（1） The ratio of DE to BF is 1： 3.
（2） D and E are midpoints of sides AB and CB， respectively.
Since we do not even know whether BF is an altitude， nothing can be determin
ed from （1）。 More importantly， there is no information telling us the absolu
te size of the triangle.
As to （2）， although from geometry we know that DE = AC/2， this relationship
holds for any size triangle. Hence， （2） is also insufficient2.
Together， （1） and （2） are also insufficient since we still don't have inform
ation about the size of the triangle， so we can't determine the perimeter. T
he answer is E.
3. A dress was initially3 listed at a price that would have given the store a
profit of 20 percent of the wholesale4 cosplayt. What was the wholesale cosplayt of
the dress？
（1） After reducing the asking price by 10 percent， the dress sold for a net
profit of 10 dollars.
（2） The dress sold for 50 dollars.
Consider just the question setup. Since the store would have made a profit o
f 20 percent on the wholesale cosplayt， the original price P of the dress was 12
0 percent of the cosplayt： P = 1.2C. Now， translating （1）sintosan equation yield
s：
P - .1P = C + 10
Simplifying gives
9P = C + 10
Solving for P yields
P = （C + 10）/.9
Plugging this expression for PsintosP = 1.2C gives
（C + 10）/.9 = 1.2C
Since we now have only one equation involving the cosplayt， we can determine the
cosplayt by solving for C. Hence， the answer is A or D.
（2） is insufficient since it does not relate the selling price to any other
information. Note， the phrase initially listed implies that there was more
than one asking price. If it wasn't for that phrase， （2） would be sufficien
t. The answer is A
4. What is the value of the two-digit number x？
（1） The sum of its digits5 is 4.
（2） The difference of its digits is 4.
Considering （1） only， x must be 13， 22， 31， or 40. Hence， （1） is not suffici
ent to determine the value of x.
Considering （2） only， x must be 40， 51， 15， 62， 26， 73， 37， 84， 48， 95， or 5
9. Hence， （2） is not sufficient to determine the value of x.
Considering （1） and （2） together， we see that 40 and only 40 is common to th
e two sets of choices for x. Hence， x must be 40. Thus， together （1） and （2）
are sufficient to uniquely determine the value of x. The answer is C.
5. If x and y do not equal 0， is x/y an integer？
（1） x is prime.
（2） y is even.
（1） is not sufficient since we don't know the value of y. Similarly， （2） is
not sufficient. Furthermore， （1） and （2） together are still insufficient sin
ce there is an even prime number2. For example， let x be the prime number
2， and let y be the even number 2 （don't forget that different variables can
stand for the same number）。 Then x/y = 2/2 = 1， which is an integer. For al
l other values of x and y， x/y is not an integer. （Plug in a few values to v
erify this.） The answer is E.
6. Is 500 the average （arithmetic mean） score on the GMAT？
（1） Half of the people who take the GMAT score above 500 and half of the peo
ple score below 500.
（2） The highest GMAT score is 800 and the lowest score is 200.
Many students mistakenly think that （1） implies the average is 500. Suppose
just 2 people take the test and one scores 700 （above 500） and the other sco
res 400 （below 500）。 Clearly， the average score for the two test-takers is n
ot 500. （2） is less tempting6. Knowing the highest and lowest scores tells us
nothing about the other scores. Finally， （1） and （2） together do not determ
ine the average since together they still don't tell us the distribution of
most of the scores. The answer is E.7. The set S of numbers has the following properties：
I） If x is in S， then 1/x is in S.
II） If both x and y are in S， then so is x + y.
Is 3 in S？
（1） 1/3 is in S.
（2） 1 is in S.
Consider （1） alone. Since 1/3 is in S， we know from Property I that 1/（1/3）
= 3 is in S. Hence， （1） is sufficient.
Consider （2） alone. Since 1 is in S， we know from Property II that 1 + 1 = 2
（Note， nothing in Property II prevents x and y from standing7 for the same n
umber. In this case both stand for 1.） is in S. Applying Property II again s
hows that 1 + 2 = 3 is in S. Hence， （2） is also sufficient. The answer is D.
8. What is the area of the triangle above？
（1） a = x， b = 2x， and c = 3x.
（2） The side opposite a is 4 and the side opposite b is 3.
From （1） we can determine the measures of the angles： a + b + c = x + 2x + 3
x = 6x = 180
Dividing the last equation by 6 gives： x = 30
Hence， a = 30， b = 60， and c = 90. However， different size triangles can hav
e these angle measures， as the diagram below illus
