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GMAT-esque Challenge Question: Today is the Day... To Get Better at GMAT Math

Brian — Thu, 15 Mar 2012 14:11:32 +0000

It’s March 15, and now that the hysteria over Pi Day (good ol’ 3-14) is over, the true GMAT math geeks can celebrate an even more exciting use of math and dates (and, no, we don’t mean impressing your dates with math tricks. Not that that’s not a good idea, of course).

Today is 3/15, a not-all-that-unique case of the month being a factor of the day (3 is a factor of 15, so you could factor the date 3/15 into 1/5. It’s almost like it’s January 5th all over again!).

Now, why is this important? Because the GMAT loves to test factors and multiples, so if you can think of something as little as the calendar each day in terms of factors and multiples, in really no extra time at all (you do, after all, check the date at least once a day, right?) become incrementally more prepared for GMAT math. So take this pop quiz:

How many days per calendar year* is the month a factor of the day?

The answer will be posted shortly; please post your answers and thought processes in the comments field, and enjoy your easily-reducing day! You won’t have another until Sunday, 3/18.

* Hint: It doesn’t matter if it’s Leap Year. 2 is not a factor of 29.

Good luck!

SOLUTION:

Solution: 90

All 31 days in January, because 1 is a factor of all integers

14 of the 28 days in February (because every other day is divisible by 2)

10 of the 31 days in March (the multiples of 3 between 3 and 30)

7 days in April (the multiples of 4 between 4 and 28)

6 days in May (the multiples of 5 between 5 and 30)

5 days in June (the multiples of 6 between 6 and 30)

4 days in July (the multiples of 7 between 7 and 28)

3 days in August (the multiples of 8 between 8 and 24… so, so close if only the month were 32 days long!)

3 days in September (9th, 18th, 27th)

3 days in October (10th, 20th,30th)

2 days in November (11th, 22nd)

2 days in December (12th, 24th)

And there you have it! As you can see, as you move through the months, your job starts to get easier as you pick up on the patterns and are able to reuse some of your previous insights… This is a very valuable skill to remember on test day!

Will you take the GMAT in June or later? On March 21 we will run a free live online seminar to help you get up to speed on the new Integrated Reasoning section coming in June. And, as always, be sure to find us on Facebook and Google+, and follow us on Twitter!

GMAT Tip of the Week AND GMAT Challenge Question: Two-for-Twentieth!

Brian — Fri, 20 May 2011 14:11:58 +0000

Hello again readers, and happy May Twentieth! In honor of that 2 in 5/20 (the day before The End of the World, of course), today’s post is dual-purposed in two ways: We have a GMAT challenge question and a GMAT tip of the week, and the GMAT tip of the week is actually two in one. First, take a look at this challenge Critical Reasoning question:

A recent Bloomberg Businessweek article cited that the average GMAT score for 20 and 21-year olds is 575, while for 22 and 23 year olds it is only 539. Therefore, all potential business school applicants should be advised to take the GMAT while they’re younger so that they can expect a higher score.

Each of the following, if true, would undermine the above conclusion EXCEPT:

(A)   Very few 20 and 21-year olds take the GMAT, and most who do have been tabbed by career planning offices as candidates for elite programs like HBS 2+2.
(B)   Students at age 20 and 21 are less likely to consider regional and part-time programs that have lower GMAT targets than are applicants just a few years older.
(C)   The older an applicant gets, the more likely he is to have professional and familial commitments that can impede study plans.
(D)   A disproportionate number of 22 and 23-year old “boomerang” college graduates have been forced by their parents to take multiple graduate school board exams as part of their career search in a down economy.
(E)    Examinees in their late 20s report average scores well into the upper 500s, perhaps because they can afford more comprehensive test preparation options.

“EXCEPT” questions can throw a twist at you in that there are four “right” answers and your job is to pick the “wrong” one; as such, they tend to be best-handled through process of elimination, as you eliminate the low-hanging-fruit (in this case, answer choices that clearly weaken the conclusion) and work your way toward the remaining answer that does not weaken the conclusion. Here, the conclusion is that all test-takers should be advised to take the GMAT while they’re younger, citing the evidence that 20 and 21-year olds statistically outperform their slightly-older counterparts.

As with any weaken question, it’s helpful to see the logic between premise and conclusion. The only actual evidence provided is the average score in two groups – 20/21 and 22/23, with 20/21 being higher. But as with any statistics questions, you should ask yourself whether there are alternative explanations for the facts that don’t include the stated conclusion; the GMAT loves to do this particularly when statistics are present. Here, the facts show a correlation between youth and success, at least in these two groups, but the conclusion suggests causality. Are there alternative explanations for why the stats would hold without a causal relationship? Sure – say that the 20/21 year old group is disproportionately full of child prodigies and fast-tracked MBA candidates (which may very well be the case…few college students consider the GMAT and those who do tend to be extremely serious and motivated compared to the general population). Or that 22/23 year olds are somehow disproportionately likely to underperform but scores tend to bounce back up. The lone statistics given do not support the blanket, causality-infused conclusion, and four of the answer choices expose that gap in logic.

Choice A hits the point we made above – it’s quite likely that the very-young applicants are taking the GMAT for a specific reason (they’ve been tabbed as elite) and so that pool is skewed toward success compared to the general population. But that doesn’t mean that the average student would do better while younger; just that those surveyed happened to be predisposed to doing well whenever they took the exam.

Choice B is somewhat inverse of A; it provides a reason to suggest that the dropoff in scores isn’t because the applicants were older. Instead, it’s because that demographic tends to feature students less inclined to pursue a very high score, and so the lower scores are a function of their lowered goals, not their lowered abilities.

Choice D is similar to B – if the average age of examinees is mid to late 20s, and we know that there’s a chance that the youngest in the pool may already be skewed, it’s possible that the 22 and 23 year olds are likely to underperform just because of their circumstances: they’re taking the test because they have to and not because they want to, and their scores may be lower as a result of that circumstance, not that they were any more likely to have done better if younger.

Choice E suggests that older applicants may actually have an advantage, as their scores are higher than the 22/23 group and there are factors in older age that indicate a potential causality in favor of older test-takers.

Only choice C fails to weaken the conclusion – in fact, it strengthens the conclusion by providing a bit more of the causal relationship than the argument alone contains. If the reason for older applicants underperforming is their lessened availability to study, then it’s more likely that students should consider taking the test while younger.

C is the correct answer, and brings us to our second tip:

There is something to be said for the advice in this conclusion, even if the logic is unsound by GMAT standards. Those who take the GMAT closer to their college days tend to report an easier study process, most often because they feel fresher with both GMAT skills (algebra, geometry, grammar, etc.) and study habits, and because (as answer choice C suggests) they’re freer from binding commitments than they may be later in life.

While it’s not an airtight argument that you’d do better on the GMAT while you’re younger than while you’re older, it’s to your advantage to heed this related advice:

Study for the GMAT when you know that your lifestyle is conducive to it, not necessarily when you absolutely need the score.

If you think you may apply to business school in the next few years, there’s a high likelihood that you can envision a few months’ period in that time in which commitments (work, travel, social, fitness, etc.) will be lighter, or you can work now to lighten the load for later. As your score becomes more necessary with impending deadlines, you lose that opportunity to clear your schedule (and your mind), and other commitments (application essays, meetings with recommenders, campus visits, recruiting events) are likely to pop up.

Your GMAT score is good for five years, so if you believe that you’ll have occasion to use a score in that time, plan out a schedule that will give you some relaxed study time. In many ways, simply knowing that you’re free from the pressure of an impending deadline allows you to learn more proactively and confidently. That situation may well occur more often for younger test-takers, but you need not turn back the clock to realize those advantages; just look for or create a lull in your hectic schedule in advance of your application dates, and you can reap the rewards of youth on the GMAT.

Getting ready to take the GMAT? We have GMAT classes starting soon in Chicago, New York, and many other locations. And, as always, be sure to find us on Facebook and follow us on Twitter!

GMAT Challenge Question: Two For Thursday

Brian — Thu, 07 Apr 2011 18:27:09 +0000

Back by popular demand…let’s try another GMAT Challenge Question today, and since we’re doing two consecutive days of challenge questions, let’s just go all out. As Ernie Banks would say, let’s play two. The questions, courtesy of San Diego GMAT instructor Matt Douglas, our 2010 worldwide Instructor of the Year, are below; post your answers in the comments field and check back later today for detailed solutions.

1. Is a = 0?

(1) a = a^²

(2) a = a^³ – a^{^2}

2. Is ab < a?

(1) a = 0

(2) b = 0

UPDATE: Solutions

Question 1 is a great example of a GMAT unscored, experimental question. If you selected B…you should be commended for your work. Clearly statement 1 is not sufficient, as both 0 and 1 satisfy the given equation, so we cannot determine whether a is exclusively 0. Statement 2 most likely leads you to “sufficient”, as 0 is the only rational solution. But further examination leads us to:

a = a^3 – a^2

0 = a^3 – a^2 – a

0 = a (a^2 – a – 1)

Here, 0 is one solution for a, and so are the factors of the quadratic a^2 – a – 1 = 0. Were you to apply the Quadratic Formula – which the GMAT will NOT require you to do – you’d note that there are, indeed, two imaginary solutions for the quadratic. Accordingly, although it’s not likely that you would go as far as to calculate those solutions past the point of determining that they do exist, statement 2 is also not sufficient.

Taking the statements together, we know that:
Statement 1: a = 0 or a = 1

Statement 2: a = 0 or a = one of two imaginary (not 1) numbers

Therefore, as 0 is the only number that satisfies both statements, the correct answer is C. However, note that because the GMAT does not explicitly require the quadratic formula, this may be the type of question that becomes weeded out due to the GMAT’s sophisticated item analysis via unscored experimental questions. If statistical analysis on a question demonstrates that there is noise in the data – that a 700 scorer may not be significantly more likely to answer this question correctly than a 600 scorer, for example, an item like this may be removed. We bring that up because, while B is a tempting but probably a valid incorrect answer given that you can solve this without using the quadratic formula, and just knowing that it does exist, E is also a possible answer that a reasonable high-scorer could confidently suggest. If you use statement 1 and substitute that into statement 2, you could replace a with a^2 to get: a^2 = a^3 – a^2. That also means that 2a^2 = a^3, leaving open the possibility that 2 is a solution in addition to 0, when clearly that solution does not work in the individual solutions. Because this question can get so dense with the quadratic formula and some unique algebraic rules associated with non-function quadratics…well, like plenty of officially-tested GMAT questions over time, this one is probably a lot more complicated than we intended when we first drew it up. It’s a great learning tool, but ultimately we predict that the GMAT’s rigorous statistical analysis would weed this one out in the experimental phase.

#2: Is ab < a?

Statement 1, that a = 0, is sufficient. If a is 0, then we’d have: 0(b) < 0 ? Clearly that is not the case; 0 = 0, so ab can never be less than a if a is 0. The answer is “no” and statement 1 is sufficient.

Statement 2, that b = 0, is not sufficient. Here we know that the left hand side of the inequality is 0, but we don’t know anything about the right hand side. a(0) < a ? That asks whether 0 < a, and it all depends on the value of a. Because statement 2 is not sufficient, the correct answer is A.

GMAT Challenge Question: Sentence Correction Is the (Tar) Pits

Brian — Wed, 06 Apr 2011 16:54:16 +0000

Once again, it’s time for a GMAT challenge question! This installment features the dreaded maximum-word-count, everything-underlined Sentence Correction device. Can you avoid getting sucked into a La Brea Tar Pit of wasted time? Here’s the question, courtesy of Boston GMAT tutor Ashley Newman-Owens; check back later for the solution and some tips for working through a problem like this:

Based on accelerator mass spectrometry, an advanced technique that makes it possible to obtain radiocarbon dates from samples much smaller than that necessary for traditional radiocarbon dating, scholars have been able to determine impressively precise radiocarbon ages for samples of Glyptodon and Holmesina recovered from the La Brea Tar Pits, extinct large mammals similar to armadillos.

(A) Based on accelerator mass spectrometry, an advanced technique that makes it possible to obtain radiocarbon dates from samples much smaller than that necessary for traditional radiocarbon dating, scholars have been able to determine impressively precise radiocarbon ages for samples of Glyptodon and Holmesina recovered from the La Brea Tar Pits, extinct large mammals similar to armadillos.

(B) Based on accelerator mass spectrometry, an advanced technique that makes it possible to obtain radiocarbon dates from samples much smaller than necessary for traditional radiocarbon dating, scholars have been able to determine impressively precise radiocarbon ages for samples of Glyptodon and Holmesina, extinct large mammals similar to armadillos, recovered from the La Brea Tar Pits.

(C) Using accelerator mass spectrometry, an advanced technique that makes it possible to obtain radiocarbon dates from samples much smaller than those necessary for traditional radiocarbon dating, scholars have been able to determine impressively precise radiocarbon ages for samples of Glyptodon and Holmesina, extinct large mammals similar to armadillos, recovered from the La Brea Tar Pits.

(D) Basing them on accelerator mass spectrometry, which allowed them to obtain radiocarbon dates from samples much smaller than those necessary for traditional radiocarbon dating, scholars have been able to determine impressively precise radiocarbon ages for samples of Glyptodon and Holmesina, extinct large mammals similar to armadillos, recovered from the La Brea Tar Pits.

(E) The use of accelerator mass spectrometry, an advanced technique that makes it possible to obtain radiocarbon dates from samples much smaller than those necessary for traditional radiocarbon dating, have enabled scholars to determine impressively precise radiocarbon ages for samples of Glyptodon and Holmesina recovered from the La Brea Tar Pits, extinct large mammals similar to armadillos.

UPDATE: Solution.

Since this sentence is underlined in its (incredibly long) entirety, you can save yourself an especially hefty chunk of time by looking for differences that jump out between the answer choices. Scanning only the ends of the answers choices reveals a split between two possible endings; the choice in the original sentence improperly situates extinct large mammals similar to armadillos, an appositive which should immediately follow Glyptodon and Holmesina. The introductory phrase is a modifier that attempts to link to scholars. The participle using makes this link legitimate, because it describes the scholars’ activity.

(A) Based on … incorrectly modifies scholars; the comparison between samples (plural) and that (singular) is awkward; extinct large mammals is not in proper apposition to Glyptodon and Holmesina.

(B) Based on … incorrectly modifies scholars; the sentence lacks a noun after than to stand in comparison to samples.

(C) Correct. Using accelerator mass spectrometry correctly modifies scholars; samples and those stand properly in comparison; extinct large mammals … is in appropriate apposition to Glyptodon and Holmesina.

(D) In both of its appearances, the pronoun them lacks a clear reference.

(E) Verb agreement problem. The singular subject, use, does not agree with the plural verb have enabled.

The correct answer is C.

GMAT Challenge Question: Taxing Sentence Correction

Brian — Wed, 09 Feb 2011 18:02:31 +0000

It’s time for another GMAT Challenge Question, and it’s also about time to start thinking about your taxes – April 15 is just over two months away, and remember that February is a short month! With those two things in mind, we thought we’d let you audit an IRS-related Sentence Correction question. Submit your answers in the comments field and we’ll be back later today with the solution and explanation.

Mutual funds, though helpful for personal investors who wish to diversify their portfolios, expose shareholders to additional taxation: not only are taxes on shareholders’ eventual sales of the securities collected by the IRS, but also on reinvested dividend stakes earned by the securities held by the fund itself.

A) not only are taxes on shareholders’ eventual sales of the securities collected by the IRS, but also on
B) collected by the IRS are taxes not only on shareholders’ eventual sales of the securities, but also on
C) taxes not only on shareholders’ eventual sales of the securities are collected by the IRS but also
D) not only taxes on shareholders’ eventual sales of the securities are collected by the IRS, but also on
E) taxes are collected by the IRS not only on shareholders’ eventual sales of the securities but also

Check back tomorrow, when we’ll reveal the answer!

UPDATE: Solution: B.

This sentence tests sentence structure and may be best solved by looking at the 3/2 split between the answer choices on the last word. Three choices use “on” as the last word, while two choices omit “on” – signifying that we’ll need to ensure that the multiple phrases in the sentence are connected properly. Connector words like “on”, “but”, “to”, “that”, etc. make for terrific decision points.

When testing connectors, you may want to quickly write your own “ideal” sentence to determine which components need to be connected. Here, ideally, the sentence would say something like:

The IRS collects taxes not only on shareholders’ sales but also on reinvested dividends.

In this ideal sentence, we need to include the word “on” for both items to denote that taxes are collected on both types of income. Answer choice E, the most popular choice on this question, does not include that word “on” to link the collection of taxes to the reinvested dividends, and is therefore wrong. We need the word “on” at the end, and we also need “on” to be logically drawn back to “taxes are collected”.

Look back at choice B, the correct answer. It’s awkward, but it does exactly what we need it to do – it leads with “taxes are collected”, and connects that phrase to both components with the word “on”. The only awkwardness is an inverted subject/verb structure. We want to see:

Taxes are collected (by the IRS) not only on shareholders’ stakes but also on reinvested dividends

But choice B gives us

Collected by the IRS are taxes not only on shareholders’ stakes but also on reinvested dividends.

As we concluded at the outset, we’re being tested on the structure of the sentence, so that’s paramount, and choice B gets that 100% correct. And inverted subject/verb structure is not an error – it may be awkward but it is okay! It throws us off the scent here, but if you look back for specifically what is necessary – connecting both types of income back to the collection of taxes – it does exactly that and is therefore correct.

GMAT Challenge Question: Bet You “Kant” Pick The Correct Idiom...

Brian — Wed, 08 Dec 2010 19:36:56 +0000

Hello again, everyone! It’s time for another GMAT Challenge Question, this time from the verbal side of the exam. Try your hand at this Sentence Correction question, log your answers and explanations in the comments field, and we’ll be back with the official solution and an important lesson regarding GMAT Sentence Correction.

By the way, we have loads more practice questions available in our free GMAT practice test! It’s free to anyone who registers on our site. If you’re just getting started with your GMAT prep, taking a full-length, computer-adaptive practice GMAT is a a great way to get a feel for the exam and get an idea of the stamina you’ll want to build up before you take the real thing.

And now, for today’s GMAT Challenge Question:

Immanuel Kant’s writings, while praised by many philosophers for their brilliance and consistency, are characterized by sentences so dense and convoluted as to pose a significant hurdle for many readers interested in his works.

A) so dense and convoluted as to pose
B) so dense and convoluted they posed
C) so dense and convoluted that they posed
D) dense and convoluted enough that they posed
E) dense and convoluted enough as they pose

Check back later for the answer and explanation!

UPDATE: Solution
Thanks, everyone, for your comments and answers! As always, the two most popular answer choices were A and C, so let’s break those down. While the idiom in A “so dense as to pose” may seem a bit awkward (as many posted, you were looking for the more-familiar “so dense that…”, it’s not incorrect.

What we do know to be incorrect is the verb tense of “posed” in B, C, and D. Have these sentences and writings ceased to be difficult? Not likely, and we are provided with the indicative-tense verb “are characterized” earlier in the sentence, so it’s safe to say that these dense, convoluted sentences still do pose a challenge to readers. Accordingly, the past-tense “posed” is incorrect.

E has a fatal meaning problem – to say that the sentences are “dense and convoluted enough as they pose” is to say that they’re dense and convoluted while they pose (during the duration of the posing), and that’s illogical. It’s not that they’re dense while the reader is reading – they’re just dense in general. Furthermore, the word “enough” is then left without a logical role in the sentence. Is there a level of sufficiency for the density of a sentence? Even if so, it’s dense enough “to do what?”. E has a fatally flawed meaning, leaving us with A.

As it turns out, the idiom “so dense and convoluted as to pose…” is a correct way to express that situation. To many test-takers, however, it seems off for some reason. What you can learn from this example is that we’re simply not great at choosing correct/incorrect idioms! There are far too many idioms to know them all, and far too many for business schools to even care whether you can memorize them all. Your role in these questions is to think and problem-solve like a manager, and an effective manager will look for decisions points at which he can make an effective impact without allowing himself to be mired in areas out of his range of expertise. On these questions, look for regularly-occurring decision points like verbs (tenses and subject-verb agreement) and pronouns (numerical agreement) as many did here. Those who did correctly selected choice A…congratulations to you!

GMAT Challenge Question: Blackout Dates

Brian — Wed, 24 Nov 2010 19:26:50 +0000

Happy Thanksgiving, everyone! With today as one of the busiest travel dates of the year, and undoubtedly a blackout date for your frequent-flier or rewards-miles program, we’ll offer this Data Sufficiency question for which blackouts can play a prominent role.

We’ll explain what we mean later today; for now, please enter your solutions in the comments field and we’ll be back this evening with an explanation and takeaway for which you’ll be thankful!

If y is an odd integer and the product of x and y equals 222, what is the value of x?

(1) x is a prime number

(2) y is a three-digit number

Update: Solution. Much of this problem’s difficulty derives from the fact that it is hard for us to forget what we’ve already been told. On Data Sufficiency questions, it’s therefore important to practice “Memory Blackout” when reading statement 2 – we must assess statement 2′s sufficiency on its own by blacking out everything we’ve learned from statement 1.
Here, statement 1 tells us that x is prime, and we already know that y is odd. For an odd y to multiply by x and produce 222, an even number, x must be even. Therefore, if x is both even and prime, x must be 2, and the statement is sufficient.

Attacking statement 2, we no longer know that x is prime – nor do we even know that x is an integer. We ONLY know that y is a 3-digit odd number. You may be baited into thinking that x is an integer, bringing all or some of what you’ve learned from statement 1 into the process, but we don’t know that at all. y could be 333 and x could be 2/3 and statement 2 is still satisfied. Or, as you were probably trapped into predicting, y could be 111 and x could be 2. But because we can’t know for certain in this case that x is an integer, the statement is not sufficient, and the correct answer is A.

GMAT Challenge Question: The Squared Circle

Brian — Wed, 10 Nov 2010 18:10:12 +0000

It’s time again for another GMAT Challenge Question, and this one features a favorite GMAT theme: you’re provided no actual numbers and need to use your conceptual knowledge to determine a proportional relationship. Please post your answers in the comments field, and we’ll be back later today with a detailed solution:

Circle A is perfectly inscribed in a square, and the square is perfectly inscribed within circle B. The area of circle B is what percent greater than the area of circle A?

(A) 50%

(B) 100%

(D) 200%

(E) 250%

UPDATE: Solution! One important note about inscribed shapes is that both squares and circles are perfectly symmetrical, meaning that if you know one length (radius, diameter, circumference, area; or side, diagonal, area, perimeter) you can solve for everything else.

In this case, is we call the radius of the smaller circle r, then the diameter of that circle is 2r and the area is pi*r^2.

If that circle is perfectly inscribed inside a square, then that means that the length of the diameter will perfectly fit within the boundaries of the square, making the side of the square also equal to 2r.

Now, if a circle is perfectly inscribed around that square, then the circle will hit each corner exactly once, making the diameter of the larger circle equal to the diagonal of the square. Using what we know about squares (or using Pythagorean Theorem), we know that the diagonal is equal to the side * √2, making the diameter of the larger circle equal to 2r*√2, and the radius of the larger circle then equal to half that: r*√2.

The area of the larger circle is the pi*(r*√2)^2, or 2*pi*r^2. Therefore, the area of the larger circle (2*pi*r^2) is twice that of the smaller circle (pi*r^2). But keep in mind that you must answer the right question! The question asks “how much GREATER is the larger circle than the smaller” not “the larger circle is what percent OF the smaller”. To get to twice the size, we only ADD 100%, so the correct answer is B.

GMAT Challenge Question: Solve This Stats Problem, Stat!

Jeremy — Thu, 14 Oct 2010 23:28:50 +0000

Set A consists of integers -9, 8, 3, 10, and J; Set B consists of integers -2, 5, 0, 7, -6, and T. If R is the median of Set A and W is the mode of set B, and R^W is a factor of 34, what is the value of T if J is negative?

(A) -2
(B) 0
(C) 1
(D) 2
(E) 5

Please include your answers in the comments field and we’ll be back later today with the solution!

UPDATE: Solution.

This problem demonstrates a helpful note about statistics problems – quite often the key to solving a stats problem is something other than stats: number properties, divisibility, algebra, etc. The statistics nature of these problems is often just a way to make a simpler problem look more difficult.

Here, the phrase “factor of 34″ should stand out to you, as there are only four factors of 34, so you can narrow down the possibilities pretty quickly to 1, 2, 17, and 34. And because the number in question must be an exponential term that becomes a factor of 34, it’s even more limited: 2, 17, and 34 can only be created by one integer exponent – “itself” to the first power.

The base of that exponent is going to be the median of Set A, and because we know that the median of Set A will be 3 (a negative term for variable J means that 3 will be the middle term), the question becomes that much clearer. 3^W can only be a factor of 34 if it’s set equal to 1, and the only way to do that is for W to be 0. REMEMBER: anything to the power of 0 is equal to 1, a great equalizer on the GMAT!

Therefore, the correct answer is 0.

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GMAT Challenge Question: Prime Time

Jeremy — Wed, 29 Sep 2010 22:44:25 +0000

It’s time again for another GMAT challenge question, and this one focuses on one of the quantitative section’s favorite themes: prime factors.

Please submit your answers in the comments field, and check back later today for the solution and a more-thorough explanation of prime factors!

What is the greatest prime factor of 12!11! + 11!10!?

(A) 7
(B) 11
(C) 13
(D) 17
(E) 19

UPDATE: Solution!

While it’s quite common for students to simply look at the numbers 12!, 11!, and 10! and recognize that the highest naturally-occurring prime number is 11, it’s important to recognize that this is an addition problem – the numbers 12!11! and 11!10! are combined to create a new number that may well have a higher prime factor than its factorial components.

When adding large numbers like factorials and exponents, as we discussed in this space last week, it’s often quite helpful to factor out common terms. In this case, it’s particularly important, because our entire goal is to break out the large sum into prime factors so that we can determine which is biggest. Each term has a common 11!, so by factoring that out we can get from:

12!11! + 11!10!

11! (12! + 10!)

Now, 12! includes a 10! – it’s essentially 12 * 11 * 10!, so we have a common 10! within the parentheses that can also be factored out, going from:

11! (12*11*10! + 10!)

11!10! (12*11 + 1)

At this point, the largest prime factor must be either the 11 outside the parentheses or a factor of the number within it, so it’s necessary to check the number within. 12*11 + 1 = 132 + 1 = 133. 133 is the product of 7*19, so 19 is a prime factor of 12!11! + 11!10!, and therefore the largest prime factor. Accordingly, E is the correct answer.

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