 6: The answer to this one is D. (1) Statement says that the sum of the integers is odd, which gives a NO answer to our question, but is SUFFICIENT to give an answer, therefore sufficient. (2) Says that the sum is odd, which is sufficient to give a Yes answer. In both cases it was sufficient to answer the question, except in the first case, the answer was NO and in the other, it was YES. Make sure you don't confuse No with insufficient because they are not related here.

Example 7: the first statement is not sufficient since a square of x can equal either positive or negative 3, therefore it is not enough. The second statement, however, provides us with a value for x, negative 3. Therefore it is sufficient to answer the question. The answer is B.

Do not combine answer choices. What ETS often does on harder DS questions, it gives the first piece of info as insufficient and the second being sufficient by itself. Yet, naturally, as one moves on during the test rush, to the second statement that nicely adds to the first and makes it sufficient to answer, he/she misses the possibility that the second choice can be sufficient by itself. Do not eliminate this possibility.

When you solve a medium/hard DS question, it is good to play a game; try to find the trick in the puzzle. If you looked through the both pieces of info and it seems both are needed to be sufficient, try finding a trick why only one could be sufficient or vise versa. This technique pays of with hard DS questions that often have a more complex solution than seems from the first glance.

As always on GMAT, make an analysis of your mistakes and see what DS questions cause the most problems.

Finally, make sure you don't confuse D and C and know the answer choices by heart.

## Traps review

1. Always write down the whole formula/equation
2. Watch out for masked statements; take extra time to check the solution, not just think that you will be able to answer a question since there are two statements; they may cancel out
3. Do not assume anything on the DS; if you think the author is pushing too much, you are probably right
4. Yes/No questions - know them
5. Do not combine answer choices
6. Play a game with yourself and try to prove yourself wrong; helps with difficult DS
7. Make sure you know the answer choices and don’t confuse C and D
8. Make analysis of your errors