So: a big leap in performance; perhaps the several 690s in a row were some sort of latent-heat period and this programme of GMAT study’s now undergoing a phase transition. A score of 760, from corrected raws of 44Q/50V. Here are the ones I got wrong.
If (x^2 +6x + 9) + 6(x + 3) + 9 = 0, then x=
I chose A. Multiplying out, x^2 + 6x + 9 + 6x + 18 + 9 = 0 is the same as x^2 + 12x + 35 = 0, so x^2 + 12x = -35 and 12x must be bigger than 35 and negative. That means the answer is A or B, the only negative options. With B, this is where my error lay: 9 -36 ≠ 0, so B is wrong. Putting A in place to get 36 -72 +35 = 0 works. It’s A. Annoying since getting this right would have meant a 770 simulated GMAT score, but I can hardly complain on the day I passed the 99th percentile.
Three musical notes have frequencies x, y, and z, respectively. If x, y, and z are positive, x/y = y/z, and 2x = z, what is y in terms of z?
(C) (1/√2) x
(D) (1/2) x
(E) (√2/3) x
I got this right, but wanted to fix the structure in my head, so I’m making sure here. The first thing to do is recast the z as 2x, to get x/y = y/2x. Move the 2x term across by multiplying both sides by 2x, and you get 2x^2/y = y, then doing the same to get rid of that y on the left gives you 2x^2 = y^2. So the square root of y^2 (i.e. what we want) is the square root of 2x^2, which (since you can take the x out of the term; it’s squared already) is √2 x, or B.
According to the incomplete table above, if each of the 6 teams in the league played each of the other teams exactly twice and there were no ties, how many games did team X win? (Only 2 teams play in a game.)
A permutations and combinations question. I chose A. First thing to do is work out how many games were played in total, so use the ‘permutations’ equation n!/(n-r)! where n is the number of teams and r is the number of teams pulled out for each game, i.e. 6 and 2. That’s 6*5*4*3*2*1 / 4*3*2*1, or 720 / 24, or 30. Each team played every other team TWICE, so double it – 60 games in total. All games were won, which means there were 30 possible wins and 30 losses, and 24 of the games were won by A-E, so team X must have won 6. The answer is C.
(Addition: A comment below adds there was an easier way of doing this in your head: with each of 6 teams playing the other 5 teams twice, that makes ten games per team, so that 60 figure is more easily get-attable.)
A Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C BOTH statements (1) and (2) TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D EACH statement ALONE is sufficient.
E Statements (1) and (2) TOGETHER are NOT sufficient.
Of the four numbers represented on the number line above, is r closest to zero?
(1) q = -s
(2) –t < q
I chose D. Oooh, kicking myself. Assume the number line is a simple -1, 0, 1, 2. That’d make q equal to -1 according to statement 1, and with r in between, r would be closest to zero. Statement 1 is sufficient. I thought Statement 2 was, too, but knowing -2 was less than q could mean q was -1, or 0, or… making it impossible to say with certainty that r is closest to zero. Good question. The answer is A.
If Carmen had 12 more tapes, she would have twice as many tapes as Rafael. Does Carmen have fewer tapes than Rafael?
(1) Rafael has more than 5 tapes.
(2) Carmen has fewer than 12 tapes.
I chose E. If Rafael has a minimum 6 tapes, then Carmen needs all 12 to double his collection, so she’s certainly got fewer tapes now. But if Rafael had 20 tapes now, Carmen would have 28 already, more than him. You can’t tell from Statement A.
Conversely, let’s say (as in Statement 2) that Carmen has 11 tapes. Giving her 12 leads to 23 tapes… so Rafael must have 11.5 tapes, more than her (even if one doesn’t work because he’s lost half of it!) If she’s got 10 now, an extra 12 gives her 22, meaning Rafael’s got 11. If she’s got 9, then Rafael’s got 10.5 tapes, still more than her. Statement 2 is enough. B is correct.
In the figure above, how many of the points on line segment PQ have coordinates that are both integers?
I guessed B. One of the few problems I don’t know how to approach yet. It’s a slopes question, but I’m not sure how the slopes equations would help… let’s think….
There are a maximum 50 values of x that are integers. And a maximum 30 values of y that are integers. So a maximum of 30 points where both x and y are integers, and probably a lot less than that in reality. There’ll be one at (0,30) of course, another at (5, 27), and more at (10,24), (15,21), (20,18), (25,15), (30,12), (35,9), (40,6), (45,3), and (50, 0). Eleven of them, answer D.
(Addition: a comment below suggests an easy way to do this: find the largest number that goes into both 30 and 50, which is 10, then add one to account for the zero co-ordinate. Faster!)
A group of 12 people plan to rent a van and agree to share equally the total cost of the rental, which is Edollars. If n of the people decide not to participate at the last minute, by how many dollars will each remaining person’s share of the total cost increase?
(A) E / 12-n
(B) 12-n / E
(C) E / 12(12-n)
(D) nE / 12(12-n)
(E) (12-n)E / 12n
I chose E. Let’s write down what I think it should look like: they planned to spend $E, so it would have been E/12 each. However, a few people haven’t turned up, so the cost is now $E / (12-n) each. The difference between the two is (E / (12-n)) – (E/12), which means the common denominator (so we can perform the minus) must be 12(12-n) (so the answer must be C or D, the only answers with this denominator) and the numerator 12E-E(12-n). No need to go further; the numerator must have an n in it. It’s D.
Until quite recently, American presidents lived in a world in which the public and private realms of their lives were largely separate, and the press cooperated in maintaining the distinction, and Americans judged national leaders without receiving, or expecting, intimate information about them.
(A) and the press cooperated in maintaining the distinction, and
(B) where the press cooperated in maintaining the distinction, and where
(C) for the press cooperated to maintain the distinction and
(D) the press cooperated to maintain the distinction, for
(E) in which the press cooperated in maintaining the distinction, and in which
I chose B. But the ‘where’ doesn’t match the ‘in which’ used previously. It can’t be A, because the ‘and’ doesn’t place the press co-operation as subordinate to the American President’s world, nor C or D, for the same reason: both change the sense of the sentence, not making the press and the American citizens examples of the world as it was. It must be E. Anyway, E looks right for another reason: all those ‘in which’es keep it grammatically pure.
Bob Wilber became Sidney Bechet’s student and protégé when he was nineteen and, for a few years in the 1940’s, came as close to being a carbon copy of the jazz virtuoso in performance as anyone has ever come.
(A) as anyone has ever come
(B) as anyone ever had been
(C) as anyone ever had done
(D) that anyone ever did
(E) that anyone ever came
An idiom question. Not realising this, I chose B. But the phrase is idiomatic, ‘as close as it ever comes’, and only A and E use it. It isn’t E, because ‘ever came’ suggests that nobody is able to try now or in the future, and other people are welcome to have a go if they want… making A the answer.
Despite its attractiveness, investing abroad can still pose big risks, ranging from the potential for political instability in some countries to the shortage of regulations to protect investors and a serious lack of information about investments in others.
(A) to the shortage of regulations to protect investors and a serious lack of information about investments in others
(B) to the shortage of regulations to protect investors and in others a serious lack of information about investments
(C) and the shortage of regulations to protect investors and a serious lack of information about investments in others
(D) and the shortage of regulations to protect investors to a serious lack of information about investments in others
(E) to the shortage of regulations to protect investors in others and a serious lack of information about investments
Hard one. I chose D. The pivot is that ‘ranging from… to’ and where the ‘to’ should go. The answer suggests that the GMAT doesn’t like any excess verbiage between the from and the to, making the only option A.
That the new managing editor rose from the publication’s “soft” new sections to a leadership position is more of a landmark in the industry than her being a woman.
(A) her being a woman
(B) being a woman is
(C) her womanhood
(D) that she was a woman
(E) that she is a woman
I chose A. The clue is the first ‘That’ in the sentence: it suggests the corrected sentence must also have a ‘that’ near the woman bit, meaning the answer must be D or E. D doesn’t make sense, so it’s E.
Of all the wild animals in their area, none was more useful to the Delaware tribes than the Virginia white-tailed deer: it was a source of meat, and its hide was used for clothing, its antlers and bones for tools, and its sinews and gut for bindings and glue.
(A) deer: it was a source of meat, and its hide was used for clothing, its antlers and bones for tools, and its sinews and gut
(B) deer: it was a source of meat, and its hide used for clothing, with its antlers and bones for tools, and its sinews and gut used
(C) deer, which was a source of meat, with its hide used for clothing, antlers and bones for tools, as well as its sinews and gut used
(D) deer, which, as well as being a source of meat, its hide was used for clothing, its antlers and bones for tools, and its sinews and gut were
(E) deer, with, as well as being a source of meat, its hide used for clothing, its antlers and bones for tools, and its sinews and gut
I put E. The clue is in the colon: the sense of the sentence is of introducing a list, for which we use colons. B doesn’t list the list items correctly (‘and its hide’ is incorrect) so it’s A.
Well, I was pleased with my result – don’t expect to better it tomorrow; I’d expect to spend the next couple of tests going downhill, especially since I’m doing my last paper-based practice test on Saturday and next week’s practices will all be proper GMAT style, on-the-screen jobs.
One thing I have noticed, though, is my weakness in sentence correction: the GMAT demands use of standard written English, and copywriters don’t write standard; we write the way people speak. I’m not sure I’m going to beat this weakness into submission with 15 years of writing conversationally behind me. I bet 760 is as high as I can go.