OK, so 670 was a decent score, but numerically I got the most wrong yet – 23 out of 113, 13 out of 52 quant and 10 out of 61 verbal. 1 cr, 4 rc, 5 sentence correction. At least there’s not a ‘bias’ any more: the mistakes are more evenly spread.
A certain college has a student-to-teacher ratio of 11 to 1. The average (arithmetic mean) annual salary for teachers is $26,000. If the college pays a total of $3,380,000 in annual salaries to its teachers, how many students does the college have?
I chose E, and I think it’s a simple arithmetic error. Getting rid of some zeroes, the college’s wage bill is 3380 and salaries 26; 3380/26 = 130. Multiply by 11 = 1430. Should have got this.
If the operation . is defined for all a and b by the equation a . b = a^2 b / 3, then 2 . (3 . -1) =
(D) – 2
(E) – 4
I chose A. Can any of the four operators, + * / -, make 2 . (3 . -1) equal to any of the answers? If it’s ‘add’, then 2 . (3 . -1) gives 4, answer A. If it’s ‘subtract’, ‘multiply’, or ‘divide’, 2 . (3 . -1) equals -2, -6, or -2/3. So it’s A or D. A’s not bad for a guess – but wrong nonetheless. The correct answer is E. Why? Because the question asks you to look at the letters, not the numbers. You can’t assume the symbol is any of the basic operators.
I see no way of solving this, and I’d definitely have got the question wrong. Add ‘missing operator questions’ to my list of conundrums.
A factory that employs 1000 assembly line workers pays each of these workers $5 per hour for the first 40 hours worked during a week and 1½ times that rate for hours worked in excess of 40. What was the total payroll for the assembly-line workers for a week in which 30 percent of them worked 20 hours, 50 percent worked 40 hours, and the rest worked 50 hours?
I chose E, probably still in a whirl from the previous question. But it should be easy. All 1000 of them worked 20 hours ($5 x 20 x 1000 = $100,000), 70 percent worked a further 20 hours up to the 40 limit ($5 x 20 x 700 = $70,000) and 20 percent worked another 10 hours on top at 1.5 times rate ($7.5 x 10 x 200 = $15,000). The answer is B.
If x ≠ 2, then 3x^2(x-2)-x+2 / x-2 =
(A) 3x^2 – x + 2
(B) 3x^2 + 1
(D) 3x^2 – 1
(E) 3x^2 – 2
I chose E. But there’s a clue in those (x-2) terms. Dividing 3x^2(x-2) by (x-2) gives plain 3x^2. I forgot to do the same to the other term and divide -x+2 by x-2, which gives -1 (x divided by x) and -1 (+2 divided by -2). -1-1 = -2. There’ll be a -2 at the end of our answer. Which is E.
1/2 / 1/4 + 1/6 =
Why did I get this wrong with C? It’s simple converting bases: to 6/12 / 3/12 + 2/12, which is 6/12 / 5/12. The answer’s easy: it must be greater than 1, since 6/12 is greater than the number we’re dividing it by. The only answer fitting that description is A.
Machines A and B always operate independently and at their respective constant rates. When working alone, machine A can fill a production lot in 5 hours, and machine B can fill the same lot in x hours. When the two machines operate simultaneously to fill the production lot, it takes them 2 hours to complete the job. What is the value of x ?
(A) 3 1/3
(C) 2 1/2
(D) 2 1/3
(E) 1 1/2
I got B. But the maths is simple: A fills at 1/5 every hour, B fills at x every hour, and A+B together fill at 1/2 every hour. So A = 0.2, B = x, and A+B = 0.5. B = 0.3, which means B will take 3 1/3 hours to fill working alone. The answer is A.
I got the next 2 questions correct, but I don’t know why, so I’m reviewing them here.
What is the units digit of (13)^4 (17)^2 (29)^3 ?
I guessed E, which is correct, but what is a ‘units digit’? Basic stuff: it’s the figure on the immediate left of the decimal point. Aha – all those numbers are primes, so it doesn’t matter about the exponents; all the results will be divisible only by 13, 17, and 29. But if I cheat with a calc, the actual number doesn’t have a 1 next to the decimal point. This question’s a rogue.
The shaded region in the figure above represents a rectangular frame with length 18 inches and width 15 inches. The frame encloses a rectangular picture that has the same area as the frame itself. If the length and width of the picture have the same ratio as the length and width of the frame, what is the length of the picture, in inches?
(D) 15(1- 1/√2)
I chose A, and here’s why. The exposed part of the frame has the same area as the smaller rectangle; in other words, the backing rectangle has twice the area of the fronting rectangle. 18 x 15 is 270, so half that is the smaller rectangle’s area, 135. What number multipled by a bit less than itself gets close to that?
Not B, which is 1.5; not C, which is about 40; not D, which is tiny (5 or so.) or E. A is the only possible option.
OK, now back to the ones I got wrong…
Pat will walk from intersection X to intersection Y along a route that is confined to the square grid of four streets and three avenues shown in the map above. How many routes from X to Y can Pat take that have the minimum possible length ?
I chose A, having run out of time on this one, but it’s about domains and ranges. The minimum walk is 5 blocks (check a couple and see); so the question is: how many walks of 5 blocks are in the set of all walks between 4 streets and 3 avenues?
It isn’t A, because I can count eight without doing any maths. But I’m not sure how to apply the equations to this problem, so I need more work on this general area. The correct answer is C.
A retailer purchased a television set for x percent less than its list price, and then sold it for y percent less than the list price. What was the list price of the
(1) x = 15
(2) x – y = 5
I chose C. Reasonable guess, but wrong. 1 alone certainly isn’t enough, because it tells us nothing about y (eliminating A) and Statement 2 tells us nothing about x (eliminating B.) But C – that ought to work? x makes a TV listed at $100 bought for $85 and sold at $90?
Wrong – because the $100 I inserted is arbitrary. Nothing here tells us anything about what the list price was, just its percentages. So the answer is E. Kicking myself over this one.
If Sara’s age is exactly twice Bill’s age, what is Sara’s age?
(1) Four years ago, Sara’s age was exactly 3 times Bill’s age.
(2) Eight years from now, Sara’s age will be exactly 1.5 times Bill’s age.
I chose C, missing the fact that Sara is twice as old as Bill today. But in fact there’s another clue this is wrong: both statements are essentially saying the same thing; neither has more info than the other.
Can we work it out? We know s = 2b. Four years ago, s-4 = 3(b-4), which is 3b-12. So s = 3b-8. Since s also equals 2b, 2b = 3b-8. b must be 8, Bill must be 8 and Sara 16 today. (Four years ago, Bill was 4 and Sara 8; all on the level.)
It works for Statement 2 as well. s = 2b and s+8 = 1.5(b+8). So s = 1.5b+12-8. Since s still equals 2b, 2b = 1.5b+4, meaning 4 must be a half of b. 2b = 16, so in eight years Bill will be 16 and Sara 24. Either statement lets us work it out alone, so the answer is D. But remember: you don’t need to work it out. If I can recognise this type of question, and that both statements are saying essentially the same thing, I can mark it D straight away and save precious minutes.
An infinite sequence of positive integers is called an “alpha sequence” if the number of even integers in the sequence is finite. If S is an infinite sequence of positive integers, is S an alpha sequence?
(1) The first ten integers in S are even.
(2) An infinite number of integers in S are odd.
I guessed B. If there are ten even integers in the sequence, there might be an infinite number more, so we don’t know whether there’s a finite number of even integers from 1 alone. Nor can we tell from 2, since the presence of an infinite number of odd integers doesn’t preclude there being an infinite number of evens, too. You can’t tell from this, so it’s E.
If xy > 0, does (x – 1)(y – 1) = 1?
(1) x + y = xy
(2) x = y
I chose C. But FOILing it out gives you xy -x -y + 1 = 1, which is the same as saying xy – x – y = 0, which is the same as xy = x + y, so statement 1 provides no additional info. But knowing x = y adds something – it’d mean x^2 – 2x +1 must equal 1, which is what the question asks. The correct answer is C: with both statements we can solve it.
I got the thinking on this totally wrong: again, not paying attention to the question – it’s not asking what x or y is; it’s asking if that equation is equal to 1.
I chose C here, thinking we needed both those digits. But the total’s only 4, so the other two signs can only be 1,2, or 3. They can’t both be 2 (different symbols) so the boat-shape must be 1 and the triangle-shape 3. Statement 1 is enough.
Statement 2, however, tells us nothing about the triangle-shape or the star-shape, and isn’t enough alone. The answer is A.
The table above shows the cancellation fee schedule that a travel agency uses to determine the fee charged to a tourist who cancels a trip prior to departure. If a tourist canceled a trip with a package price of $1,700 and a departure date of September 4, on what day was the trip canceled?
(1) The cancellation fee was $595.
(2) If the trip had been canceled one day later, the cancellation fee would have been $255 more.
I chose B, daftly enough. We don’t need to do any working out here. Statement 1 gives us a range of dates but not the exact date. Statement 2 narrows it down to a single day, adding enough info to let us work out the exact date (but not enough that we could work it out based on statement 2 alone, since more than one range of dates goes up in 15% increments.) The answer is C.
A report on acid rain concluded, ‘Most forests in Canada are not being damaged by acid rain.’ Critics of the report insist the conclusion be changed to, ‘Most forests in Canada do not show visible symptoms of damage by acid rain, such as abnormal loss of leaves, slower rates of growth, or higher mortality.’ Which of the following, if true, provides the best logical justification for the critics’ insistence that the report’s conclusion be changed?
(A) Some forests in Canada are being damaged by acid rain.
(B) Acid rain could be causing damage for which symptoms have not yet become visible.
(C) The report does not compare acid rain damage to Canadian forests with acid rain damage to forests in other countries.
(D) All forests in Canada have received acid rain during the past fifteen years.
(E) The severity of damage by acid rain differs from forest to forest.
I chose D. It’s a reasonable choice, but wrong. At least it’s not A – ‘some’ could mean ‘minimal’ – nor is it C, since this is about Canada only. D hardly supports the critic’s case, since it implies acid rain has caused no damage. And E is wrong; this isn’t about severity. The best choice is B.
Historians of women’s labor in the United States at first largely disregarded the story of female service workers — women earning wages in occupations such as salesclerk, domestic servant, and office secretary. These historians focused instead on factory work, primarily because it seemed so different from traditional, unpaid “women’s work” in the home, and because the underlying economic forces of industrialism were presumed to be gender-blind and hence emancipatory in effect. Unfortunately, emancipation has been less profound than expected, for not even industrial wage labor has escaped continued sex segregation in the workplace.
To explain this unfinished revolution in the status of women, historians have recently begun to emphasize the way a prevailing definition of femininity often determines the kinds of work allocated to women, even when such allocation is inappropriate to new conditions. For instance, early textile-mill entrepreneurs in justifying women’s employment in wage labor, made much of the assumption that women were by nature skillful at detailed tasks and patient in carrying out repetitive chores; the mill owners thus imported into the new industrial order hoary stereotypes associated with the homemaking activities they presumed to have been the purview of women. Because women accepted the more unattractive new industrial tasks more readily than did men, such jobs came to be regarded as female jobs. And employers, who assumed that women’s “real” aspirations were for marriage and family life, declined to pay women wages commensurate with those of men. Thus many lower-skilled, lower-paid, less secure jobs came to be perceived as ‘female.’
More remarkable than the origin has been the persistence of such sex segregation in twentieth-century industry. Once an occupation came to be perceived as ‘female,’ employers showed surprisingly little interest in changing that perception, even when higher profits beckoned. And despite the urgent need of the United States during the Second World War to mobilize its human resources fully, job segregation by sex characterized even the most important war industries. Moreover, once the war ended, employers quickly returned to men most of the ‘male’ jobs that women had been permitted to master.
Which of the following best describes the relationship of the final paragraph to the passage as a whole?
(A) The central idea is reinforced by the citation of evidence drawn from twentieth-century history
(B) The central idea is restated in such a way as to form a transition to a new topic for discussion.
(C) The central idea is restated and juxtaposed with evidence that might appear to contradict it.
(D) A partial exception to the generalizations of the central idea is dismissed as unimportant.
(E) Recent history is cited to suggest that the central idea’s validity is gradually diminishing.
I chose D. Because I didn’t read the question properly: it asks not what the final paragraph does, but about its relationship to the rest of the passage! Well, it’s not B or E – there’s no new topic in sight, nor does it diminish the central idea about women’s gains not being as obvious as you might think – leaving C and A. Nothing’s juxtaposed here, so it’s not C. The answer must be A.
According to a recent theory, Archean-age gold-quartz vein systems were formed over two billion years ago from magmatic fluids that originated from molten granitelike bodies deep beneath the surface of the Earth. This theory is contrary to the widely held view that the systems were deposited from metamorphic fluids, that is, from fluids that formed during the dehydration of wet sedimentary rocks.
The recently developed theory has considerable practical importance. Most of the gold deposits discovered during the original gold rushes were exposed at the Earth’s surface and were found because they had shed trails of alluvial gold that were easily traced by simple prospecting methods.
Although these same methods still lead to an occasional discovery, most deposits not yet discovered have gone undetected because they are buried and have no surface expression.
The challenge in exploration is therefore to unravel the subsurface geology of an area and pinpoint the position of buried minerals. Methods widely used today include analysis of aerial images that yield a broad geological overview; geophysical techniques that provide date on the magnetic, electrical, and mineralogical properties of the rocks being investigated; and sensitive chemical tests that are able to detect the subtle chemical halos that often envelop mineralization. However, none of these high-technology methods are of any value if the sites to which they are applied have never mineralized, and to maximize the chances of discovery the explorer must therefore pay particular attention to selecting the ground formations most likely to be mineralized. Such ground selection relies to varying degrees on conceptual models, which take into account theoretical studies of relevant factors.
These models are constructed primarily from empirical observations of known mineral deposits and from theories of ore-forming processes. The explorer uses the models to identify those geological features that are critical to the formation of the mineralization being modeled, and then tries to select areas for exploration that exhibit as many of the critical features as possible.
According to the passage, the widely held view of Archean-age gold-quartz vein systems is that such systems
(A) were formed from metamorphic fluids
(B) originated in molten granitelike bodies
(C) were formed from alluvial deposits
(D) generally have surface expression
(E) are not discoverable through chemical tests
I chose D, since the whole passage is about the old view of the systems being visible at the surface. Yet the passage clearly states that the widely-held view is that they were deposited from metamorphic fluids. A is correct.
While there is no blueprint for transforming a largely government-controlled economy into a free one, the experience of the United Kingdom since 1979 clearly shows one approach that works: privatization, in which state-owned industries are sold to private companies. By 1979, the total borrowings and losses of state-owned industries were running at about £3 billion a year. By selling many of these industries, the government has decreased these borrowings and losses, gained over £34 billion from the sales, and now receives tax revenues from the newly privatized companies. Along with a dramatically improved overall economy, the government has been able to repay 12.5 percent of the net national debt over a two-year period.
In fact, privatization has not only rescued individual industries and a whole economy headed for disaster, but has also raised the level of performance in every area. At British Airways and British Gas, for example, productivity per employee has risen by 20 percent. At Associated British Ports, labor disruptions common in the 1970’s and early 1980’s have now virtually disappeared. At British Telecom, there is no longer a waiting list –as there always was before privatization –to have a telephone installed.
Part of this improved productivity has come about because the employees of privatized industries were given the opportunity to buy shares in their own companies. They responded enthusiastically to the offer of shares: at British Aerospace, 89 percent of the eligible work force bought shares; at Associated British Ports, 90 percent; and at British Telecom, 92 percent. When people have a personal stake in something, they think about it, care about it, work to make it prosper. At the National Freight Consortium, the new employee-owners grew so concerned about their company’s profits that during wage negotiations they actually pressed their union to lower its wage demands.
Some economists have suggested that giving away free shares would provide a needed acceleration of the privatization process. Yet they miss Thomas Paine’s point that “what we obtain too cheap we esteem too lightly.” In order for the far-ranging benefits of individual ownership to be achieved by owners, companies, and countries, employees and other individuals must make their own decisions to buy, and they must commit some of their own resources to the choice.
It can be inferred from the passage that the author considers labor disruptions to be
(A) an inevitable problem in a weak national economy
(B) a positive sign of employee concern about a company
(C) a predictor of employee reactions to a company’s offer to sell shares to them
(D) a phenomenon found more often in state-owned industries than in private companies
(E) a deterrence to high performance levels in an industry
I chose D. Well, he does consider labor disruptions a problem, but doesn’t single out nationalised industries for this treatment. Definitely not B or C – there’s no evidence there – and A is too broad. He does, however, link performance levels clearly to reduced labor disruption, so the answer is E.
Which of the following can be inferred from the passage about the privatization process in the United Kingdom?
(A) It depends to a potentially dangerous degree on individual ownership of shares.
(B) It conforms in its most general outlines to Thomas Paine’s prescription for business ownership.
(C) It was originally conceived to include some giving away of free shares.
(D) It has been successful, even though privatization has failed in other countries.
(E) It is taking place more slowly than some economists suggest is necessary.
I chose B here. A is clearly wrong; there’s no inference about share ownership being risky. So is C; share giveaways aren’t mentioned until the final para. D is wrong, since the passage says nothing about other countries. Between B and E, it seems B infers too much; there’s no suggestion the UK is following Paine’s rules. And although it’s not stated outright, some economists talk about a ‘needed acceleration’, implying they indeed think it’s all going too slowly. E is correct.
Unlike the United States, where farmers can usually depend on rain or snow all year long, the rains in most parts of Sri Lanka are concentrated in the monsoon months, June to September, and the skies are generally clear for the rest of the year.
(A) Unlike the United States, where farmers usually depend on rain or snow all year long, the rains in most parts of Sri Lanka
(B) Unlike the United States farmers who can usually depend on rain or snow all year long, the rains in most parts of Sri Lanka
(C) Unlike those of the United States, where farmers can usually depend on rain or snow all year long, most parts of Sri Lanka’s rains
(D) In comparison with the United States, whose farmers can usually depend on rain or snow all year long, the rains in most parts of Sri Lanka
(E) In the United States, farmers can usually depend on rain or snow all year long, but in most parts of Sri Lanka the rains
I chose A, missing ‘where farmers usually depend on rain or snow’ – implying the Sri Lankans depend on something else. Wrong. In B there are too many the’s. C is just clumsy. D comes close, but implies the rains in some parts of Sri Lanka don’t depend on the monsoons, changing the sense of the sentence. E is correct.
In recent years cattle breeders have increasingly used crossbreeding, in part that their steers should acquire certain characteristics and partly because crossbreeding is said to provide hybrid vigor.
(A) in part that their steers should acquire certain characteristics
(B) in part for the acquisition of certain characteristics in their steers
(C) partly because of their steers acquiring certain characteristics
(D) partly because certain characteristics should be acquired by their steers
(E) partly to acquire certain characteristics in their steers
I chose D. The answer’s got to start with ‘partly’ to agree with the rest of the sentence, so it’s C, D, or E. But C suggests the farmers are being forced to use crossbreeding because their steers are acquiring characteristics (no causal relationship between the two) and D suggests they’re not sure about whether it’ll produce certain characteristics and are just trying it on. E gets the sense right, but this is a hard question – about sense, not strict balance of grammar.
Teratomas are unusual forms of cancer because they are composed of tissues such as tooth and bone not normally found in the organ in which the tumor appears.
(A) because they are composed of tissues such as tooth and bone
(B) because they are composed of tissues like tooth and bone that are
(C) because they are composed of tissues, like tooth and bone, tissues
(D) in that their composition, tissues such as tooth and bone, is
(E) in that they are composed of tissues such tooth and bone, tissues
I chose B. But they’re not composed of tissues ‘like’ tooth and bone; they’re composed of tissues that are tooth and bone. C broadens the definition to all kinds of tissues. D does the same, implying the composition isn’t limited to tooth and bone. E is too wordy, using ’tissues’ twice. A is correct.
Scientists have recently discovered what could be the largest and oldest living organism on Earth, a giant fungus that is an interwoven filigree of mushrooms and rootlike tentacles spawned by a single fertilized spore some 10,000 years ago and extending for more than 30 acres in the soil of a Michigan forest.
(D) it extended
(E) is extending
I chose B, misreading the para. It’s talking in the present continuous, C suggests a passive voice use of ‘to extend’ that isn’t supported in the text. D puts it into past tense; E sounds clumsy by adding that unnecessary ‘is’. It’s A.
The period when the great painted caves at Lascaux and Altamira were occupied by Upper Paleolithic people has been established by carbon-14 dating, but what is much more difficult to determine are the reason for their decoration, the use to which primitive people put the caves, and the meaning of the magnificently depicted animals.
(A) has been established by carbon-14 dating, but what is much more difficult to determine are
(B) has been established by carbon-14 dating, but what is much more difficult to determine is
(C) have been established by carbon-14 dating, but what is much more difficult to determine is
(D) have been established by carbon-14 dating, but what is much more difficult to determine are
(E) are established by carbon-14 dating, but that which is much more difficult to determine is
I put A. Silly mistake: ‘the reason’ must be followed by ‘is’ not ‘are’. C, D, and E lack subject-verb agreement (‘The period… have’, ‘The period… are’) so it must be B.
Conclusions: whoa, this test is where my lack of methodical maths really made itself evident. I need to hit the books on learning:
- Rote-learn some more rules about proportions of shapes
- Practice adding, subtracting, dividing and multiplying algebraic terms
- Practice dividing and multiplying fractions
- Learn where you can cancel algebraic terms and where you can’t
- Learn how to calculate domains and ranges in sets
- Practice more permutations and combinations questions
- Learn how to handle ‘missing operation’ questions
- Properties of prime numbers
Next test tomorrow, and some study before then.