MODEL TEST 3
SECTION 1 —VERBAL ABILITY
Select the best answer to the following questions, then fill in the
appropriate space on your Answer Sheet.
Directions: In each of the following antonym questions, a word
printed in capital letters precedes five lettered words or phrases.
From these five lettered words or phrases, pick the one most nearly
opposite in meaning to the capitalized word.
1. PARIAH:
(A) miser
(B) nomad
(C) servant
(D) idol
(E) renegade
2. EXACERBATE:
(A) alleviate
(B) bewilder
(C) contemplate
(D) intimidate
(E) economize
Directions: Each of the following sentence completion questions
contains one or two blanks. These blanks signify that a word or set
of words has been left out. Below each sentence are five words or
sets of words. For each blank, pick the word or set of words that
best reflects the sentence's over-all meaning.
3. Although he was generally considered an extremely ______individual,
his testimony at the trial revealed that he had been very ______.
(A) intrepid...valiant
(B) guileless...hypocritical
(C) abstemious...temperate
(D) meek...timorous
(E) ingenuous...obtuse
4. The perpetual spinning of particles is much like that of a top,
with one significant difference: unlike the top, the particles have
no need to be wound up, for ______ is one of their ______ properties.
(A) revolution...radical
(B) motion...intangible
(C) rotation...intrinsic
(D) acceleration...lesser
(E) collision...hypothetical
Directions: Each of the following analogy questions presents a
related pair of words linked by a colon. Five lettered pairs of words
follow the linked pair. Choose the lettered pair of words whose
relationship is most like the relationship expressed in the original
linked pair.
5. DEFLECT : MISSILE ::
(A) defend : fortress
(B) reflect : mirror
(C) diversify : portfolio
(D) dismantle : equipment
(E) distract : attention
6. MULISH : PLIANCY ::
(A) piggish : gluttony
(B) sluggish : reluctance
(C) kittenish : motility
(D) apish : servility
(E) shrewish : amiability
Directions: Each of the following reading comprehension questions is
based on the content of the following passage. Read the passage and
then determine the best answer choice for each question. Base your
choice on what this passage states directly or implies, not on any
information you may have gained elsewhere.
How is a newborn star formed? For the answer
to this question, we must look to the familiar
physical concept of gravitational instability. It is a
Line simple concept, long-known to scientists, having
(5) been first recognized by Isaac Newton in the late
1600s.
Let us envision a cloud of interstellar atoms
and molecules, slightly admixed with dust. This
cloud of interstellar gas is static and uniform.
(10) Suddenly, something occurs to disturb the gas,
causing one small area within it to condense. As
this small area increases in density, becoming
slightly denser than the gas around it, its gravitational field likewise increases somewhat in
(15) strength. More matter now is attracted to the area,
and its gravity becomes even stronger; as a result,
it starts to contract, in the process increasing in density even more. This in turn further increases its
gravity, so that it accumulates still more matter
(20) and contracts further still. And so the process
continues, until finally the small area of gas gives
birth to a gravitationally bound object, a newborn
star.
7. It can be inferred from the passage that the author views the
information contained within it as
(A) controversial but irrefutable
(B) speculative and unprofitable
(C) uncomplicated and traditional
(D) original but obscure
(E) sadly lacking in elaboration
8. The author provides information that answers which of the
following questions?
Ⅰ. How does the small area's increasing density affect its
gravitational field?
Ⅱ. What causes the disturbance that changes the cloud from its
original static state?
Ⅲ. What is the end result of the gradually increas-ing concentration
of the small area of gas?
(A) Ⅰ only
(B) Ⅱ only
(C) Ⅰ and Ⅱ only
(D) Ⅰ and Ⅲ only
(E) Ⅰ, Ⅱ and Ⅲ
Antonyms
9. CONTENTIOUS:
(A) amenable
(B) inactive
(C) dispassionate
(D) callow
(E) severe
10. DEBACLE:
(A) effort
(B) success
(C) drought
(D) transience
(E) dominance
Sentence Completion
11. Whereas off-Broadway theater over the past several seasons has
clearly ______ a talent for experimentation and improvisation, one
deficiency in the commercial stage of late has been its marked
incapacity for
(A) manifested...spontaneity
(B) lampooned...theatricality
(C) cultivated...orthodoxy
(D) disavowed...histrionics
(E) betrayed...burlesque
Analogies
12. CLOY : PALATE ::
(A) sniff : nose
(B) slit : tongue
(C) surfeit : appetite
(D) cling : touch
(E) refine : taste
13. PRATFALL: EMBARRASSMENT ::
(A) deadlock : mortification
(B) checkup : reluctance
(C) downfall : penitence
(D) diehard : grievance
(E) windfall : jubilation
Reading Comprehension
With Meredith's The Egoist we enter into a
critical problem that we have not yet before faced
in these studies. That is the problem offered by a
Line writer of recognizably impressive stature, whose
(5) work is informed by a muscular intelligence,
whose language has splendor, whose "view of
life" wins our respect, and yet for whom we are at
best able to feel only a passive appreciation which
amounts, practically, to indifference. We should
(10) be unjust to Meredith and to criticism if we
should, giving in to the inertia of indifference,
simply avoid dealing with him and thus avoid the
problem along with him. He does not "speak to
us," we might say; his meaning is not a "meaning
(15) for us"; he "leaves us cold." But do not the challenge and the excitement of the critical problem
as such lie in that ambivalence of attitude which
allows us to recognize the intelligence and even
the splendor of Meredith' s work, while, at the
(20) same time, we experience a lack of sympathy, a
failure of any enthusiasm of response?
14. According to the passage, the work of Meredith is noteworthy for
its elements of
(A) sensibility and artistic fervor
(B) ambivalence and moral ambiguity
(C) tension and sense of vitality
(D) brilliance and linguistic grandeur
(E) wit and whimsical frivolity
15. All of the following can be found in the author's discussion of
Meredith EXCEPT
(A) an indication of Meredith's customary effect on readers
(B) an enumeration of the admirable qualities in his work
(C) a selection of hypothetical comments at Meredith' s expense
(D) an analysis of the critical ramifications of Meredith's effect on
readers
(E) a refutation of the claim that Meredith evokes no sympathy
16. It can be inferred from the passage that the author finds the
prospect of appraising Meredith's work critically to be
(A) counterproductive
(B) overly formidable
(C) somewhat tolerable
(D) markedly unpalatable
(E) clearly invigorating
17. It can be inferred from the passage that the author would be most
likely to agree with which of the following statements about the role
of criticism?
(A) Its prime office should be to make our enjoyment of the things
that feed the mind as conscious as possible.
(B) It should be a disinterested endeavor to learn and propagate the
best that is known and thought in the world.
(C) It should enable us to go beyond personal prejudice to appreciate
the virtues of works antipathetic to our own tastes.
(D) It should dwell upon excellencies rather than imperfections,
ignoring such deficiencies as irrelevant.
(E) It should strive both to purify literature and to elevate the
literary standards of the reading public.
Sentence Completion
18. Soap operas and situation comedies, though given to distortion,
are so derivative of contemporary culture that they are inestimable
______ the attitudes and values of our society in any particular
decade.
(A) contraventions of
(B) antidotes to
(C) indices of
(D) prerequisites for
(E) determinants of
19. Perry's critics in the scientific world ______ that many of the
observations he has made during more than a decade of research in
Costa Rica have been reported as ______ in popular magazines rather
than as carefully documented case studies in technical journals.
(A) intimate...hypotheses
(B) charge...anecdotes
(C) applaud...rumors
(D) claim...scholarship
(E) apologize...fabrications
Antonyms
20. GAUCHE:
(A) grotesque
(B) tactful
(C) rightful
(D) fashionable
(E) inane
21. HAPLESS:
(A) fortuitous
(B) fortunate
(C) fortified
(D) forbidden
(E) forestalled
22. PROLIXITY:
(A) proximity
(B) disinclination
(C) circuitousness
(D) extremity
(E) terseness
Analogies
23. CONTEMPORANEOUS : EVENTS ::
(A) adjacent : objects
(B) modem : times
(C) temporary : measures
(D) gradual : degrees
(E) repetitive : steps
24. LIMERICK : POEM ::
(A) motif : symphony
(B) prologue : play
(C) catch : song
(D) sequence : sonnet
(E) epigraph : novel
Sentence Completion
25. Slander is like counterfeit money: many people who would not coin
it______it without qualms.
(A) waste
(B) denounce
(C) circulate
(D) withdraw
(E) invest
Antonyms
26. DIATRIBE:
(A) medley
(B) dilemma
(C) afterthought
(D) rebuttal
(E) praise
27. GAINSAY:
(A) estimate
(B) corroborate
(C) forfeit
(D) expend
(E) neglect
Reading Comprehension
The Quechua world is submerged, so to speak,
in a cosmic magma that weighs heavily upon it.
It possesses the rare quality of being as it were
Line interjected into the midst of antagonistic forces,
(5) which in turn implies a whole body of social and
aesthetic structures whose innermost meaning
must be the administration of energy. This gives
rise to the social organism known as the ayllu, the
agrarian community that regulates the procure(10) ment of food. The ayllu formed the basic structure of the whole Inca empire.
The central idea of this organization was a
kind of closed economy, just the opposite of our
economic practices, which can be described as
(15) open. The closed economy rested on the fact that
the Inca controlled both the production and consumption of food. When one adds to this fact the
religious ideas noted in the Quechua texts cited
by the chronicler Santa Cruz Pachacuti, one
(20) comes to the conclusion that in the Andean zone
the margin of life was minimal and was made
possible only by the system of magic the Quechua
constructed through his religion. Adversities,
moreover, were numerous, for the harvest might
(25) fail at any time and bring starvation to millions.
Hence the whole purpose of the Quechua administrative and ideological system was to carry on
the arduous task of achieving abundance and
staving off shortages. This kind of structure pre(30) supposes a state of unremitting anxiety, which
could not be resolved by action. The Quechua
could not do so because his primordial response
to problems was the use of magic, that is,
recourse to the unconscious for the solution of
(35) external problems. Thus the struggle against the
world was a struggle against the dark depths of
the Quechua's own psyche, where the solution
was found. By overcoming the unconscious, the
outer world was also vanquished.
(40) These considerations permit us to classify
Quechua culture as absolutely static or, more
accurately, as the expression of a mere state of
being. Only in this way can we understand the
refuge that it took in the germinative center of the
(45) cosmic mandala as revealed by Quechua art. The
Quechua empire was nothing more than a mandala, for it was divided into four zones, with
Cuzco in the center. Here the Quechua ensconced
himself to contemplate the decline of the world as
(50) though it were caused by an alien and
autonomous force.
28. The term "mandala" as used in the last paragraph most likely
means
(A) an agrarian community
(B) a kind of superstition
(C) a closed economic pattern
(D) a philosophy or way of regarding the world
(E) a figure composed of four divisions
29. The author implies that the Quechua world was
(A) uncivilized
(B) highly introspective
(C) vitally energetic
(D) free of major worries
(E) well organized
30. With which of the following statements would the author most
likely agree?
(A) Only psychological solutions can remedy economic ills.
(B) The Quechua were renowned for equanimity and unconcern.
(C) The Quechua limited themselves to realizable goals.
(D) Much of Quechua existence was harsh and frustrating.
(E) Modern Western society should adopt some Quechua economic ideas.
SECTION 2—QUANTITATIVE ABILITY
In this section use scrap paper to solve each problem. Then decide
which is the best of the choices given and fill in the corresponding
oval on the Answer Sheet.
Directions: In the following type of question, two quantities appear,
one in Column A and one in Column B. You must compare them. The
correct answer to the question is
A if the quantity in Column A is greater
B if the quantity in Column B is greater
C if the two quantities are equal
D if it is impossible to determine which quantity is greater
Notes: Sometimes information about one or both of the quantities is
centered above the two columns. If the same symbol appears in both
columns, it represents the same thing each time.
Directions: In the following questions, choose the best answer from
the five choices listed.
5. If 80% of the adult population of a village is registered to vote,
and 60% of those registered actually voted in a particular election,
what percent of the adults in the village did NOT vote in that
election?
(A) 20 (B) 40 (C) 48 (D) 50 (E) 52
6. If of a number is 7 more than
number?
of the number, what is
of the
(A) 12 (B)15 (C) 18 (D) 20 (E) 24
7. An operation, *, is defined as follows: for any positive numbers a
and b.
Which of the following is an integer?
(A) 11*5 (B) 4*9 (C) 4*16
(D) 7*4 (E) 9*9
10. Two sides of a right triangle are 5 and 6. Which of the following
could be the length of the third side?
(A) Ⅰ only (B) Ⅲ only (C) Ⅰ and Ⅱ only
(D) Ⅰ and Ⅲ only (E) Ⅰ, Ⅱ, and Ⅲ
14. In which of the following pairs of years were the ratios of
Republican receipts to Democratic receipts most nearly equal?
(A) 1981-82 and 1985-86
(B) 1983-84 and 1995-96
(C) 1987-88 and 1989-90
(D) 1987-88 and 1995-96
(E) 1991-92 and 1993-94
15. Between which two consecutive two-year periods was there the
greatest percent increase in the Democratic receipts?
(A) 1981-82 to 1983-84
(B) 1985-86 to 1987-88
(C) 1989-90 to 1991-92
(D) 1991-92 to 1993-94
(E) 1993-94 to 1995-96
18. Which of the following points lies in the interior of the circle
whose radius is 10 and whose center is at the origin?
(A) (-9, 4) (B) (5,-9) (C) (0,-10)
(D) (10,-1) (E) (-6, 8)
19. For any numbers a, b, and c,
For which of the following equations is it true that there is exactly
one positive integer that satisfies it'?
(A) none (B) Ⅰ only (C) Ⅲ only
(D) Ⅰ and Ⅲ only (E) Ⅰ, Ⅱ, and Ⅲ
20. The revenue from lottery ticket sales is divided between prize
money and the various uses shown in the graph labeled "Proceeds." In
1997, what per-cent of the money spent on tickets was returned to the
purchasers in the form of prize money?
(A) 23.5% (B) 50% (C) 60% (D) 66%
(E) 74%
21. Approximately what percent of the proceeds that went to the
states' General fund would have to be given to the senior citizen
programs so that the proceeds for the senior citizen programs and the
Cities would be equal?
(A) 0.9% (B) 9% (C) 31% (D) 48%
(E) 69%
22. If x+y=a,y+z=b, andx+z=c, whatisthe average (arithmetic mean) of
x, y, and z?
26. In the figure above, what is the value of h?
(A) 2 (B) 2.2 (C) 2.4 (D) 2.6 (E) 2.8
27. Let P and Q be points which are two inches apart, and let A be
the area, in square inches, of a circle which passes through P and Q.
Which of the following is the set of all possible values for A?
(A) 0＜A (B) 0＜A ≤π (C) A=π
(D) A＞π (E) A ≥π
28. In 1950 Roberto was four times as old as Juan. In 1955 Roberto
was three times as old as Juan. How old was Roberto when Juan was
born?
(A) 5 (B)10 (C) 20 (D) 30 (E) 40
Answer Key
Section 1—Verbal Ability
1. D. The opposite of a pariah or person rejected by society is an
idol or person greatly loved by society.
Think of being "shunned as a pariah."
2. A. The opposite of to exacerbate (to worsen or make more harsh) is
to alleviate or lighten.
Think of "exacerbating a quarrel."
3. B. In reputation he was a guileless or undeceitful person; in real
life he showed himself to have been hypocritical or deceptive.
Note the use of although to signal the contrast
4. C. Particles have no need to be wound up because the property of
spinning (rotation) is built into their makeup: it is intrinsic.
5. E. By definition, a missile is deflected when it turns aside from
its original direction. Likewise, someone's attention is distracted
when it turns aside from its original direction. (Definition)
6. E. Someone mulish (stubborn) is not characterized by pliancy
(readiness to yield). Someone shrewish (ill-tempered) is not
characterized by amiability. (Antonym Variant)
7. C. To the author the concept is both simple and traditional,
dating as it does from Newton's time.
8. D. You can answer this question by the process of elimination.
Question I is answerable on the basis of the passage. As the area's
density increases, its gravitational field increases in strength.
Therefore, you can eliminate Choice B. Question Ⅱ is not answerable
on the basis of the passage. The passage nowhere states what disturbs
the gas. Therefore, you can eliminate Choices C and E.
Question Ⅲ is answerable on the basis of the passage. The end result
of the process is the formation of a gravitationally bound object, a
newborn star. Therefore, you can eliminate Choice A.
Only Choice D is left. It is the correct answer.
9. A. The opposite of contentious (quarrelsome, belligerent) is
amenable (readily brought to yield, tractable).
Note that contentious derives from the verb to contend (to struggle
or argue), not the adjective content.
Think of "a particularly contentious argument."
10. B. The opposite of a debacle (downfall; failure; collapse) is a
success.
Think of "the Wall Street debacle of 1987."
11. A. The off-Broadway and Broadway theaters are contrasted here.
The former has manifested or shown a talent for improvisation,
extemporaneous or spontaneous performance. The latter has manifested
no such talent for spontaneity. Note the use of whereas to establish
the contrast.
12. C. By definition, an excess of once-pleasing flavors cloys or
sates the palate (seat of the sense of taste). An excess of oncetempting foodstuffs surfeits or sates the appetite. (Definition)
13. E. A pratfall is a humiliating mishap that causes you to feel
embarrassment. A windfall is an unexpected piece of good fortune that
causes you to feel jubilation. (Cause and Effect)
14. D. The author cites Meredith's intelligence (brilliance) and his
splendor of language (linguistic grandeur).
15. E. Rather than refuting the claim, the author clearly
acknowledges Meredith's inability to evoke the reader's sympathy.
Choice A is incorrect. From the start the author points out how
Meredith leaves readers cold.
Choice B is incorrect. The author reiterates Meredith's virtues,
citing muscular intelligence and literary merit.
Choice C is incorrect. The author quotes several such imagined
criticisms.
Choice D is incorrect. The author indicates that if readers choose to
avoid dealing with Meredith, they shall be doing a disservice to the
cause of criticism.
Only Choice E remains. It is the correct answer.
16. E. Speaking of the "challenge and excitement of the critical
problem as such," the author clear-ly finds the prospect of
appraising Meredith critically to be stirring and invigorating.
17. C. The author wishes us to be able to recognize the good
qualities of Meredith's work while at the same time we continue to
find it person-ally unsympathetic. Thus, she would agree that
criticism should enable us to appreciate the virtues of works we
dislike.
Choices A, B, and E are unsupported by the passage.
Choice D is incorrect. While the author wishes the reader to be aware
of Meredith's excellences, she does not suggest that the reader
should ignore those qualities in Meredith that make his work
unsympathetic. Rather, she wishes the reader to come to appreciate
the very ambivalence of his critical response.
18. C. Soap operas and situation comedies are derivative of
contemporary culture: they take their elements from that culture.
Therefore, they serve as indices (signs or indications) of what is
going on in that culture; they both point to and point up the social
attitudes and values they portray.
Note that the soap operas and comedies here cannot be determinants of
our society's attitudes and values: they derive from these attitudes
and values; they do not determine them.
19. B. The critics charge (make the accusation) that Perry has
published only anecdotes of his observations and not detailed
analyses. Note that critics would be unlikely to applaud the
publication of rumors or apologize for Perry's publication of
fabrications or lies. Thus, you can eliminate Choices C and E.
Similarly, popular magazines would be unlikely to publish scientific
hypotheses or examples of scholarship. You therefore can rule out
Choices A and D as well.
20. B. The opposite of gauche (awkward; lacking in social grace or
tact) is tactful.
Think of being embarrassed by "a gauche remark."
21. B. The opposite of hapless (unlucky) is fortunate. Think of
"hapless unfortunates."
22. E. The opposite of prolixity (wordiness) is terse-ness or brevity.
Think of "long-winded prolixity."
23. A. Events that are contemporaneous (occurring within the same
time frame) exist in temporal reference to one another. Objects that
are adjacent exist in spatial reference to one another. (Defining
Characteristic)
24. C. A limerick is a kind of poem. A catch is a kind of song.
Note how simple the relationship of the original pair of words is.
Analogy questions seldom are this easy. This should alert you to be
on the lookout for something particularly deceptive among the answer
choices. In this case, catch is used in an uncommon manner. (Class
and Member)
25. C. Whatever word you choose here must apply equally well both to
slander and to counterfeit money. People who would not make up a
slanderous statement circulate slander by passing it on. So too
people who would not coin or make counterfeit money circulate
counterfeit money by passing it on. Note how the extended metaphor
here influ-ences the writer's choice of words.
26. E. The opposite of a diatribe (abusive criticism) is praise.
Think of "a bitter diatribe."
27. B. The opposite of to gainsay or contradict is to corroborate or
support.
Beware eye-catchers. To gainsay derives from to say against, not from
to gain. Think of "gainsaying an assertion."
28. E. The passage compare the Quechua empire to a mandala because
"it was divided into four parts." Thus, a mandala is most likely a
figure composed of four divisions.
29. B. The author refers to the Quechua as existing in "a state of
unremitting anxiety, which could not be resolved by action" and which
the Quechua could only deal with by looking into himself and
struggling with the depths of his own psyche. This suggests that the
Quechua world was highly introspective.
30. D. Both the unremitting anxiety of Quechua life and the recurring
harvest failures that brought starvation to millions illustrate the
harshness and frustration of Quechua existence.
Section 2—Quantitative Ability
Two asterisks (**) indicate an alternative method of solving.
1. B. In each column, the sum includes the numbers from -3 to 3.
Since all the other numbers in Column A are negative and those in
Column B are positive, Column B is greater. (Note that we didn't have
to calculate either sum. We just used TACTIC 5, Chapter 12 and compared the columns.)
2. A. Since Y is inside the circle it is closer to the center than X,
which is on the circle. Column A is greater.
3. B. Since x + y = 1, at least one of the numbers is positive. If
either x or y is 0, the product xy = 0; and if either one is negative,
then xy is negative. In each case, xy is less than 1. If both x and y
are positive, then each is less than 1, and so is their product.
Column B is' greater.
4. A. There is not enough information provided to determine the
values of a, b, c, d, e, f, and g, but they are irrelevant. Since the
sum of the measures of the seven angles is 360°, their average is
360° + 7 = 51.4°. Column A is greater.
5. E. If there are x adults in the village, then .8x of them are
registered and .6(8x) = .48x voted. Therefore, x -.48x = .52x or 52%
of the adults did not vote.
**You can avoid the algebra by assuming there are 100 adults. Then 80
of them are registered and 60% of 80 = 48 of them voted. So 52 did
not vote, and
.
6. D. Let the number be x, and write the equation:
Multiply both sides by 12:
9x = 84 + 2x
Subtract 2x from each side and divide by 7:
7x = 84
x=12
Be careful: 12 is not the answer. You were asked for
of the
number:
7. D. There's nothing to do except check each choice until you find
one that works. In ques-tions such as this, it is often faster to
start'with E and work towards A.
E:
, which is not an integer.
D:
an integer.
Once you find the answer, do not waste any time trying the other
choices—they won't work.
8. C. Let r and R be the radii of the two circles. From the figure,
you can see that ΔOAB is a 45-45-90 right triangle, and so R =
(KEY FACT J8). Therefore,
The ratio is 2:1.
**Do exactly the same thing except use TACTIC 2, Chapter 11. Let r =
1 ; then R =
and the ratio is
9. D. If x = 3 and y = 7 (or vice versa), then x + y = 10, and Column
B is greater. Eliminate Choices A and C. If x = 1 and y = 21 (or vice
versa), then x + y = 22. This time, Column A is greater. Eliminate
Choice B. Neither column is always greater, and the two columns are
not always equal.
10. D. Either (i) 5 and 6 are the lengths of the two legs, or (ii) 5
is the length of a leg, and 6 is the hypotenuse. In either case use
the
Pythagorean theorem:
Statements Ⅰ and Ⅱ only are true.
11. B. The average of x and y is less than y, so having another y
raises the average [KEY FACT E4]. Column B is greater.
**Use TACTIC 1, Chapter 12. Plug in numbers. Column A: the average of
2 and 4 is 3.
Column B: the average of 2, 4, and 4 is more than 3, because the
extra 4 raises the average (it's 3.333). The answer is B.
12. B. If you draw a diagram, it is immediately clear that the area
of the large triangle is more than twice the area of the small one.
In fact, it is 4 times as great. Column B is larger.
**Use the formula for the area of an equilateral triangle of side s:
Column B is larger.
13. B. The area of the large circle is πR2 and the area of the small
circle is πr2, so the area of the shaded region is πR2 -πr2 = π(R2
-r2). Since the shaded region and the white region have the same area,
which is less than 1.5. Column B is greater.
14. C. For each of the pairs of years in question, use the graph to
approximate the ratio of Republican to Democratic receipts. For example, in 1981-82, Republican receipts were slightly over $200 million
and Democratic receipts were about $40 million, a ratio of 5: 1.
The only two pairs of years in which the ratio was very close were
1987-88 and 1989-90; in both of those pairs of years the ratio was
very nearly 2:1.
15. A. In 1981-82 the Democratic receipts were about $40 million and
in 1983-84 they had increased to about $100 million, an increase of
150%. From 1991-92 to 1993-94 (Choice D), receipts decreased. During
the periods covered by Choices B, C, and E, receipts increased, but
by less than 150%.
16. A. Column A: the area of a square of side a is a:. Column B:
since the diameter of the circle is a, the radius is
area of the circle is
Column A is greater.
which is less than a2,
, and so the
＜ 1.
17. B. To find the average speed, in miles per hour, divide the
distance, in miles, by the time, in hours. All drove 90 miles
in 2.25 hours (135 minutes = 2 hours and 15 minutes = hours).
90 + 2.25 = 40. Column B is greater.
18. A. Find the distance from each point to (0,0), the center of the
circle. We're looking for a point that is less than 10 units from the
center. The distance from (a,b) to (0,0) equals
Check each point. A: (-9,4)
＜10 (KEY FACT N2).
**Clearly, (0,-10) is 10 units from the origin, and so is on the
circle. Also, since (10,0) is on the circle, (10,-1) is outside. The
others are too close to call without knowing the formula or using the
Pythagorean theorem, so if you're not sure, guess.
19. C. Check each choice to see which equation has exactly one
positive integer solution.
Ⅰ. For every number a: (0)(a)(-a) = 0 and 0 + a + (-a) = 0, so for
every positive integer a,
Ⅱ.
We're looking for positive solutions,
so assume a ≠ 0, and divide by a:
But
is not an
integer. (Ⅱ is false.)
Ⅲ.
a2 = 1. This equation has one
positive integer solution, a = 1. (Ⅲ is true.)
Statement Ⅲ only is true.
20. D. The difference between the total ticket sales ($35.5 billion)
and the total distribution of the proceeds ($12.0 billion) was the
amount returned to the purchasers of lottery tickets in the form of
prize money:
$35.5 billion -$12.0 billion = $23.5 billion.
Divide 23.5 by 35.5 (or approximate, by dividing 24 by 36) to see
that 66% of the tick-et sales was allocated to prize money.
21. C. In order for the amount received by senior cit-izens programs
to be the same as the amount received by the Cities, an additional
$0.9 bil-lion would have to be allocated to the senior citizens
programs: $0.9 billion is approxi-mately 31% of the $2.9 billion
currently going to the General fund.
22. D.
**Use TACTIC 2, Chapter 11: substitute for the variables. Let x = 1,
y = 2, and z = 3. Then the average of x, y, and z is 2. When a = 1 +
2 = 3, b=2+3 =5, andc= 1 + 3 = 4, which of the choices equals 2? Only
23. B. The area of the large square is S2, and the area of the small
square is s2, so the area of the shaded region is S2 -s2. Since the
shaded region and the unshaded region have the same area,
which is less than 1.5 Column B is greater.
24. A. You do not need to add the lengths of the steps. Together, all
the horizontal steps are equal to the bottom, and all the vertical
risers are equal to the left side. The sum of the left side, 5 feet 4
inches, or 64 inches, and the bottom, 9 feet 2 inches, or 110 inches,
is half the perimeter. The perimeter is 2(64 + 110) = 2(174) = 348
inches. Column A is greater.
25. A. If the average of the three digits is 2, the sum of the digits
is 6. The simplest thing is to list them. If there are only a few,
list them all; if it seems that there will be too many to list, look
for a pattern. The list starts this way: 105, 114, 123, 132, 141, 150,
so there are6 of them in the 100s. Continue: 204, 213, 222, 23I, 240.
There are 5 in the 200s. You can conclude, correctly, that there are
4 in the 300s, 3 in the 400s, 2 in the 500s, and 1 in the 600s. So,
the total is 6 + 5 +4 + 3 + 2 + 1 = 21. If you don't spot the pattern,
just continue the list: 303, 312,…, 501,510, 600.
26. C. Since the area of a right triangle is
the of its legs, the
area is
= 6. product But the area can also be calculated as
Since this is a 3-4-5 triangle, the base is 5.
So,
27. E. If PQ is a diameter of the circle, then the radius is 1 and A,
the area, is π. This is the smallest possible value of A, but A can
be any number larger than π if the radius is made sufficiently large,
as shown by the figures below.
The answer is A ≥ π.
28. D. Make a table to determine Roberto's and Juan's ages. Let x
represent Juan's age in 1950, and fill in the table as shown.
1950
1955
Roberto
4x
4x+5
Juan
x
x+5
In 1955, Roberto was 3 times as old as Juan,
so
Therefore, in 1950, Juan was 10 and Roberto was 40. Because Roberto
is 30 years older than Juan, Roberto was 30 when Juan was born.