How to ace the GMAT in 28 days: Day 16 (analysing day 15)

Okay, time to analyse my first 700 score. (Or 90th percentile, which means I’m beating 9 out of 10 people who take the GMAT.) 107 questions, corrected raw scores of 50V/40Q: 3 sentence correction, 1 critical reasoning, and 0 reading comprehension errors, and 7 problem solving quants, and 3 data sufficiency questions wrong. I’m getting the hang of those data sufficiency things.

Quant

Harry started a 6-mile hike with a full 10-cup canteen of water and finished the hike in 2 hours with 1 cup of water remaining in the canteen. If the canteen leaked at the rate of 1 cup per hour and Harry drank 3 cups of water during the last mile, how many cups did he drink per mile during the first 5 miles of the hike?

(A) 4/5
(B) 5/6
(C) 1
(D) 6/5
(E) 5/4

I chose C. Well, if Harry started with 10c, spilled 2c, and drank 3c we know of, then there are 5 cups left in the flask to last 5 miles… which is where my mistake occurred. He doesn’t drink it all; there’s a cupful left, so he only drank 4 cups in 5 miles. Answer: A.

If y is an integer, then the least possible value of | 23-5y | is

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

I chose C. (This is a |range| question: number of values that satisfy, not the value any y produces.) To produce a minimum value for range 23-5y of 5 you’d need y to equal 18/5 – not an integer, so discount E; the value can’t be 5. D doesn’t work either (y would have to be 19/5, again not an integer). Why not C? y=4 works, so C is possible. Is it the lowest? Let’s try substituting y=3; the value of 23-5y would be 8, higher than B, and for lower values of y the numbers get bigger. There can only be 2 possible values of the range |23-5y|, so it’s B.

The volume of a sphere with radius r is 4/3 ∏r^3 and the surface area is 4 ∏r^3. If a spherical balloon has a volume of 972∏ cubic centimeters, what is the surface area of the balloon in square centimeters?

(A) 324
(B) 729
(C) 243∏
(D) 324∏
(E) 729∏

I guessed A. Close, but not close enough. The question contains a very subtle misdirection. Did you think it was being kind telling you the formulae for calculating volume and surface area of a sphere? It’s not. Those expressions represent the surface and volume of this specific sphere, not as general formulae. Clever.

If the general expressions for surface area and volume were 4 ∏r^3 and 4/3 ∏r^3, that means the figure for surface area (in square cm) would always be several times bigger than the figure for volume (in cubic cm). This is wrong: the formula for finding surface area of a sphere is 4/3 ∏r^2, not 4/3 ∏r^3. Which means the surface area figure in square cm is a lot smaller than the volume in cubic cm. The answer is a third of the figure amount (to turn 4 into 4/3, i.e reducing it to the third of its value) and dividing by r (to compensate the r^3 value that ‘should’ be r^2). It’s around 300∏ , which is D.

If the perimeter of square region S and the perimeter of circular region C are equal, then the ratio of the area of S to the area of C is closest to

(A) 3/2
(B) 4/3
(C) 3/4
(D) 2/3
(E) 1/2

I chose B. First off, we need to confirm which of them has the bigger area, so do a quick substitution, assuming r is one unit in length. If the perimeter of the circle is 2∏r, then the perimeter of the square is 4 x 1/4 (2∏r) . (Because a square has four equal sides, each a quarter of 2∏r long.) The area of the square will be 1/2 ∏r times 1/2 ∏r, roughly 1.6 times 1.6, which is 2.6 or so.

The area of the circle is ∏r^2, roughly 3.14. So the circle’s area is bigger, ratio S to C must be small to big, so the answer is C, D, or E. The ratio 2.6 : 3.14 is about 5:6, which is closest to answer C.

If n and k are integers whose product is 400, which of the following statements must be true?

(A) n + k > 0
(B) n ≠ k
(C) Either n or k is a multiple of 10.
(D) If n is even, then k is odd.
(E) If n is odd, then k is even.

Oooooh, sneaky! I chose A after some thought, but it’s wrong. n and k could both be -20, which would give 400. B’s wrong too, since we’ve just realised n and k can be equal. D’s wrong, because n and k could be 16 and 25 for example, neither divisible by 10. But D and E seem to be saying the same thing. Hmmm.

D can’t work, because we know both numbers can be even. (20 * 20.) So the answer’s E. When you’ve eliminated the possible, what remains, however impossible, must be true.

If x < 12, then it must be true that

(A) –x < -12
(B) –x – 2 < 14
(C) –x + 2 < – 10
(D) x + 2 < 10
(E) x – 2 < 11

D was my answer. A is wrong, because x could be -20 for example, and 20 is more than -12. B and C have the same problem. D is less wrong, but still wrong, since x could be 10, and 12 is more than 10. It must be E.

What is the difference between the sixth and the fifth terms of the sequence 2, 4, 7, … whose nth term is n + 2n-1 ?

(A) 2
(B) 3
(C) 6
(D) 16
(E) 17

Great question. I chose D, having spent too long on the sequence. Let’s see… every n’th number is n+2 to the power of n-1, and the power of n-1 means the number preceding it in the sequence.

Applying this to the bit of the sequence we know we get: 4 equals 2 plus 2 to the power 1 (correct), 7 equals 3 plus 2 to the power 2 (correct), so the 4th number equals 4 plus 2 to the power 3, i.e. 12, the 5th number equals 5 plus 2 to the power 4, i.e 21, and the 6th number equals 6 plus 2 to the power 5, i.e. 38. So the difference between the 5th and 6th is 17, or E.

Which of the following could be the sum of the reciprocals of two different prime numbers?

(A) 7/13
(B) 10/21
(C) 11/30
(D) 23/50
(E) 19/77

I chose E. Let’s substitute a few reciprocals. 1/3 and 1/7? Sum to 10/21; well, that’s in the list, so I didn’t need to look far. Stop at B.

Verbal

Selling several hundred thousand copies in six months, the publication of “Maple Leaf Rag” in 1899 was an instant hit, helping to establish Scott Joplin as the preeminent ragtime composer.

(A) Selling several hundred thousand copies in six months, the publication of “Maple Leaf Rag” in 1899 was an instant hit, helping to establish Scott Joplin as the preeminent ragtime composer.
(B) The publication in 1899 of “Maple Leaf Rag” was an instant hit; in six months they sold several hundred thousand copies and it helped establish Scott Joplin as the preeminent ragtime composer.
(C) Helping to establish Scott Joplin as the preeminent ragtime composer was the publication of “Maple Leaf Rag” in 1899, which was an instant hit; it sold several hundred thousand copies in six months.
(D) “Maple Leaf Rag” was an instant hit; it helped establish Scott Joplin as the preeminent ragtime composer, published in 1899 and selling several hundred thousand copies in six months.
(E) Published in 1899, “Maple Leaf Rag” was an instant hit, selling several hundred thousand copies in six months; it helped establish Scott Joplin as the preeminent ragtime composer.

I chose C. Well A’s wrong, because it suggests the publication date was a hit, not the song. B’s wrong too, since ‘they’ is used without specifying who ‘they’ are. C is okay grammatically, just clumsily constructed. D is a complete dog, ‘published in 1999’ floating aimlessly in the middle of the sentence. E must be correct, and is.

Migraine, the most debilitating common form of headache, afflicts perhaps 18 million Americans, who collectively lose 64 million workdays a year, and they cost the nation $50 billion in medical expenses and lost work time.

(A) year, and they cost the nation $50 billion in medical expenses and lost
(B) year and thus cost the nation $50 billion in medical expenses and lost
(C) year, so as to cost the nation $50 billion in medical expenses and lost
(D) year that costs the nation $50 billion in lost medical expenses and
(E) year, which thus cost the nation $50 billion in lost medical expenses and

I chose E, unsure. A’s wrong because ‘they cost’ would refer to the workdays rather than the migraines or the Americans. C suggests the migraines are doing it deliberately. D and E sort of work, but the ‘lost’ should refer to work time, not medical expenses. B is correct.

Sales of United States manufactured goods to nonindustrialized countries rose to $167 billion in 1992, which is 14 percent more than the previous year and largely offsets weak demand from Europe and Japan.

(A) which is 14 percent more than the previous year
(B) which is 14 percent higher than it was the previous year
(C) 14 percent higher than the previous year’s figure
(D) an amount that is 14 percent more than the previous year was
(E) an amount that is 14 percent higher than the previous year’s figure

I chose C, because it’s grammatically correct. We can get rid of those ‘more’ ones first (A and D) since $167bn and 14% are countable numbers, where we should use ‘higher’. B is subtly wrong: we’re talking many years from 1992, and the ‘is 14 percent higher’ should be ‘was 14 percent higher’. C doesn’t work since it destroys the agreement with ‘offsets’ later on. E is left over, which is grammatically correct and gets the sense right, so it must be E.

Local residents claim that San Antonio, Texas, has more good Mexican American restaurants than any city does in the United States.

(A) any city does
(B) does any other city
(C) other cities do
(D) any city
(E) other cities

I chose D. Deceptively hard question. A and C add an extra ‘do’, so do not work. E would mean San Antonio’s stuffed so full of burrito joints that the total’s higher than all other US cities added together, so is wrong. D is written usage but not standard written; we all know what it means, but there should be an ‘other’ or equivalent in there to complete the comparative sentence. B is left over, and must be correct.

Unlike other arachnids, which have their nerve cells evenly distributed along their bodies, the scorpion’s nerve cells are clustered in its head, like a mammal’s

(A) bodies, the scorpion’s nerve cells are clustered in its head, like a mammal’s
(B) bodies, the scorpion’s head has a cluster of nerve cells, as a mammal does
(C) body, the scorpion has a cluster of nerve cells in its head, as a mammal does
(D) body, nerve cells are clustered in the scorpion’s head, like a mammal’s
(E) body, a cluster of nerve cells is in the scorpion’s head, like a mammal’s

A looks ok, which is why I chose it. B doesn’t complete the comparison, since it implies mammals could have body clusters, too; D and E have similar issues. So it’s A or C. C pins down where the nerve cells are, uses ‘clustered’ to balance ‘distributed’, and uses ‘body’ to denote the use of a singular (arachnid the species) although the usage is plural (arachnids the individual creepy crawlies). It’s C, but this is a hard one.

Over the last century, paleontologists have used small differences between fossil specimens to classify triceratops into sixteen species. This classification is unjustified, however, since the specimens used to distinguish eleven of the species come from animals that lived in the same area at the same time.

Which of the following, if true, would enable the conclusion of the argument to be properly drawn?

(A) Not every species that lived in a given area is preserved as a fossil.
(B) At least one individual of every true species of triceratops has been discovered as a fossil specimen.
(C) No geographical area ever supports more than three similar species at the same time.
(D) In many species, individuals display quite marked variation.
(E) Differences between fossil specimens of triceratops that came from the same area are no less distinctive than differences between specimens that came from different areas.

I chose E after much thought (a luxury, having several minutes at the end to ponder.) So: we’re looking for something that makes classifying fossils from the same area a valid technique. A, B, and D are irrelevant, since we’re talking specifically about different known species of a single type of creature. It’s C or E. But E doesn’t specify what kind of differences or whether they’re important. C, however, gives us a hard fact, and if eleven Triceratop ‘species’ came from one area, the established fact that no one area can support more than three would allow the right conclusion (those eleven can’t all be different species) to be drawn. It’s C.

Lessons learned today: I need to concentrate more on elimination for ‘hard’ verbal questions; most of these aren’t a simple right or wrong, just whatever the best choice is. Eliminate, eliminate.

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