How to ace the GMAT in 28 days: Day 2 (analysing Day 1)

Yesterday’s 640 was cheering, since I got so many wrong – 23 out of 113. In other words, plenty of opportunity to STOP making those errors and raise my game. (Remember, all I need is to get one less question wrong every practice test.) It’s time to check what I got wrong on the first practice test. This is where I find out where my weak areas are.

Quant

The GMAT maths sections contain 2 types of question: data sufficiency and problem solving. On this practice, I got 4 out of 32 problem-solving questions wrong; in data sufficiency, 7 out of 20 wrong. So data sufficiency is my big issue. But first, let’s review the problem solving gaffes.

root463 is between

(A) 21 and 22
(B) 22 and 23
(C) 23 and 24
(D) 24 and 25
(E) 25 and 26

Looks simple. But with two minutes per question, you don’t have time to evaluate root463. I chose B after frantically trying to find the square root of 463 in my head. (Note how the answers are close together? Makes it unguessable.)

The method here is to pick the middle value. What’s 23 x 23? Hmmm, 20 x 23 is 460.. plus 3 x 23 = 529. Too big. The answer’s got to be smaller, so it’s A or B. Attack from the other end: what’s 22 x 22? 440+44.. 484… still too big… but there are no answers before A. The answer must be under 484, so the answer must be A.

The ratio of two quantities is 3 to 4. If each of the quantities is increased by 5, what is the ratio of these two new quantities?

(A) 3/4
(B) 8/9
(C) 18/19
(D) 23/24
(E) It cannot be determined from the information given.

It can’t be A, so I chose B. Surprise surprise, it looks a bit like a data sufficiency question – my weak area! B is wrong: we don’t know how many of each quantity we had to begin with, only their ratios, so adding 5 to each quantity doesn’t work. If I’d learned the method for this, I could have dealt with this question in three seconds, not four minutes.

The answer’s in algebra. 3x + 5 : 4y + 5 = the ratio we want. OK, but we have no other information: the equation’s unsolvable; it doesn’t even equal 0. So it must be E. E is correct.

My next error’s about co-ordinates.

The figure: an x-y plane, marked into quadrants I, II, III, and IV. (Quadrants are always anticlockwise from top right. So the quadrant containing positive numbers is always I, the quadrant to the left where y is positive and x negative is II, the quadrant below that where x and y are both negative is III, and the quadrant at bottom right where x is positive and y negative is IV.

In the rectangular coordinate system shown above, which quadrant, if any, contains no point ( x, y ) that satisfies the inequality 2x – 3y <= -6?

(A) None
(B) I
(C) II
(D) III
(E) IV

This stuff ties my head in knots, so I guessed B and moved on. Bad idea.

If 2x minus 3y can less than or equal to -6, let’s see which quadrants it MUST appear in. Put in some numbers, using that 6 as the clue. Let x = 3 and y = 4. 6 minus 12 is -6, which satisfies the inequality. This point can definitely appear in quadrant I, so the answer isn’t B.

Let’s go negative, with x and y equal to -3 and -4. -6 minus -12 is +6, which doesn’t satisfy the inequality. But that doesn’t make the answer C; it just means my randomly chosen values for x and y don’t work. Let’s change y to positive: x=-3 and y=4. -6 minus 12 = -18. Yes, that’s less than -6, so quadrant II is back in the game. The answer isn’t C.

if the answer’s there, it’s in the lower two quadrants, which means y must be negative. Try our negative y again, but with a positive x: x=3, y=-4. 6 minus -12 = +18. Quadrant IV may be the loser. Can we rule it out? Let x=4 and y=-3 for a change. 8 minus -9. Still more than -6. In fact, there can’t be any values of positive x where minusing a negative y would work, since minusing a negative simply adds it. Without needing to check quadrant III, it must be quadrant IV. The answer is E.

Whoa, I think guessing was a reasonable strategy. Next question.

The size of a television screen is given as the length of the screen’s diagonal. If the screens were flat, then the area of a square 21-inch screen would be how many square inches greater than the area of a square 19-inch screen?

(A) 2
(B) 4
(C) 16
(D) 38
(E) 40

I chose D. It looks do-able by breaking it down into triangles: two squares, each of two similar right-angled triangles with hypotenuse 21 and 19 inches. Easy. Whoops, no it isn’t – to find the areas I’d have to square 21 and 19, then find two perfect squares in each of the resulting numbers, then square root them to find the lengths of the other two sides. There must be a better way.

Or is there? 19 squared is 361; 21 squared is 441. But we don’t have to find the roots: 361 is the sum of the squares of the sides of the smaller screen, and 441 is the sum of the squares of the larger screen. (Both sides of the triangle also being sides of the screens.) Since each screen is square, all the sides are the same length, so each squared side is 180.5 for the smaller screen and 220.5 for the larger screen.

So far so headachey. But it’s an area question, so we don’t need to ‘unsquare’ it: as the squares of sides, we already have the areas of each screen, 180.5 and 220.5. The question asks how many square inches differentiate the squares, and here’s our answer: 40. The answer is E.

Let’s look at my data sufficiency errors. These are fun but hard: instead of solving the mathematical problem, you get two statements 1 and 2, and have to decide if there’s enough info in them (individually or together) to answer the question without assumptions. Your answer A-E is chosen from this set for every question:

(A) if statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
(B) if statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
(C) if BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient;
(D) if EACH statement ALONE is sufficient to answer the question asked;
(E) if statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

A——B—-C—-D

In the figure above, is CD>BC?

(1) AD=20
(2) AB=CD

Like this one, data sufficiency questions often look simple. I chose C: both statements together give us enough info. Which was a very silly mistake: I know better than this.

We know AD. We know that the segment AB is the same as CD. What we don’t know (and shouldn’t assume) is that BC also equals AB and CD just because it looks the same on the diagram. We don’t know BC, so we can’t answer the question even if we know the length of the whole line. The answer is E: both statements together are NOT sufficient.

Next crushing failure:

A jar contains 30 marbles, of which 20 are red and 10 are blue. If 9 of the marbles are removed, how many of the marbles left in the jar are red?

(1) Of the marbles removed, the ratio of the number of red ones to the number of blue ones is 2 : 1.
(2) Of the first 6 marbles removed, 4 are red.

I chose D. Stupid, stupid. I’m starting to see a pattern here: I keep assuming info I haven’t got.

OK, so we’ve taken out twice as many reds as blues. No half marbles, so we must have 6 reds and 3 blues, the only 2:1 ratio in 9 marbles. 1 is sufficient, so the answer’s A or D.

As for statement 2, we’ve got 4 reds in the first 6 – but we took 9 out of the jar. Not enough info in 2 alone, ruling out B and D. The answer is A.

Onwards:

What is the value of the integer x ?

(1) x is a prime number.
(2) 31 <= x <= 37

I chose C. Stupid again. Even both of them together don’t cut it. Even if x is prime, there are two prime numbers between or equal to 31 and 37. The answer is E.

What is the number of female employees in Company X ?

(1) If Company X were to hire 14 more people and all of these people were females, the ratio of the number of male employees to the number of female employees would then be 16 to 9.
(2) Company X has 105 more male employees than female employees.

I chose A. Like the ‘ratio’ question earlier, I’ve blindly assumed . The algebra is 16m + 9f = number of employees + 14 … but there’s no base to work out the ratio without the 14 extra girls, so 1 isn’t sufficient. You need the concrete number in 2 to work it out. Answer: C.

What is the value of a – b?

(1) a = b + 4
(2) (a-b)^2 = 16

I chose E. Close but not close enough. I thought I’d dodged the trap, in that (a-b)^2 could be 4 or -4… a negative number squared is a positive, so 2 alone isn’t enough. but combined with 1, which rearranges to a – b = 4, 1 alone is sufficient. This was an EASY question, and I’m annoyed I looked too deeply into it.

Is rst = 1 ?

(1) rs = 1
(2) st = 1

I guessed C, since if rs and st both equal 1, rst must equal 1 … which isn’t true. One of the terms could be -1, which would make rst negative. Both these statements are insufficient to answer the question, which means E is correct.

And lastly:

In a certain office, 50 percent of the employees are college graduates and 60 percent of the employees are over 40 years old. If 30 percent of those over 40 have master’s degrees, how many of the employees have masters’ degrees?

(1) Exactly 100 of the employees are college graduates
(2) Of the employees forty years old or less, 25% have masters’ degrees

I guessed E, outatime. If I’d had another minute, I’d have seen that 50% of the company are graduates, which means 200 employees in total. So 120 of them will be over 40, and 30% of that 120 is 36… but that only gives the number of oldies. Statement 1 is not sufficient on its own.

Checking out statement 2, it’s easy to see 25% of 60% of the company have degrees… but there’s no base figure allowing us to work out how many people work for the company. So 2 alone won’t work. Making the answer C – we need both. Which I really should have got right. (NOTE: this question was edited on 21 Jan 2009 after an email pointing out an earlier error of my own!)

Verbal

On this practice test, I got 1 of 16 critical reasoning questions, 3 of 23 reading comprehension questions, and 1 of 22 sentence correction questions wrong. So straight off the bat, it’s obvious I’m okay at critical reasoning and sentence correction. Which means I have to work on reading comprehension. But first: why did I get a single question wrong in the other two sections?

The critical reasoning blooper was this question:

Manufacturers sometimes discount the price of a product to retailers for a promotion period when the product is advertised to consumers. Such promotions often result in a dramatic increase in the amount of product sold by the manufacturers to retailers. Nevertheless, the manufacturers could often make more profit by not holding the promotions.

Which of the following, if true, most strongly supports the claim above about the manufacturer’s profit?

(A) The amount of discount offered by manufacturers to retailers is carefully calculated to represent the minimum needed to draw consumers’ attention to the product.
(B) For many consumer products the period of advertising discounted prices to consumers is about a week, not sufficiently long enough for consumers to become used to the sale price.
(C) For products that are not newly introduced, the purpose of such promotions is to keep the products in the minds of consumers and to attract consumers who are currently using competitive products.
(D) During such a promotion retailers tend to accumulate in their warehouses inventory bought at discount; they then sell much of it later at their regular price.
(E) If a manufacturer fails to offer such promotions but its competitor offers them, that competitor will tend to attract consumers away from the manufacturer’s product.

It’s a reasonably hard one. And I made a stupid mistake. Because it’s about marketing – my field – I rushed into what pricing means within consumer markets, and skated over the most important part of the passage: it’s not about discounts to consumers, it’s about discounts offered to retailers who then sell to consumers.

My answer, E, was as wrong as it gets. E implies that promotions are essential, or your competitors will grab your customers. Well, maybe they will, but that has nothing to do with consumers, who buy from retailers. It tries to draws a link between manufacturers and consumers, without involving the middleman retailer. And so is wrong.

My first guess – crossed out before I chose E – was D. The argument requires that consumers will buy the product at regular price, regardless of what price the retailer bought it at. D supports the assertion that consumers will buy at regular price. D is correct.

Now the sentence correction blooper:

The prime lending rate is a key rate in the economy: not only are the interest rates on most loans to small and medium-sized businesses tied to the prime, but also on a growing number of consumer loans, including home equity loans.

(A) not only are the interest rates on most loans to small and medium-sized businesses tied to the prime, but also on
(B) tied to the prime are the interest rates not only on most loans to small and medium-sized businesses, but also on
(C) the interest rates not only on most loans to small and medium-sized businesses are tied to the prime, but also
(D) not only the interest rates on most loans to small and medium-sized businesses are tied to the prime, but also on
(E) the interest rates are tied to the prime, not only on most loans to small and medium-sized businesses, but also

It’s a grammar issue. The problem’s in the last underlined ‘on’: it doesn’t agree with the rest of the sentence. I chose E, which is again the ‘wrongest’ of the five. Blast. It’s at the end of the section, so I may have been rushing. Not sure why I got this wrong; it’s not hard.

The correct answer will pay off the first half of the sentence before the colon, so ‘tied to the prime’ is instantly the best candidate. Does B deal with the ‘on’? … not only on… but also on… yes it does. B is correct. Blast.

OK, now those reading comprehension issues.

Two recent publications offer different assessments of the career of the famous British nurse Florence Nightingale. A book by Anne Summers seeks to debunk the idealizations and present a reality at odds with Nightingale’s heroic reputation. According to Summers Nightingale’s importance during the Crimean War has been exaggerated: not until near the war’s end did she become supervisor of the female nurses. Additionally, Summers writes that the contribution of the nurses to the relief of the wounded was at best marginal. The prevailing problems of military medicine were caused by army organizational practices, and the addition of a few nurses to the medical staff could be no more than
symbolic. Nightingale’s place in the national pantheon, Summers asserts, is largely due to the propagandistic efforts of contemporary newspaper reporters.

By contrast, the editors of a new volume of Nightingale’s letters view Nightingale as a person who significantly influenced not only her own age but also subsequent generations. They highlight her ongoing efforts to reform sanitary conditions after the war. For example, when she learned that peacetime living conditions in British barracks were so horrible that the death rate of enlisted men far exceeded that of neighboring civilian populations, she succeeded in persuading the government to establish a Royal Commission on the Health of the Army. She used sums raised through public contributions to found a nurses’ training hospital in London. Even in administrative matters, the editors assert her practical intelligence was formidable: as recently as 1947 the British Army’s medical services were still using the cost-accounting system she had devised in the 1860’s.

I believe that the evidence of her letters supports continued respect for Nightingale’s brilliance and creativity. When counseling a village schoolmaster to encourage children to use their faculties of observation she sounds like a modern educator. Her insistence on classifying the problems of the needy in order to devise appropriate treatments is similar to
the approach of modern social workers. In sum, although Nightingale may not have achieved all other goals during the Crimean War, her breadth of vision and ability to realize ambitious projects have earned her an eminent place among the ranks of social pioneers.

1. The passage is primarily concerned with evaluating
(A) the importance of Florence Nightingale’s innovations in the field of nursing
(B) contrasting approaches to the writing of historical biography
(C) contradictory accounts of Florence Nightingale’s historical significance
(D) the quality of health care in nineteenth-century England
(E) the effect of the Crimean War on developments in the field of health care

I chose A. Wrong, because it’s emotive: the author is obviously in the Florence fan club, and I took that to mean making Florence look important was his goal. This is totally wrong.

The passage is all about contrasting Summer’s approach with the editors’ approach. Two approaches set against each other, and the fact the author favours one side doesn’t matter. C is correct.

My next mistake was on the same passage:

With which of the following statements regarding the differing interpretations of Nightingale’s importance would the author most likely agree?

(A) Summers misunderstood both the importance of Nightingale’s achievements during the Crimean War and her subsequent influence on British policy.
(B) The editors of Nightingale’s letters made some valid points about her practical achievements but they still exaggerated her influence on subsequent generations.
(C) Although Summers’ account of Nightingale’s role in the Crimean War may be accurate, she ignored evidence of Nightingale’s subsequent achievement that suggests that her reputation as an eminent social reformer is well deserved.
(D) The editors of Nightingale’s letters mistakenly propagated the outdated idealization of Nightingale that only impedes attempts to arrive at a balanced assessment of her true role.
(E) The evidence of Nightingale’s letters supports Summers’ conclusions both about Nightingale’s activities and about her influence.

I chose A. The trap: Summers does (in the author’s opinion) misunderstand Nightingale’s achievements, but there’s nothing attributed to her about subsequent influence. A looks right, but is wrong. Not as wrong as D though, which is 180 degrees away from the author’s opinion.

At first C looks totally wrong – because there’s no praise for Summers in the passage, and this is giving her a stroke. But here’s the catch: the author doesn’t denigrate Summers’ work, only comments on how Nightingale’s ideas later captivated British policy, and it was these policy decisions that made Nightingale a significant figure. C is correct.

Last reading comprehension mistake:

Most large corporations in the United States were once run by individual capitalists who owned enough stock to dominate the board of directors and dictate company policy. Because putting such large amounts of stock on the market would only depress its value, they could not sell out for a quick profit and instead had to concentrate on improving the long-term productivity of their companies. Today, with few exceptions, the stock of large United States corporations is held by large institutions—pension funds, for example—and because these institutions are prohibited by antitrust laws from owning a majority of a company’s stock and from actively influencing a company’s decision-making, they can enhance their wealth only by buying and selling stock in anticipation of fluctuations in its value. A minority shareholder is necessarily a short-term trader. As a result, United States productivity is unlikely to improve unless shareholders and the managers of the companies in which they invest are encouraged to enhance long-term productivity (and hence long-term profitability), rather than simply to maximize short-term profits.

Since the return of the old-style capitalist is unlikely, today’s short-term traders must be remade into tomorrow’s long-term capitalistic investors. The legal limits that now prevent financial institutions from acquiring a dominant shareholding position in a corporation should be removed, and such institutions encouraged to take a more active role in the operations of the companies in which they invest. In addition, any institution that holds twenty percent or more of a company’s stock should be forced to give the public one day’s notice of the intent to sell those shares. Unless the announced sale could be explained to the public on grounds other than anticipated future losses, the value of the stock would plummet and, like the old-time capitalists, major investors could cut their losses only by helping to restore their companies’ productivity. Such measures would force financial institutions to become capitalists whose success depends not on trading shares at the propitious moment, but on increasing the productivity of the companies in which they
invest.

It can be inferred from the passage that which of the following is true of majority shareholders in a corporation?

(A) They make the corporation’s operational management decisions.
(B) They are not allowed to own more than fifty percent of the corporation’s stock.
(C) They cannot make quick profits by selling off large amounts of their stock in the corporation.
(D) They are more interested in profits than in productivity.
(E) They cannot sell any of their stock in the corporation without giving the public advance notice.

I chose A. Why the FUCK did I do that? Majority shareholders can own the company AND work for it; not ALL the stock is owned by pension funds.

But the other answers don’t leap out either. B and E are factually wrong; D can’t be inferred. C is left. It’s a weak inference – you COULD make quick profits, if you managed to sell all your stock higher than you bought it for, even in a falling market – but it’s the only one left. C wins.

So after one test, I’m getting three times as many reading comprehension questions wrong as either sentence correction or critical reasoning. Reading comp’s what I need to work on.

Tomorrow: I’ll apply these learnings to another practice test, and aim to score a bit higher.

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