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:
...
(GMAT 800)The function g(x) is defined for integers x such that if x
(GMAT 800) Natural selection, the central doctrine of Darwinism
Natural selection, the central doctrine of
Darwinism, has been explained as the "survival of the
fittest." On this process has depended the progress
observable throughout organic nature to which the term
(5) evolution is applied; although there has been from time
to time degradation, this has had relation only to
particular forms, organic life as a whole evidencing
progress towards perfection. When man appeared as the
culmination of evolution under terrestrial conditions,
(10) natural selection would seem almost to have finished its
work, which was taken up, however, by man himself, who
...
Grockit GMAT Sentence correction general strategies
GMAT Sentence correction(SC) comprises 15 of the total 41 verbal questions, which means that the majority of verbal questions are from GMAT SC. With SC questions, you will be presented with a question followed by five answer choices. The question will be underlined in part. You have to select the best answer choice that rephrases the underlined part of the question. Remember - the first answer choice will repeat the original text so don't bother to read it again.
Here is a step by step action plan to solve GMAT SC Questions
1. Read the whole sentence slowly and carefully. We all have different reading speeds, but as a good rule of thumb, you’ll want to read the sentence significantly slower than you would read a novel. For you fast readers who don’t subvocalize as you read, you might want to try subvocalizing SC sentences; sometimes it’s best to hear the mistake rather than see it.
2. If you notice what looks like an error in the underlined portion, try to identify the type of error before you move on to the answer choices. Why? The test writers are clever, and many of the incorrect choices appear correct.
Remember, there are basically three ways an answer can be wrong:
i. ...
GMAT Word Problems - Basics
Word problems on the GMAT get an unfair reputation for being especially challenging. However, it’s helpful to think of them as just dressed-up algebra. The real challenge is that they are (1) long, (2) boring, and (3) require translation from ‘English’ to ‘Math.’ Here are a few questions to ask yourself to make sure you fully break down and understand the problem BEFORE you start to solve!
What is the problem really asking?
Make sure to understand what the answer choices represent. Are they the total number of dollars of profit? The profit accumulated by Jenny only? The percent increase in profit from June to July? Taking the time to do this will also ensure you never leave a problem half finished. If you dive into setting up an equation too quickly, you may realize half-way through that you’re solving for the wrong variable. Sometimes word problems will add an extra step at the end. You may be busy solving for “x” and forget that the problem is asking for the value of “1/x”.
What information am I given?
The best...
GMAT Simple Interest and Compound Interest
Simple interest and compound interest - essential topics for an MBA. GMAC thinks the same too. So you will find these questions randomly distributed in your GMAT Exam.
Simple interest is the most basic and is a function of P, the principle amount of money invested, the interest rate earned on the principle, i, and the amount of time the money is invested, t (this is usually stated in periods, such as years or months).
The resulting equation is:
Interest = iPt
In basic terms, the above equation tells us the amount of interest that would be earned on a principle amount invested (P), for a given time (t) at a given interest rate (i).
Example
If you invested $1,000 (P = your principle) for one year (t = one year) at 6% simple interest (i = given interest rate), you would get $60 in interest at the end of the year and would have a total of $1,060.
For compound interest, you would earn slightly more. Let’s look at similar type problem, though this one involves compound interest.
...
Set A consists of integers -9, 8, 3, 10, and J; Set B consists of integers -2, 5, 0, 7, -6,
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
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...
GMAT Critical Reasoning – How to solve the weakness question type?
Start solving the GMAT Critical Reasoning weaken question by reading the question first. Why? This would help you determine the task before you go into the argument.
For example:
Healica, a new drug that can cure a common disease that until now has been fatal for 50% of those infected, is made from the root of the New Zealand banananut tree. The banananut tree is rare in New Zealand, and large quantities of the root are necessary in order to make Healica. Therefore, if Healica remains in production, the banananut tree will eventually become extinct.
If true, which of the following most calls into question the conclusion above?
a) The company that holds the patent to Healica has exclusive rights to produce the drug for another 10 years.
b) Healica is expensive, and is not currently covered by most major insurance plans.
c) Banananut leaves are considered a gourmet delicacy in many parts of the world.
d) The banananut tree, although native to New Zealand, can easily be grown in other parts of the world.
e) Producing Healica is time-consuming and expensive for the drug manufacturer.
...
Understanding "Of" for GMAT Quant and Verbal Sections
One of the smallest and least noteworthy words in the English language, the word “of” is crucial to your success on the GMAT, on both the quantitative and verbal sides of the exam. It is of great importance that you recognize these two common appearances of, and traps set by, the word “of“:
1) Sentence Correction
In Sentence Correction questions, the word “of” is usually employed as a modifier, which the GMAT often throws in to lengthen sentences and distract you from subject-verb agreement errors. Consider the following items:
The number of applicants to business schools are increasing given the current economic climate.
The House of Representatives are meeting this week to continue working on an environmental bill.
In each instance, the subject is actually the singular noun before the word “of” – “of applicants to business schools” just tells us “which number?”, and “of Representatives” simply indicates “which House?”. The authors of the GMAT know that examinees are often unsure of which noun to choose as the subject; by using the word “of” to set up modifiers with multiple nouns, the writers can exacerbate this problem. If you...
Area , Perimeter and Circumference
A sizeable number of GMAT math test questions belong to the Geometry section. Some of these questions test a candidate’s ability to understand 2-Dimensional Geometry by asking the candidate to calculate the area, perimeter or circumference of a geometrical shape.
The following geometrical shapes are most common – Triangles, Quadrilaterals, Rectangles, Rhombuses, Squares, Circles and Trapeziums.
Triangles – A triangle represents an enclosed shape made by joining three straight lines. The area of a triangle can be calculated as follows:
Area = ½*Base Side*Height of the triangle
In this formula, the Base Side can be any side of the triangle. However, depending on the base side chosen, height of the triangle needs to be ascertained. Height of the triangle is the shortest perpendicular distance from the Base side to the height of the Apex of that triangle. Note that the height of a triangle may need to be calculated outside the triangle, depending on the base side chosen. 
...
Top 10 GMAT Problem Solving Tips
The Problem Solving (PS) section of the GMAT may not be as quirky as the Data Sufficiency section of the test – but that doesn’t mean you don’t need to study for it! PS questions require more “straight math” than Data Sufficiency questions; in other words, they’ll probably be more like the questions you’re used to seeing on high school and college math tests. The best way to study? Master the basic concepts from geometry, algebra, statistics, and arithmetic — then check out these 10 helpful tips!
1. Make sure your fundamentals are strong.
The GMAT doesn’t allow you to use a calculator—which means you need to be quick and accurate with basic calculations. Be able to multiply and divide decimals. Know common higher powers and roots. Have fractions down to a science: Knowing right away whether 3/8 is less than 5/12 will mean you have more time later to work on more complicated calculations.
2. Choose numbers wisely.
Even questions that don’t contain variables can still be tackled by choosing numbers wisely. For example, if a question asks you about “a multiple of 6,” it’s probably quicker...
GMAT Sentence Correction: Subject-Verb Agreement
Sentence corrections on the GMAT tests many of the same issues in subject-verb agreement as in pronoun-antecedent agreement: it’s important to distinguish singular nouns from plural ones, even when the test-makers have made it difficult to do so. For example, take a look at the first sentence of this article: there’s a mistake. The subject of that sentence is “[s]entence corrections,” which is plural, but the verb, “tests,” is singular. Because the singular “GMAT” is placed between them, the singular verb SOUNDS right, but is actually incorrect.
Let’s look at a couple more examples:
The team of football players are accompanied by their trainer and head coach.
This sentence demonstrates the same common trick, which is that a singular subject (team) is associated with a plural noun (players); a plural verb (are) is then placed next to that plural noun, and the unwary test-taker, relying on his or her sense of what “sounds right,” is lulled into thinking that the sentence is correct as written.
Incidentally, there’s a second, similar issue here: the pronoun-antecedent problem. While the test tricks you into thinking that “team of football...
4 Tricks that will Keep you focused on your GMAT Reading Comprehension
GMAT Reading Comprehension passages are complicated and boring texts that will test your concentration and stamina. It is easy to lose your focus after an energy draining AWA and Math section. Most GMAT test takers will start to zone out at this stage and will just stare at the screen, re-reading the same sentence again and again. This is a sure shot step to crash your GMAT 700+ dream.
Follow these four preparation and test day tricks and you will learn to keep your focus for a long duration of time
Start practicing GMAT-like texts
It’s obvious that a reading comp passage won’t be as thrilling as your favorite Dan Brown novel, but the GMAT actually makes RC passages boring on purpose. The test-makers go out of their way to make the text complex, and they like to use natural science and social science topics with which potential business-school students may not be familiar. To prepare yourself, start reading real-world texts that mimic GMAT passage structures. The Economist, Scientific American, and The Wall Street Journal are good places to start, and magazines like Time and Newsweek feature editorial articles that can help you learn...
GMAT Solid Geometry - Rectangular Solids and Cylinders
Rectangular Solid
Learn the concepts behind volume and surface area before you start solving GMAT Solid geometry problems. All solid geometry problems come down to this - length, breadth and height. For data sufficiency questions, look out for values of l, b and h. if any of them are missing then it would be easy to eliminate answer choices.
6 rectangular faces constitute a rectangular solid
The formulas you need to remember for a rectangular solid are
Volume = Length (l) x Width (w) x Height (h)
Surface Area = (2 x Length x Width) + (2 x Length x Height) + (2 x Width x Height)
"If length = width = height, that means that the rectangular solid is, in fact, a cube."
Terminologies
Vertex: Wow! quite a confusing word? Not really
Vertex = Corner
a) Vertex is the number of corners in a...
(GMAT 800) Conventional wisdom holds that financial markets
Conventional wisdom holds that financial markets are informationally efficient—that stocks are always priced and traded at the intrinsic value of their underlying assets. Thus, investors cannot expect to achieve returns consistently in excess of average returns, given information that is publicly available at the time, without taking on large economic risks akin to gambling risks. In other words, one can only obtain higher returns by purchasing riskier investments, and not through expert timing or speculative stock selection. There are three major interpretations of this efficient market hypothesis: Weak Efficient Market Hypothesis (EMH), which holds that current prices for assets, such as stocks, bonds, and property, reflect all past prices, Semi-strong EMH, which argues that prices change instantly to reflect all new public information (such as news of a take-over or a change in fiscal policy), and Strong EMH, which claims that prices adjust perpetually to reflect hidden, insider information not yet made public.
Weak EMH holds that technical analysis, the analysis of past stock performance, will not consistently produce excess returns because future price movements are only determined by...
Understanding "Of" for GMAT Quant and Verbal Sections
One of the smallest and least noteworthy words in the English language, the word “of” is crucial to your success on the GMAT, on both the quantitative and verbal sides of the exam. It is of great importance that you recognize these two common appearances of, and traps set by, the word “of“:
1) Sentence Correction
In Sentence Correction questions, the word “of” is usually employed as a modifier, which the GMAT often throws in to lengthen sentences and distract you from subject-verb agreement errors. Consider the following items:
The number of applicants to business schools are increasing given the current economic climate.
The House of Representatives are meeting this week to continue working on an environmental bill.
In each instance, the subject is actually the singular noun before the word “of” – “of applicants to business schools” just tells us “which number?”, and “of Representatives” simply indicates “which House?”. The authors of the GMAT know that examinees are often unsure of which noun to choose as the subject; by using the word “of” to set up modifiers with multiple nouns, the writers can exacerbate this problem. If you...
