DS 大全

SECTION 1

30 Minutes 25 Questions

1. If today the price of an item is $3,600, what was the price of
the item exactly 2 years ago?

(1) The price of the item increased by 10 per-cent per year during
this 2-year period.

(2) Today the price of the item is 1.21 times its price exactly 2
years ago.

2. By what percent has the price of an overcoat been reduced?

(1) The original price was $380.

(2) The original price was $50 more than the reduced price.

3. If the Longfellow Playground is rectangular, what is its width?

(1) The ratio of its length to its width is 7 to 2.

(2) The perimeter of the playground is 396 meters.

4. What is the value of x –1?

(1) x + 1 =3

(2) x – 1 < 3

5. Is William taller than Jane?

(1) William is taller than Anna.

(2) Anna is not as tall as Jane.

6. In parallelogram ABCD
above, what is the measure of ∠ADC?

(1) The measure of ∠ABC is greater than 90^o.

(2) The measure of ∠BCD is 70^o

7. Is x² equal
to xy?

(1) x² – y² = (x + 5)(y - 5)

(2) x = y

8. Was 70 the average (arithmetic mean) grade on a class test?

(1) On the test, half of the class had grades below 70 and half of
the class had grades above 70.

(2) The lowest grade on the test was 45 and the highest grade on the
test was 95.

9. What was John’s average driving speed in miles per hour during a
15-minute interval?

(1) He drove 10 miles during this interval.

(2) His maximum speed was 50 miles per hour and his minimum speed
was 35 miles per hour during this interval.

10. Is ΔMNP isosceles?

(1) Exactly two of the angles, ∠M and ∠N, have the same measure

(2) ∠N and ∠P do not have the same measure.

11. Is n an integer
greater than 4?

(1) 3n is a positive
integer.

(2)  is a positive integer.

12. In ΔJKL shown above, what is the length of
segment JL?

(1) JK = 10

(2) KL = 5

13. A coal company can choose to transport
coal to one of its customers by railroad or by truck. If the railroad charges
by the mile and the trucking company charges by the ton, which means of
transporting the coal would cost less than the other?

(1) The railroad charges $5,000 plus $0.01 per mile per railroad car
used, and the trucking company charges $3,000 plus $85 per ton.

(2) The customer to whom the coal is to be sent is 195 miles away
from the coal company.

14. Is x – y > r – s?

(1) x > r and y < s?

(2) y = 2, s = 3, r = 5, and x = 6.

15. On a certain day it took Bill three times as long to drive from
home to work as it took Sue to drive from home to work. How many kilometers did
Bill drive from home to work?

(1) Sue drove 10 kilometers from home to work, and the ratio of distance
driven from home to work time to drive from home to work was the same for
Bill and Sue that day.

(2) The ratio of distance driven from home to work time to
drive from home to work for Sue that day was 64 kilometers per hour.

16. The figure above represents the floor of a square foyer with a
circular rug partially covering the floor and extending to the outer edges of
the floor as shown. What is the area of the foyer that is not covered by the
rug?

(1) The area of the foyer is 9 square meters.

(2) The area of the rug is 2.25π
square meters.

17. At a certain university, if 50 percent of the people who inquire
about admission policies actually submit applications for admission, what
percent of those who submit applications for admission enroll in classes at the
university?

(1) Fifteen percent of those who submit applications for admission
are accepted at the university.

(2) Eighty percent of those who are accepted send a deposit to the
university.

18. If x and y are nonzero integers, isan integer?

(1) x is the product of 2
and some other integer.

(2) There is only one pair of positive integers whose product equals
y.

19. If x is an integer,
what is the value of x?

(1)

     (2)

20. Is quadrilateral Q a
square?

(1) The sides of Q have
the same length.

(2) The diagonals of Q
have the same length.

21. If K is a positive
integer less than 10 and N = 4,321 + K, what is the value of K?

(1) N is divisible by 3.

(2) N is divisible by 7.

22. A jewelry dealer initially offered a bracelet for sale at an
asking price that would give a profit to the dealer of 40 percent of the
original cost. What was the original cost of the bracelet?

(1) After reducing this asking price by 10 percent, the jewelry
dealer sold the bracelet at a profit of $403.

(2) The jewelry dealer sold the bracelet for $1,953.

23. If n is an integer
between 2 and 100 and if n is also
the square of an integer, what is the value of n?

(1) n is the cube of an
integer.

(2) n is even.

24. Is x² – y² a positive number?

(1) x – y is a positive
number.

(2) x + y is a positive
number.

25. The surface area of a square tabletop was changed so that one of
the dimensions was reduced by 1 inch and the other dimension was increased by 2
inches. What was the surface area before these changes were made?

(1) After the changes were made, the surface area was 70 square
inches.

(2) There was a 25 percent increase in one of the dimensions.

SECTION 2

30 Minutes 25 Questions

1. Who types at a faster rate, John or Bob?

(1) The difference between their typing rates is 10 words per minute.

(2) Bob types at a constant rate of 80 words per minute.

2. What is the average distance that automobile D travels on one full tank of gasoline?

(1) Automobile D averages
8.5 kilometers per liter of gasoline.

(2) The gasoline tank of automobile D holds exactly 40 liters of gasoline.

3. If l₁,l₂ and l₃ are lines in a plane, is l₁
            perpendicu­lar
to l₃?

(1) l₁
is perpendicular to l_2.

(2) l₂ is
perpendicular to l₃

4. In a certain packinghouse, grapefruit are packed in bags and the
bags are packed in cases. How many grapefruit are in each case that is packed?

(1) The grapefruit are always packed 5 to a bag and the bags are
always packed 8 to a case.

(2) Each case is always 80 percent full.

5. What is the value of x?

(1) x + y = 7

(2) x – y = 3 – y
    

6. A rectangular floor that is 4 meters wide is to be completely
covered with nonoverlapping square tiles, each with side of length 0.25 meter,
with no portion of any tile remaining. What is the least number of such tiles
that will be required?

(1) The length of the floor is three times the width.

(2) The area of the floor is 48 square meters.

7. If a rope is cut into three pieces of
unequal length, what is the length of the shortest of these pieces of rope?

(1) The combined length of the longer two pieces of rope is 12
meters.

(2) The combined length of the shorter two pieces of rope is 11
meters.

8. A certain company paid bonuses of $125 to each of its executive
employees and $75 to each of its nonexecutive employees. If 100 of the
employees were nonexecutives, how many were executives?

(1) The company has a total of 120 employees.

(2) The total amount that the company paid in bonuses to its
employees was $10.000.

9. What fraction of his salary did Mr. Johnson put into savings last
week?

(1) Last week Mr. Johnson put $17 into savings.

(2) Last week Mr. Johnson put 5% of his salary into savings.

10. For integers a, b, and
c, , What is the value of ?

(1)

(2) a and b have no common factors greater than 1.

11. If the price of a magazine is to be doubled, by what percent
will the number of magazines sold decrease?

(1) The current price of the magazine is $1.00.

(2) For every $0.25 of increase in price, the number of magazines
sold will decrease by 10 percent of the number sold at the current price.

12. If J,
K, L, M, and N and positive
integers in ascending order, what is the value of L?

(1) The value of K is 3.

(2) The value of M is 7.

13. If a, b, and c are integers, is the number  divisible by 3?

(1) a + b is divisible by 3.

(2) c is divisible by 3.

14. Each M-type memory
unit will increase the base memory capacity of a certain computer by 3
megabytes. What is the base memory capacity, in megabytes of the computer?

(1) 2 M-type memory units
will increase the computers base memory capacity by 300 percent

(2) The memory capacity of the computer after 2 M-type memory units are added to the base memory capacity is 1.6
times the memory capacity of the computer after 1 M-type memory unit is added to the base memory capacity.

15. If xyz≠0, what is the value of

(1) x = 1

(2) y = 3

16. What fractional part of the total surface area of cube C is red?

(1) Each of 3 faces of C
is exactly  red.

(2) Each of 3 faces of C
is entirely white.

17. If positive integer x
is divided by 2, the remainder is 1. What is the remainder when x is divided by 4 ?

(1) 31 < x < 35

(2) x is a multiple of 3.

18. In the figure above, D
is a point on side AC of ΔABC. Is ΔABC is isosceles?

(1) The area of triangular region ABD is equal to the area of triangular region DBC.

(2) BD┴AC and AD = DC

19. If x is an integer,
what is the value of x?

(1) –2(x + 5) < -1

(2) – 3x > 9

20. The table above gives the number of calories and grams of
protein per kilogram of foods S and T. If a total of 7 kilograms of S and T are combined to make a certain food mixture, how many kilograms
of food S are in the mixture?

(1) The mixture has a total of 12,000 calories.

(2) The mixture has a total of 810 grams of protein.

21. If y≠0 and y≠-1, which is greater,

(1) x≠0

(2) x > y

22. Each person on a committee with 40 members voted for exactly one
of 3 candidates, F, G, or H. Did Candidate F receive the most votes from the 40 votes cast?

(1) Candidate F received
11 of the votes.

(2) Candidate H received
14 of the votes.

23. S is a set of integers
such that

i) if a is in S, then –a is in S, and

ii) if each of a and b is in S, then ab is in S.

  Is –4 in S?

(1) 1 is in S.

(2) 2 is in S.

24. If the area of triangular region RST is 25, what is the perimeter of RST?

(1) The length of one side of RST
is .

(2) RST is a right
isosceles triangle.

25. If x and y are consecutive odd integers, what is
the sum of x and y?

(1) The product of x and y is negative.

(2) One of the integers is equal to –1.

Answer:

Section
1:                  DCCAE        BBEAA         EDEDA        DEECC       BAACD

            Section 2:     ECCAB         DEDBA        CEBDA        CABCD      EABBA

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