Data Sufficiency
Answers & Explanations
1. B
(1) Insufficient. It may look like the two are equal,
but not necessarily. All the statement tells us is that
x2 is equal to y2. That
doesn't mean that x equals y, because one could be
negative and the other positive.
(2) Sufficient. This tells us that (x -
y) (x - y) = 0. So, (x - y) =
0. The only way the difference between the two variables can be 0
is if they are the same.
2. A.
(1) Sufficient. Since the quantity 2R is
divisible by 3, one of those two factors must be divisible by 3.
Since 1 isn't; R must be.
(2) Insufficient. We know that quantity 3R is
evenly divisible by 3, which means that at least one of the
factors must be divisible by 3. The problem, though, is that 3 is
evenly divisible by 3, making it impossible for us to determine
if R is.
3. D
(1) Sufficient. With the distance known, we could plug
it into the rate formula and computer Bill's rate.
(2) Sufficient. If he covered the same distance at 30
mph as he did at 60 mph, he must have been traveling at 30 mph
for twice as long as he was at 60 mph. Given that he traveled for
3 hours, he traveled at 30 mph for 2 hours and 60 mph for 1 hour.
That comes to 120 miles total distance, and again we solve for
the rate.
4. E
(1) Insufficient. Pick 10 for x and 5 for
y. This satisfies the statement and would allow us to
answer "yes" to the question. We can't stop here though; we have
to try different values to see if we can answer the question,
"no." Try 5 for x and -10 for y. These values
satisfy statement (1) but allow us to answer the question
"no."
(2) Insufficient. Try the same values. Those values
allow us to answer "no" to the question. But we need to consider
other values. If we set y equal to -5 and x equal
to 10, we can answer "yes" to the question.
You could guess between (C) and (E) or you could plug in some
more numbers. As it turns out the two statements are equivalent.
So they are just as insufficient together as they are
separate.
5. E
(1) Insufficient. Only information about the tie is
given. We know nothing about the belt.
(2) Insufficient. Only information about the belt is
given. We know nothing about the tie.
All we can determine is that a greater percentage discount was
obtained on the belt. Whether this translates into a greater
dollar discount cannot be determined.
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