|
Even though Data Sufficiency questions test the same math
content as Problem Solving, most GMAT students find that
they can’t use the same strategies on both question
types. One of the common errors students make in their approach
to Data Sufficiency questions is jumping to the two statements
without analyzing the question first and figuring out what
information is missing. You wouldn’t start hunting
for a jigsaw puzzle piece without first looking at the shape
of the hole you’re trying to fill, would you? Most
Data Sufficiency questions can be simplified with the Pieces
of the Puzzle approach, and some would be nearly impossible
to solve without it.
There are a two principles that underlie the Pieces of
the Puzzle strategy:
- It’s easier to do one thing at a time than to
do two things simultaneously.
- It’s easier to find something when you know what
you’re looking for.
Let’s look at some examples.
|
A bicycle rider rides four stages of a race in 2
hours and 45 minutes. The four stages are named with
four different colors: blue, yellow, red, and white.
What is the rider’s average speed for the whole
race?
1) The red and blue stages combined are 55 miles
long.
2) The blue and yellow stages combined are 42 miles
long.
|
Before looking closely at the statements, we should consider
the question and determine what we’re looking for.
The question asks for an average speed, so this is a question
about rates and we should write down the rate formula: Rate
= Distance / Time. The time is given to us, so the only
thing we need to know in order to find the rate is the distance.
That’s the missing piece of this puzzle. This means
that when we turn to the statements we’re no longer
thinking about rate, we’re thinking about distance.
If the statement allows us to find the total distance of
the race then it is sufficient. If not, it’s insufficient.
Statement 1 tells us the combined distance of two of the
stages, but that isn’t enough to know the distance
of the whole race. Thus Statement 1 is insufficient.
Statement 2 also tells us the combined distance of only
two stages, and is therefore insufficient for the same reason
as Statement 1. When we combine the statements we have to
be a bit careful. It may seem that now we have all four
stages, but in fact the blue stage was mentioned twice,
and nowhere do we have any information about the white stage.
There is no way to know the total distance of the race,
and the answer is (E).
Let’s look at another example:
| If x is an integer, is 3x
a factor of 15! ?
1) x is the sum of two distinct single-digit prime
numbers.
2) 0 < x < 6
|
This is a much more complicated question than the first
one, and we really have to do some thinking up front before
we worry about the statements. First, this is a Yes/No question,
so we need to be clear that it doesn’t matter whether
the answer is yes or no, whether 3x is a factor
of 15! or not. All that matters is that we know for certain
one way or the other. So how will we know?
3x describes a certain number of 3s multiplied
together. If 3x is a factor of 15! then all those
3s divide evenly into 15! with nothing left over (if z is
a factor of some number then that number is divisible by
z). The question becomes, “How many factors of 3 are
there in 15! ?” Write out 15! and count the factors
of 3.
15! = 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x
4 x 3 x 2 x 1.
There’s one in the 15 (3 x 5), one in the 12 (3 x
4), two in the 9 (3 x 3), one in the 6 (3 x 2) and one in
the 3 (3 x 1). That’s a total of six 3s. So now we
can finally say what the missing piece of the puzzle is.
Since 15! contains six factors of 3, if x = 6 or anything
less than 6 then 3x will be a factor of 15! and
the answer will be Yes. If x is anything larger than 6 then
3x will not be a factor of 15! because it will
have too many 3s. The answer will be No. So the key question
we’re concerned with as we turn to the statements
is do we know whether x<=6 or x>6? If we know the
answer to that question then our data is sufficient; if
we don’t, it’s not.
Statement 1 tells us that x is the sum of two distinct
single-digit prime numbers. The single-digit prime numbers
are 2, 3, 5, and 7. Now 2 + 3 = 5 which is less than 6,
but 3 + 5 (for example) = 8 which is greater than 6. We
have numbers less than 6 and greater than 6 that both satisfy
Statement 1, so we can’t answer our question with
certainty. Statement 1 is insufficient. Statement 2 tells
us that x is between 0 and 6. This means it must be 1, 2,
3, 4, or 5, all of which are of course less than 6. We know
for certain that x<6 so we have answered our question
definitively. Statement 2 is sufficient and the answer to
the question is (B).
That last question was a lot of work! But we were able
to get the answer because we knew what we were looking for
when we turned to the statements. Without that initial investment
in analyzing the question and figuring out the missing piece
of the puzzle, we would have had a hard time seeing anything
useful in the statements. Remember to use the Pieces of
the Puzzle approach on Data Sufficiency questions, and you’ll
find yourself solving them more quickly and more accurately.
|
