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(GMAT 800)The function g(x) is defined for integers x such that if x



The function g(x) is defined for integers x such that if x is even, g(x) = x/2 and if x is odd, g(x) = x + 5.  Given that g(g(g(g(g(x))))) = 19, how many possible values for x would satisfy this equation?

A. 1
B. 5
C. 7
D. 8
E. 11

Explanation:

The easiest way to approach this problem is probably to work backwards, at least until we see a pattern.

With g(...) = 19, then we can consider which operation applied to (...).  If it was x/2, then (...)= 38.  38 is even so that is fair.   If it was x + 5, then (...) was 14.  14 is even, so that operation would not have been applied.

On paper, you could make a tree, with 19 as the root, and 38 as the first node.  

Next consider 38.  38 could have come from 76/2 or 33 + 5.  Two possibilities give us two nodes branching from 38:

19  -> 38 -> 76, 33.

We can now observe the pattern that with an odd number, it must have come from an even, but an even could come from either of two numbers.

Therefore our 76 will branch into 2 numbers, and the 33 into just one.

33 -> 66
76 -> 73, 152..

We can represent this as shown here:

...


How to Handle Passive and Active Voices in GMAT Sentence Corrections


Categories : Sentence Correction, Voice

GMAT Active Voice vs Passive VoiceThese two sentences have an important difference.  Can you spot it?

1) She spoke persuasively, arguing for major legislative changes.

2) Major legislative changes were argued for in her persuasive speech.

The first sentence is written in the active voice, and the second is written in the passive voice.

In the first sentence above, the subject is “she,” and the verb is “spoke.” In the second sentence, the subject is “major legislative changes” and the verb is “were argued for.”

Writing in the active voice means that the subject of the sentence is performing the action; writing in the passive voice means that the subject of the sentence is the object of an action. It’s tricky sometimes to distinguish between passive and active voices, but it’s worth practicing, because sometimes on GMAT Sentence Corrections, the difference between two grammatically sound answers is passive and active voice.  Many people in this situation end up guessing because they can’t think of any good reason to reject either of the choices. By learning how to use passive and active...


Top 10 Ways to Save Time in GMAT



1. Prepare: This one is on the obvious side, but too important to leave off the list. The most important things you can do to prepare for the GMAT is to understand all the concepts tested and to be familiar with all the question types. There is no magic formula–the best strategy is to spend a lot of time beforehand practicing and familiarizing yourself with the various concepts and question formats.

2. Be confident: If you know the right answer, stick with it. Often on, say, a Problem Solving question, you’ll need to figure out the right answer before you even get to the choices. Don’t waste time second guessing yourself when you see a different answer that looks appealing; you studied for this, you did the question properly. Select your answer and proceed to the next question.

3. Don’t spend time on calculation: This one is obvious but often overlooked. Data Sufficiency problems ask you to say when you have enough information to answer the question in the prompt, not to actually compute the answer. Sometimes you need to work all the way to a solution, but often, all you need to know is how to get the...


Exponents Lead to Cumbersome, Time-Consuming Calculations involving Large Numbers but it is Pattern-Driven


Categories : Exponents

GMAT ExponentsThe 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.

Exponents

• 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...


Top 5 Tips to Improve your GMAT Critical Reasoning Score


Categories : Critical Reasoning

Top GMAT Critical Reasoning Score ImprovementGMAT Critical Reasoning Questions comprises nearly 1/3rd of all the Questions in the GMAT Verbal Section. It is important that you learn to analyze and identify various parts of the arguments. Follow these 5 Tricks and you will improve your GMAT CR Score:

1. Understand GMAT Critical Reasoning Definitions

Know the definition for terms like assumption, inference, evidence, conclusion, logical flaw, paradox, etc., like the back of your hand. As you go through practice tests, write down any words in the argument, question stem, or answer choice that confuse you – and then look them up!  When you have the essential definitions down, you can jump into arguments much more quickly — and you won’t waste any time second-guessing what a question is asking you to find.

2. Identify parts of CR Passages

If you’re having a hard time sorting out the meaning of a passage, take a moment to identify its conclusion and the evidence (statements of fact) and assumptions (unstated ideas) it uses to make that conclusion (the conclusion will often be signaled by words like “as a...


5 Steps for GMAT Data Interpretation



Data Interpretations GMAT1. Read the labels first. Mentally categorize each graph, chart and table. (EX: “This is a graph showing the change in the price of gas per gallon over the course of one year.”) Do not just skip the statistics entirely and go straight to the question! While you may think this will save you time, it actually significantly decreases your accuracy.

Data Interpretation questions are like an open-book test. You wouldn’t skip a Reading Comp passage, so don’t skip the data. Make sure you read every tiny piece of writing on or near the data, including titles, the labels for the x and y-axes, column names, and even footnotes. Scroll down to make sure you’ve caught everything.

2. Note the units. Once you understand the labels, take special care to note the units (mph, m/sec, cm2, etc.). Are we dealing with seconds, minutes, or hours? Does one graph represent the month of June, while the other graph represents the entire year? The units may change from graph-to-graph or chart-to-table. Especially note any given information about percentages, as DI questions frequently require you to work with...


GMAT Grammar



You may feel confident with the most commonly tested grammar rules on the GMAT Sentence Corrections - subject-verb agreement, verb tense, pronoun reference, pronoun number, misplaced modifiers, parallelism, idioms, false comparisons, and quantities. It’s hard to imagine any other grammar rules that could possibly be tested, but you can bet the GMAT test writers are pretty exhaustive. Here are four grammar rules that don’t receive as much attention; you’ll need to master these if you’re going for a top score.

1. Subjunctive Mood

You won’t see the subjunctive mood tested on college entrance exams like the SAT and ACT; it’s purposely reserved for the GMAT for good reason. Most of the English verbs we use are in the indicative mood - that is, verbs that have happened, are happening, or will happen. The subjunctive mood is used to express wishes or possibilities that have not happened.
The most common subjunctive verb that you might encounter is were, the subjunctive form of was.

Example 1: If he were athletic, he could make the football team. (He is not actually athletic, so the verb communicates an idea that does not really exist).

Notice that “If he was athletic…” would be incorrect, even though you may not reconize such an error in speech or writing.

Example 2: The teacher requires...


How to identify modifying Phrases In GMAT Sentence Correction



Modifying PhraseA common trick used by GMAT test makers is to insert modifying phrase incorrectly. Here are some sentences that incorrectly use modifying phrases:

Sentence A: Ever since her paw was crushed in the front door, Mrs. Benson has been worried about Muffin, her pet cat.

Sentence A starts off with the modifying phrase “Ever since her paw was crushed in the front door,” and then talks about Mrs. Benson and her worry for her cat.  But Mrs. Benson sounds like a person, and as a person, she probably doesn’t have a paw to be crushed.  It’s MUCH more likely that Muffin’s paw got crushed, causing Mrs. Benson’s worry.  This sentence needs to be corrected to put the modifying phrase next to the item it modifies. 

Here are a couple of ways that we can do that, depending on where the sentence’s underlining is placed:

Sentence A1: Ever since her paw was crushed in the front door, Mrs. Benson has been worried about Muffin, her pet cat.

If the modifying phrase isn’t underlined, we don’t have the opportunity to fix it-- but we can rearrange the rest of the sentence so that the thing that is modified (...


Here is how you should Prepare for the GMAT While Working


Categories : GMAT Preparation

Studying for GMAT While WorkingIt would have been nice if you could take a break from your work and devote yourself fully into GMAT preparation. Unfortunately, lot of us don't have that luxury. If you have found balancing GMAT prep and your work schedule a near impossible task, don't worry! Our 6 Step plan will help you cross this hurdle:

1. Start with a realistic plan

First you should know where you stand. Start with a full-length GMAT practice CAT under test-like conditions to get a realistic assessment of your skills. The result of your diagnostic should be used to evaluate and better understand your strengths and weaknesses.

The diagnostic will also give you a better idea of how much time you’ll need to set aside for GMAT prep (this also depends on how many hours/week of study time you’ll be able to squeeze in around your work schedule). If you’re only looking to increase your score a few points, you may only need a month or so of prep work. If you’re looking for a bigger gain, don’t worry — it’s definitely possible, but it might take you a bit longer to get there.

2....


How to score well in GMAT Number properties?



Number Properties GMATGMAT Number properties may sound scary, but they just constitute elementary mathematical principles. You probably know most of these principles by memory; if not, you could easily execute a calculation to ascertain them. The best option, though, is to study these principles enough that they seem intuitive. The GMAT Quantitative section is all about saving time; making number theory second nature will definitely save you some valuable seconds.

1.Odds and Evens

Addition
Even + even = even (12+14=36)
Odd+ Odd = even (13+19=32)
Even + Odd =  odd (8 + 11 = 19)

To more easily remember these, just think that a sum is only odd if you add an even and an odd.
Multiplication

Even x even = even (6 x 4 = 24)
Odd x odd = odd  (5 x 3 = 15)
Even x odd = even (6 x 5= 30)

To more easily remember these, just think that a product is only odd if you multiply two odds.

Example Question

If r is even and t is odd, which of the following is odd?

A. rt
B. 5rt
C. 6...


How to handle nerves on GMAT test day?


Categories : GMAT Exam Day Tips

Handling Nerves on GMAT Test DayTest day is no different than any other GMAT prep days. You have to be focused, prepared and give your best shot. But we are not robots, we are humans. So it is natural to feel a little bit anxious. But if you feel: cold sweats, night terrors, the shakes, and so on, then you are showing signs of acute anxiety. Knowing what to expect in the testing center will help you relieve some of the unnecessary anxiety. Here is Knewton's minute by minute breakdown of what to expect in the test center.

1. Arrive early, but don’t plan on studying at the testing center. 30 minutes before liftoff

Show up to the test center 30 minutes before the official time, as the GMAC suggests. Although this may mean waking up even earlier than expected, avoiding any feeling of being rushed is priceless. However, many testing centers don’t allow studying in the waiting room, so don’t plan on getting there early and reviewing notes. Use the time before the test to relax and focus on the task at hand.

2. Locker Room. 10 minutes before liftoff

After presenting your identification and test reservation, you may be given...


Read about Properties of Zero Before attempting GMAT Questions


Categories : Number Properties

Zero Properties GMATThe number 0 on the GMAT is tricky as its properties are the trap in to which a seemingly logical solution can lead you or are often either the key to unlocking a difficult solution. Learning the properties of zero (keep in mind that it is an even number) is a crucial skill, particularly on data sufficiency problems. Even more importantly, never forget to consider zero as a potential value for a variable, as it often produces surprising results. Consider the case of zero as an exponent:

x^0 is, by definition, equal to 1. Noting the properties of exponents can help you to prove and more easily remember this useful device: take, for example, the expression x^2 * x^-2. You could rearrange this two ways:

a) (x^2) / (x^2) --> The negative exponent moves that term to the denominator

b) x^(2-2), or x^0 --> When multiplying terms with the same base, taken to different exponents, you add the exponents

Because we can prove that (x^2) / (x^2) must be equal to 1, and that the two expressions above are...


How to prepare for the GMAT in 3 months?


Categories : GMAT Study Plan

GMAT Prep Plan 3 monthsKnewton: At Knewton, we generally recommend a prep period of around three months for GMAT Preparation. It’s enough time to build a solid foundation in critical areas of GMAT study, but not so long that you burn out by the rigorous focus and training.

Here is the 3 Month GMAT Prep Plan:

Week 1: Take a diagnostic practice test to see where you stand overall.  Learn the basic parameters of each section including scoring and question types.

Weeks 2 – 4: Do as many practice problems as possible for each section and read explanations for any wrong answers. The goal is not just to see whether you are better at Verbal or Quant, but specifically which sections (Critical Reasoning, Sentence Correction) and which question types (strengthening arguments, usage of idioms) are the most difficult for you.

Weeks 4 – 8: Now that you have a lot of practice questions under your belt, you want to focus on the...


(GMAT 800) Data Sufficiency Quadratic Equations with Explanation



Grockit Questions

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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D.    EACH statement ALONE is sufficient.
E.    Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.



Explanation:
This question asks whether the information in one or both statements is sufficient to find a specific value. But we don't actually have to determine the value, just know that it can be determined.

(1) Quadratic equations have two solutions. However, sometimes those two solutions are identical with each other. If they are different, then solving this equation will lead to two possible values of x, and presumably also two possible values of f(x), so this would not be sufficient. But if they are the same, i.e. if there's really only one solution to this equation, then we would definitely know x, definitely know f(x), and...


How to correctly use Pronouns and Antecedents in GMAT Sentence Corrections



Pronoun GMATErrors in pronouns—words like he, she, it, they, our, etc.—and antecedents—the words that the pronouns refer to—are among the most common errors in English Grammar.  Take this sentence as an example:

Sentence A:  I spoke to someone at the help desk, and asked what kinds of product returns the company allows; they told me that they only take unopened items.

This sentence wouldn’t set off any “grammar alarms” for the average reader and speaker of English; however, you, intrepid GMAT test-taker, need to be wiser than average and spot a couple of pronoun/antecedent errors, such as:

1.  “They” and “their” are plural pronouns, and CAN’T be used as gender-neutral singular pronouns

One of the most frequently-committed grammar sins in every day speech is the use of “they” and “their” to indicate gender neutrality.  Sentence A, above, says “I spoke to someone.”  The sentence later says, “they told me,” and based on context it is clear that the “they” in question is the “someone at the help desk.”  “Someone” is...

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