5-Step Game Plan

You’ll apply these fundamental steps to the following three sample questions. At the risk of giving away the answers up front, the correct answer is different for each question. Take a minute or two to attempt each one. (We’ll analyze all three questions below.)

Sample Questions

1. If a jewelry merchant bought a particular ring for $10,000 and sold the ring to Judith, how much did Judith pay for the ring?
   
   
   1. The merchant’s profit from the sale was 50%.
   
   
   
   2. The amount that the merchant paid for the ring was two-thirds the amount that Judith paid for the ring.
   
   
   1. Statement (1) ALONE is sufficient, but statement (2) alone is NOT sufficient to answer the question asked.
   2. Statement (2) ALONE is sufficient, but statement (1) alone is NOT sufficient to answer the question asked.
   3. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
   4. Each statement ALONE is sufficient to answer the question asked.
   5. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

2. The symbol ¤ represents the third digit in the 5-digit number 62,¤79. What number does ¤ represent?
   
   
   1. 62,¤79 is a multiple of 3.
   
   
   
   2. The sum of the digits of 62,¤79 is divisible by 4.
   
   
   1. Statement (1) ALONE is sufficient, but statement (2) alone is NOT sufficient to answer the question asked.
   2. Statement (2) ALONE is sufficient, but statement (1) alone is NOT sufficient to answer the question asked.
   3. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
   4. Each statement ALONE is sufficient to answer the question asked.
   5. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

3. If xy ≠ 0, is x > y?
   
   
   1. |x| > |y|
   
   
   
   2. x = 2y
   
   
   1. Statement (1) ALONE is sufficient, but statement (2) alone is NOT sufficient to answer the question asked.
   2. Statement (2) ALONE is sufficient, but statement (1) alone is NOT sufficient to answer the question asked.
   3. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
   4. Each statement ALONE is sufficient to answer the question asked.
   5. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

The 5-Step Plan

Here’s the 5-step approach that will help you to handle any Data Sufficiency question.

Step 1: Size up the question first. As with Problem Solving questions, assess what specific mathematical area is being tested (e.g., what mathematical rules and formulas come into play). By determining what you’re up against, you’re well on your way to dealing with the question. Data Sufficiency questions, just like Problem Solving questions, vary widely in difficulty level. Try to get a feel for your limitations in handling complex questions. Determine how much time you’re willing to spend on the question, if any.

Step 2: Size up the two statements and look for a shortcut to the correct answer. Before you plunge into a full-blown analysis of statement (1), read both statements and ask yourself:

• Do the statements provide essentially the same information? If so, the answer is probably either choice (D) or choice (E).



• Does either statement establish a solvable system of equations (for example, two equations in two variables)?



• Does a statement seem to merely repeat (paraphrase) all or some of the information in the question? (If so, you can’t answer the question with that statement alone.)

Asking yourself questions such as these may in some cases enable you to determine the correct answer choice without doing any more work. Otherwise, proceed to step 3.

Step 3. Consider statement (1) alone. If the information provided in statement (1) suffices to answer the question, eliminate choices (B), (C), and (E) as viable answer choices. On the other hand, if statement (1) is insufficient alone, eliminate choices (A) and (D) as viable answer choices.

Step 4. Consider statement (2) alone. If the information provided in statement (2) suffices to answer the question, eliminate choices (A), (C), and (E) as viable answer choices. On the other hand, If statement (2) is insufficient alone, eliminate choices (B) and (D) as viable answer choices.

Step 5. If neither statement alone suffices to answer the question, consider both statements together. Now if you can answer the question, the correct answer choice is (C). If you still don’t have enough information, the correct answer choice is (E).

Apply the 5-Step Plan

It’s time to go back to the three sample questions you looked at a few pages back. Let’s walk through them—one at a time—using the 5-step game plan you just learned.

Note: By now you’re probably familiar with the five answer choices, so we won’t bother including them with the questions from now on.

Question 1

Question 1 is a relatively easy question. Approximately 85% of test-takers respond correctly to questions like it. Here’s the question again:

1. If a jewelry merchant bought a particular ring for $10,000 and sold the ring to Judith, how much did Judith pay for the ring?
   
   
   1. The merchant’s profit from the sale was 50%.
   
   
   
   2. The amount that the merchant paid for the ring was two-thirds the amount that Judith paid for the ring.

Step 1: The focus of this question is the concept of percent increase—in the context of a word problem involving profit. This type of question is usually fairly easy, so you can expect to determine the correct response within a minute—without resorting to an educated guess. It should be worth investing your time on this one.

Step 2: Notice that the two statements (1 and 2) provide the same information—only in different ways! This is a huge clue that the correct answer choice is either (D) or (E). You’ll still have to consider one of the two statements alone, but that should suffice.

Step 3: Consider the premise, along with statement (1) alone. (Disregard statement (2) for now.) Given that the merchant paid $10,000 for the ring, if the merchant earned a 50% profit from the sale to Judith, determining Judith’s ring price is a simple matter of adding 50% of $10,000 to $10,000:

$10,000 + .5($10,000) = Judith’s ring price

At this point, it’s clear that you can determine Judith’s ring price by simple multiplication and addition. Don’t waste time actually computing Judith’s ring price. You know that statement (1) alone suffices to answer the question and that’s all you need to know! Eliminate choices (B), (C), and (E) from consideration. The correct choice must be either (A) or (D).

Step 4: If you’re not convinced that both statements say essentially the same thing, go ahead and consider the premise along with statement (2) alone. (Disregard statement (1) for now.) If the merchant’s cost was 2/3 of the amount Judith paid, then Judith paid 3/2 of the merchant’s cost. Determining Judith’s ring price is a simple matter of multiplying $10,000 by 3/2:

$10,000 × 3/2 = Judith’s ring price

At this point, it’s clear that you can determine Judith’s ring price by simple multiplication. As in step 3, don’t waste time actually computing that price. You know that statement (2) alone suffices to answer the question and that’s all you need to know!

Step 5: This step is unnecessary here. There’s no need to consider both statements together. You know that either statement (1) or (2) alone suffices to answer the question, so you can eliminate choices (C) and (E). The correct answer must be D.

Question 2

Question 2 is average in difficulty level. Approximately 65% of test-takers respond correctly to questions like it. Here’s the question again:

2. The symbol ¤ represents the third digit in the 5-digit number 62,¤79. What number does ¤ represent?
   
   
   1. 62,¤79 is a multiple of 3.
   
   
   
   2. The sum of the digits of 62,¤79 is divisible by 4.

Step 1: This question is testing on factors and divisibility. The peculiar use of a “placeholder” is a typical GMAT technique for testing your understanding of integers and digits. Questions such as these are usually straightforward once you know the basic rules as well as a few shortcuts for divisibility.

Step 2: Both statements appear to add different information to the question. So there’s no obvious shortcut here. (Go on to step 3.)

Step 3: Consider statement (1) alone. If the sum of the digits of a number is divisible by 3, the number is also divisible by 3. Excluding the digit represented by ¤, the sum of the digits in the number 62, ¤79 is 24. Accordingly, if the number is a multiple of (divisible by) 3, the missing digit must be 0, 3, 6, or 9. Since there’s more than one possible value for ¤, statement (1) alone is insufficient to answer the question. Eliminate answer choices (A) and (D).

Step 4: Consider statement (2) alone. The number that ¤ represents can be 0, 4, or 8. Thus, statement (2) alone is insufficient to answer the question. Eliminate answer choice (B).

Step 5: Consider statements (1) and (2) together. The two statements together establish that the missing digit is 0, because 0 is the only common number in between the two lists of possible values for ¤. Thus, statements (1) and (2) together are sufficient to answer the question, and the correct answer choice is (C).

Question 3

Question 3 is moderately difficult. Approximately 45% of test-takers respond correctly to questions like it. Here’s the question again:

3. If xy ≠ 0, is x > y?
   
   
   1. |x| > |y|
   
   
   
   2. x = 2y

Step 1: This is a typical absolute value question. Whenever you see inequalities and variables but no numbers, that’s a clue that you’ll need to consider different types of numbers—such as negative numbers, positive numbers, fractions, and perhaps the numbers 0 and 1—to determine the correct answer choice. Getting to the answer might entail performing some simple calculations, and perhaps a bit of trial and error (plugging in possible values).

Step 2: Both statements appear to add different information to the question. So there’s no obvious shortcut here. But a good reasoned guess at this point would be that the correct answer choice is (E). Why? Because the question doesn’t restrict the value of either x or y (except that neither can equal 0). So if you’re pressed for time, guess choice (E) and move on to the next question. Otherwise, go on to step 3.

Step 3: You must consider both positive and negative values for x and y. Given |x| > |y|, an x-value of either 4 or –4 and a y-value of 2, for example, satisfies the inequality but results in two different answers to the question. Thus, statement (1) alone is insufficient to answer the question. Eliminate answer choices (A) and (D).

Step 4: Similarly, given x = 2y, if you use negative values for both x and y (for example, x=(-4) and y=(-2), the answer to the question is no; but if you use positive values (for example, x = 4 and y = 2), the answer to the question is yes. Thus, statement (2) alone is insufficient. Eliminate answer choice (B).

Step 5: Statements (1) and (2) together are still insufficient. For example, if x=(-4) and y=(-2), both statements (1) and (2) are satisfied, x < y, and so the answer to the question is no. However, if x = 4 and y = 2, statements (1) and (2) are both satisfied, but x > y, and the answer to the question is yes. Eliminate answer choice (C). The correct answer must be E.

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