What is the greatest prime factor of 12!11! + 11!10!?
While it is common for students to simply look at the numbers 12!, 11!, and 10! and see that the highest naturally-occurring prime number is 11, it is important to know 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, it is 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...
What is the greatest prime factor of 12!11! + 11!10!?
What is the greatest prime factor of 12!11! + 11!10!?
(GMAT 800 CR Bold Faced) A leading board member of AutoSnip
A leading board member of AutoSnip Co., makers of an automated home haircutting system, recently stated that the company was in terrible shape and headed for a disastrous year. His concern was that, since the introduction of the AutoSnip III last year, calls to the customer service line have nearly doubled, indicating that people are very unhappy with the new product. Although it's true that it is the job of responsible board members to raise issues of concern, in this case the board member's analysis of the situation is mistaken. The customer service line handles not only complaints but also sales, and the majority of the new calls have been to place new orders.
What role do the two boldfaced selections play in the above argument?
A.The first provides evidence supporting the main conclusion of the argument; the second provides evidence supporting a conclusion that the argument opposes.
B. The first provides evidence, an interpretation of which supports the main conclusion of the argument; the second provides evidence supporting the main conclusion of the argument.
C. The first provides incontrovertible evidence opposing the main conclusion of the argument; the second provides evidence supporting the main conclusion of the...
Top 10 Tips to Ace GMAT Data Sufficiency
Ever heard of a Math problem that you actually don't have to solve. If you have just started your GMAT prep, then this can be confusing. Don't worry! With some practice, your mind will be trained to think like a DS Wizard. Follow these 10 tips and you will be on your way to mastering GMAT Data Sufficiency.
1. Familiarize with the Answer Choices
No excuses: On Data Sufficiency, they’re always the same! Know in the blink of an eye what choice C is. On test day, if you find that Statement 1 is insufficient, be able to cross out choices A and D without hesitation.
2. Takes notes efficiently
Each statement alone will be sufficient if both of the statements on their own contain all the information necessary to answer the question. The statements will be sufficient together if they contain every piece of necessary information between them. Take the area of a parallelogram: Do you need to know every side length to determine the area? If you have every side length, can you find the area?
3. Don’t look at the statements together.
Statement 2 may tell you that x is negative, but that fact has no bearing on Statement 1 when viewed by itself. Explore all the possibilities offered by each statement individually. If you’ve...
GMAT Will Wear you Down: Avoid Unnecessary calculations and Don't Analyze Unnecessary Verbiage
The GMAT finds much of its competitive advantage in its ability to wear down its unsuspecting challengers, who perform unnecessary calculations on the quantitative side and reading and analyzing unnecessary verbiage on the verbal side, while all the while the GMAT packs its "knockout punch" in the form of a subtle uniqueness in the line of questioning that a tired examinee is unlikely to notice.
In order to combat this opponent, be sure to seek out opportunities to save time and energy when possible:
• When answering a Data Sufficiency question, once you know that you will get one definitive answer, you can stop performing the calculation. The actual answer does not matter, as the question is only concerned with whether you will, indeed, arrive at an answer.
• When calculating the answer for a Problem Solving question, consider the answer choices and whether an estimate, or a property of the correct value (does it have to be even? Must it be negative?) will be...
How to study for the GMAT in Two Weeks?
Knewton: Let us start by saying "Try not to prepare for your GMAT in 2 Weeks". Two weeks is not enough time to master the topics or the test taking strategies (Read GMAT One Month Study Plan and GMAT Three Month Study Plan) But circumstances like a B-School Deadline might force you to cram for the test in two weeks. Follow this efficient GMAT Study Plan:
Day 1 – Diagnosis: Take a practice test. This will likely be your one and only assessment. If you score evenly on both sections, then you will need a more comprehensive study plan. If you ace verbal but bomb the quant, then you know to focus your attention there.
Days 2 to 4 – Prime the Pump: After you take an official practice test, spend the next few days going through as many practice problems as possible. If you have an Official Guide, make certain you read the explanations for all of the questions you answer incorrectly. Try to focus...
Learn when Diction Impacts Grammar in GMAT Sentence Correction Questions
As you may know, diction refers to word choice. Usually, we use the term “diction” to describe an author’s tone or style - rarely does word choice have an effect on grammar. In some cases, though, it does. The GMAT Sentence Corrections will test you only on those occasions when word choice affects grammar, not when one word will be more effective than another.
1. Adverbs vs. Adjectives
While the subject of adverb usage may deserve its own category, the topic can be included under diction. Simply put, an adverb (those words that often end in ly) describes a verb, adjective, or another adverb, while an adjective describes a noun.
Adverb usage is the reason we say “I did well on my test” and not “I did good on my test;” well is an adverb while good is an adjective.
Example 1. Scientists dream of one day creating armies of nanobots, tiny robots smaller than a cell, that can enter the human body and use their practical unlimited access to find and repair defects in bodily structures.
Never actually understood Absolute Values ? Here is your chance!
Absolute Values (AVs) questions in GMAT can be a time saver for you if you understand a few rules. Capture the following notes and use it as a reference for your GMAT exam.
1. Absolute Value equations are two equations disguised as one
You can split up any equation involving absolutes into two, and solve for each solution. One will look identical to the given, and the other is found by multiplying the inside by -1. Remember to multiply the entire expression by -1.
| (x + 5)/3 | = 11 turns into:
(x + 5)/3 = 11, and
(x+5)/3 = -11
x + 5 = 33
x + 5 = -33
x = 28 x = -38
Note that plugging either x = 28 or x = -38 into the original equation will check out. Also note that solutions for variables within absolute value questions can be negative. What is spit out of the AV cannot be negative, but what goes in can be anything.
2. Think of Absolute Values as distances from zero
If an AV = 15, that means whatever is inside the AV is exactly 15 above or below zero on the number line.
Using “Whom” and “Who” in Sentence Corrections on the GMAT
Some GMAT sentence correction questions test not only for the accepted rules of grammar but also for the specific preferred style of the GMAT. Luckily, “who” vs. “whom,” is not one of those issues; this is a pretty straightforward issue, and is usually not tested in a complicated way. However, since even the most knowledgeable and educated writers sometimes misuse “who” and “whom,” it’s worth reviewing a couple of rules that can help guide you in determining the correct usage of these pronouns.
1. If someone were to ask a question about the sentence, would the answer be “him/her/them” or “he/she/they”?
This is probably the most effective way to remember the difference between “whom” and “who,” and most of the time, this will be enough to help you answer correctly. If a question about the action being described would be answered with “him,” “her,” or “them,” then the correct form is “whom.” If a question about the action being described would be answered with “he,” “she,” or “they,” then the correct form is “who.” Just remember this: the words with M’s at the end go together. They = Who, and Them = Whom. Here’s a basic sentence addressing this issue:
The Dalmation is a high-strung, energetic dog, and has historically been associated with firefighters, who/whom originally used the animal to guard...
GMAT Performance Tips
Your performance on the GMAT, like all peak performances tend to come in a familiar three-step pattern: ready, set, go; bump, set spike; game plan, warm up, perform. All signs point to I came, I saw, I conquered.
The GMAT begins with the AWA essays, a pair of 30-minute writing samples designed to test your communication ability, and for which the scores are used sparingly in MBA admissions. Effectively, the biggest threat to your MBA candidacy from the AWA section is not necessarily the essay score itself, but more likely the way in which that hour will impact your overall performance on the ever-important Quantitative and Verbal sections, which combine for your score between 200 and 800. How can you use the AWA section as a competitive advantage, and not a threat?
Assume that the AWA section comes first for a reason - in spending an hour writing about generic topics, students are apt to lose track of (or at least worry that they'll lose track of...
How to use Active Thinking in GMAT Problem Solving
Quick brainteaser for you: If 3 bunnies can eat 3 carrots in one hour, how many carrots can 1.5 bunnies eat in one hour?
Really take a moment to think about it.
Do you have an answer?
Ok. If you answered, or even were tempted to answer, “1.5 carrots,” then I’m glad that you’re reading this article! The thing is, while the bunnies are eating carrots at the rate of one per hour, it doesn’t follow that 1.5 bunnies will eat 1.5 carrots. 1.5 bunnies will only eat one carrot, because 1.5 bunnies is really just 1 bunny. (That half a bunny isn’t feeling very well and doesn’t want any carrots.)
I don’t mean to say that this is a GMAT-style problem, but if you found yourself answering “1.5 carrots,” then you are prone to operating on autopilot. Students who operate on autopilot will often fall into traps, and they may become overwhelmed by questions that don’t fall clearly into easily recognized patterns. And let me tell you – you will likely see many problems on the GMAT that don’t fall into common patterns!
Exponents Lead to Cumbersome, Time-Consuming Calculations involving Large Numbers but it is Pattern-Driven
The GMAT's quantitative section is increasingly emphasizing problem solving skills over calculation abilities, and often does so in the form of "Number Properties" questions. The authors of the exam are also quite adept at recognizing "mathematical psychology", and creating questions that increase an examinee's anxiety by enough to make that process of problem solving a bit more difficult. One of the major themes that arises as a result is the use of exponents, which carry with them a number of properties extremely useful to the writers of the GMAT.
• Inspire fear (or at least apprehension) in test takers
• Lead to cumbersome, time-consuming calculations involving large numbers
• Are actually quite pattern-driven, and reward those who seek out those patterns rather than attempt to perform the extensive calculations
How can this help you on the exam?
If you embrace the pattern-driven quality of exponents, you can rest easy on exponent questions...
International Students - Are you ready for GMAT Verbal?
For some international students who are new to the language, ESL classes might be a necessary step before they even start thinking about business school . For others, whose foundation in English grammar is stronger, study time may be better spent reading books in English, writing essays, taking practice tests, or doing focused grammar drills. So how can you know whether your English is at the right level for the GMAT?
Simply put, to do well on the GMAT you should know enough English to function in a university environment. First, check your proficiency by listening to sample lectures on Youtube. This is a practical recommendation that pertains to spoken as well as written English. In business school you will be expected to make arguments, back up opinions, and discuss case studies in depth. You should be comfortable stating your opinions and answering questions. Though you want to have better grammar than Borat or Jackie Chan, don’t worry if you have an accent or make a few mistakes when speaking.
Here’s an easy test: Watch a movie in English without subtitles; try something business related, like Glengarry GlenRoss, Wall Street, or Working Girl if you can. When you’re done, read a detailed summary of its plot online. If you find that you missed out on...
GMAT Sentence Correction Strategies - Spot Decision Points
As stated in GMAT SC - Use Logic, the pool of required grammar knowledge for the GMAT is likely shallower than you would think; those who memorize hundreds of idiomatic rules or read the cover off of their copy of Strunk & White’s “Elements of Style” are studying counter to the real purpose of the GMAT’s inclusion of Sentence Correction: the idea of “core competencies.” Corporate Strategy courses in business school will spend quite a bit of time on that notion that each business needs to recognize the handful of things it does extremely well and find opportunities to leverage that. When businesses stray from their core competencies they tend to struggle mightily, throwing away resources and providing diminishing returns with increased risk.
For example, McDonald’s has a set of core competencies that allow it to run extremely efficient fast-food operations in high-traffic areas. It’s natural, then, to acquire Chipotle and replicate the same processes with a different type of fast food...
How GMAT Scoring Algorithm Works?
The GMAT is a computer-adaptive test where your score is calculated by an algorithm that provides you with harder questions (and higher score returns) when you answer previous questions correctly, and with easier questions (and lower returns) when you’ve answered previous questions incorrectly.
Through this method, the GMAT can determine your ability level in a relatively short period – 37 math and 41 verbal questions – and provide you with an immediate score upon completion of the test. To save you the stress of trying to figure out the secrets of the algorithm, here are some important things you should know about GMAT scoring:
1) Good news: You can get a lot of questions wrong and still do well!
The job of the GMAT scoring algorithm is to determine your ability level by asking you questions that begin to close in on it. Think of how you’d play a game of 20 Questions as you attempt to zero in on the historical figure that your “opponent” has selected:
Was this person famous in the era BC? (No – too early)
Was this person famous before the Middle Ages? (No – still too early)
Was this person famous before the...
How to study for the GMAT in one month?
Ideally you should spend 3 months for your GMAT Prep(Read How to prepare for the GMAT in 3 months?). If you have one month, here is a focused way to plan your studies:
Week 1: Diagnosis and Practice
Take a practice test and carefully go over your wrong answers. Look for patterns. You want to see if there is one particular section or problem type that is hurting you more than all others. Do additional practice problems if the practice test yields inconclusive information. Read explanations for wrong answers and map out three to five consistent weaknesses. You will focus on these in the next week.
Week 2: Focused Study
Now is the time to deal with your weaknesses. Depending on how many you identified, you will want to spend 1 – 2 days focusing on each. If strengthening arguments questions are your Kryptonite, put a night or two of studying into that. If data sufficiency algebra is killing you, spend an afternoon reading strategies and explanations related to it. You should spend this week doing a combination of practice problems and content coursework about math and English. Take super-concise notes that you can review later.
The goal during this period is...
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