This Method is the essential systematic approach to mastering Data Sufficiency. Use
this approach for every Data Sufficiency question. It will allow you to answer questions
quickly and will guarantee that you avoid the common Data Sufficiency mistake of subconsciously
combining the statements instead of considering them separately at first.
Step 1: Analyze the Question Stem
There are three things you should accomplish in this step:
Determine Value or Yes/No. Which type of Data Sufficiency question is this? Depending on whether the question
is a Value question or a Yes/No question, the rules for sufficiency are a little different.
If you treat the two types the same way, you probably won’t get the right answer.
Later in this chapter, you’ll learn the critical differences between these two types.
Simplify. If the given information is an equation that can be simplified, you should do so
up front. Likewise, any word problems should be translated into math or otherwise
paraphrased in your scratchwork. When a question asks for the value of a specific
variable and gives you a multi-variable equation, isolate the variable being asked
for so you can more clearly see what kind of information you need in order to solve.
Identify What Is Needed to Answer the Question. What kind of information would get you the answer to the question? The more you think
up front about what information would be sufficient, the better you’ll be able to
evaluate the statements.
Don’t rush through this step, even for seemingly simple questions. The more you glean
from the question stem, the easier it will be to find the right answer.
Step 2: Evaluate the Statements Using 12TEN
Since the answer choices depend on considering each statement alone, don’t let the
information you learn from one statement carry over into your analysis of the other.
Consider each statement separately, in conjunction with the question stem. Remember
that each statement is always true. Don’t waste time verifying the statements; just
evaluate whether this information lets you answer the question.
On Test Day, you don’t want to spend even a second reading the answer choices or thinking
about which answer choice is which. They will never change, so you will save yourself
much time and confusion by memorizing what the answer choices mean and working with
them until you’ve fully internalized them.
A helpful way to remember how the answer choices are structured is to use the acronym
1-2-TEN.
1
Only Statement (1) is sufficient.
2
Only Statement (2) is sufficient.
T
You must put the statements together for them to be sufficient.
E
Either statement alone is sufficient.
N
Neither separately nor together are the statements sufficient.
In fact, it’s so important to memorize the answer choices that after this initial
sample question, we will no longer print the choices along with the questions. For
each practice question, you should follow the routine you will use on Test Day: write
12TEN in your scratchwork for each question and cross out the incorrect answer choices
as you eliminate them. We’ll teach you patterns for eliminating answer choices later
in this chapter.
Applying the Kaplan Method for Data Sufficiency
Now, let’s apply the Kaplan Method for Data Sufficiency to the question you saw at
the beginning of this chapter:
Is the product of x, y, and z equal to 1?
x + y + z = 3
x, y, and z are each greater than 0.
Statement (1) ALONE is sufficient, but Statement (2) is not sufficient.
Statement (2) ALONE is sufficient, but Statement (1) is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
Step 1: Analyze the Question Stem
This is a Yes/No question. If xyz = 1, then the answer is yes. If xyz ≠ 1, then the answer is no. Either answer—yes
or
no—would be sufficient. There’s
nothing that needs to be simplified in this step; all variables are in their simplest
terms, and there are no common variables to combine. It’s often worth thinking about
how you could get the
yes
or
no
that you’re looking for. For instance, if x, y, and z all equal 1, you would get an answer of
yes.
But is this the only way? This question
is short but definitely not simple, since there may be many other possibilities to consider.
Step 2: Evaluate the Statements Using 12TEN
Picking numbers for Statement (1), you can readily see how to get a
yes: x = 1, y = 1, and z = 1. Can you pick numbers in such a way that the sum is 3 but the product is not
1? Not if you only consider positive integers. But if you consider different kinds
of numbers, you can easily find some. Zero doesn’t alter a sum, but it forces a product
to be 0. So x = 3, y = 0, and z = 0, while they follow the restrictions given in Statement (1), will give you an
answer of no to the original question. Since you can get both a
yes
and a
no,
Statement (1) is insufficient. Eliminate (A) and (D)—or choices “1” and “E,” if you’ve written 12TEN in your scratchwork.
Now that you’ve reached a verdict on Statement (1) on its own, completely put Statement
(1) out of your mind as you evaluate Statement (2) independently. Statement (2) rules
out the possibility of using 0 but not the possibility of using fractions or decimals.
So x = 1, y = 1, and z = 1 is also permissible here, but so is something like x = 100, y = 100, and z = 100. So xyz could equal 1, but it could also equal 1,000,000. So you can get both a
yes
and
a
no
here, as well. Statement (2) is also insufficient, so you can eliminate (B)—which is the “2” of 12TEN.
Since each statement is insufficient on its own, you need to consider them together.
Can you pick numbers that add to 3 and are all positive? Again, x = 1, y = 1, and z = 1 makes the cut and answers the question with a
yes.
Can you think of numbers
that don’t multiply to 1 that also are consistent with both statements? Once again, you have
to expand your thinking to include other types of numbers besides positive integers.
Fractions and decimals make things bigger when added but smaller when multiplied.
For example, x = 2.8, y = 0.1, and z = 0.1 fit the bill. They are all positive and sum to 3. Their product is 2.8(0.1)(0.1)
= 0.028; this answers the question with a
no.
Since you can get both a
yes
and
a
no
answer, the statements are insufficient to answer the question even when combined.
The answer is (E)—which corresponds to the “N” of 12TEN.
Now take a few minutes and answer the questions in the following practice set. Don’t
worry if they’re challenging at first; you’re only getting started working with this
unique question type. For now, do not concentrate on speed—or even on getting the
correct answer in the end—but rather on building your technique for approaching Data
Sufficiency questions systematically using the Method. You’ll get much more practice
with these questions throughout the chapter.
Practice Set: The Kaplan Method for Data Sufficiency
How many employees of Company R are surveyors?
Exactly
of the employees of Company R are not surveyors.
The 18 architects in Company R constitute 25 percent of the company’s total employees.
If a5 ≥ −32 and a is an integer, what is the value of a?
6a + 18 ≤ 12
a2 > 2
If 3b − |a| = 27, what is the value of b?
a2 = 81
a3 > 0
The nth term of a sequence of distinct positive integers is determined by
, where n ≥ 3 and k is a constant. If a2 = 4, and a3 = 36, what is the value of
?
a1 = 2
k = 3
A ferry crosses a lake and then returns to its starting point by the same route. The first time it crosses the lake, the ferry travels at 15 kilometers per hour. The ferry’s return trip takes 3 hours. How many hours does the ferry take for the first leg of the trip?
The ferry’s average speed for the entire round trip is 12 kilometers per hour.
The distance the ferry covers to cross the lake once is 30 kilometers.
of the employees of Company R are not surveyors.
, where n ≥ 3 and k is a constant. If a2 = 4, and a3 = 36, what is the value of
?