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GMAT


(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:

...


Solving GMAT Questions with two linear equations and two unknowns


Categories : Equations, Problem Solving

In order to solve such equations, you need at least 2 distinct equations involving these unknowns.

For example, if we are trying to solve for x and y, we won't be able to solve it using these 2 equations.

2x + y = 14
4x + y - 14 = 14 - y

Why?  Because the two equations on top are the same.  If you simplify the second equation, you get 4x + 2y = 28 which reduces to 2x + y = 14 - the same equation as the first.  If the two equations are the same, then there will be infinitely many values for x and y that will satisfy the equations.  For example, x = 2 and y = 10 satisfies the equation.  So does x = 4 and y = 8.  And so does x = 6 and y = 2.

In order to solve for an actual value of x and y, we need 2 distinct equations.

For example, if we had

2x + y = 14 --------(1)
x - y = 4 ----------(2)

Then from equation (2), we can get x = 4 + y and substitute that into equation (1) to get:
2(4 + y) + y = 14  We can then solve for y.  See if you got y = 2  Once you've got y = 2, you can substitute that into x= 4 + y to get x = 6.

An important lesson here is that you need as many distinct equations...


4 Summer Habits for GMAT Preparation


Categories : GMAT Preparation

As you read this article, the entire summer is ahead of you.  But if you are planning to apply to business school this fall, you should heed the warning that you learned in your earlier scholastic days – time flies when you’re having fun, and the fall, like those objects in your rearview mirror, is probably closer than it appears.

Rest assured that you can still enjoy most of your summer even if you don’t plan on taking the GMAT until later in the fall.  But even without dedicating much of the summer to studying, there are at least four habits you can add to your day-to-day lifestyle that will get you ready to hit the ground running when you do begin your GMAT preparation in earnest sometime soon:


1) Read

The GMAT verbal section is a test of focus and concentration, assessing your ability to process written information on a variety of topics and to do so while tired and distracted.  There are certainly techniques to help you navigate the GMAT-specific passage formats and question types, and you’ll learn those when you’re ready to buckle down on GMAT study.  But in the meantime, you can improve your ability to process that information simply by reading more, and by reading articles and books on topics that aren’t as natural of choices for you.  Traveling this summer?  Bring The Economist on...


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 800 with Video Explanation - A newborn kangaroo, or joey



A newborn kangaroo, or joey, is born after a short gestation period of only 39 days. At this stage, the joey’s hind limbs are not well developed, but its forelimbs are well developed, so that it can can climb from the cloaca into its mother’s pouch for further development. The recent discovery that ancient marsupial lions were also born with only their forelimbs developed supports the hypothesis that newborn marsupial lions must also have needed to climb into their mothers’ pouches.

The argument in this passage relies on which of the following assumptions?

[A] All animals that are born after a short gestation period are born with some parts of their bodies underdeveloped.
[B] Well developed forelimbs would have been more advantageous to ancient marsupial lions than well developed hind limbs would have been.
[C] If the newborn marsupial lion did not climb into its mother’s pouch, then paleontologists would be able to find evidence of this fact.
[D] Newborn marsupial lions that crawled into their mothers’ pouches could not have done so had they not had only their forelimbs developed at birth.
[E] Newborn marsupial lions would not have had only their forelimbs developed if this development were of no use to the marsupial lions.


...

GMAT Sentence Correction Flow Chart



GMAT Sentence correction


The above is no substitute for reading each sentence carefully, predicting what the correct answer might look like, and finding it in the answer choices of course.  A little more on each of the decision points:

•  Whole sentence underlined: There isn't much to say about this.  With no part of the sentence left static, there's more to keep in mind; the other decisions still help.

Answer start or end with a verb: Beware nouns close to the verb that may distract you from the real subject

Answer start or end with a pronoun: Read carefully for the pronoun's antecedent (the word it's replacing in the sentence)

Modifying phrase, set apart by comma(s): These phrases are easier to spot and work with when they start the sentence, since you need only look at the first thing after the first comma, but these modifying phrases can appear anywhere.

Separation of subject and verb: The further apart they are, the more words there will be to confuse you.  Try...


GMAT Statistics Fundamentals - Mean, Mode, Range, Median and Standard Deviation



GMAT StatisticsEven if you fear statistics by its reputation, it is one of the easiest sections in the GMAT because a standard set of questions is asked and anyone who understands the fundamentals that I shall describe will be able to ace the questions. The three most basic topics in stats are mean, mode, and median. Usually, the GMAT will go one step further into range and standard deviation.

Mean: Mean is the average. Let’s say there are two numbers: 6 and 8. The mean would be:
(6+8)/2 =14/2 =7. If you analyze the number 7, it makes sense that it is average of 6 and 8. Using the same approach, the mean of n numbers a1,a2,a3…….an would be (a1+a2+a3…..+an)/n. If you remember this formula, you should be able to do well with mean questions. We shall discuss some of the standard questions in subsequent blogs, but for right now, remember the key formula and start doing some mean and average questions from Grockit games.

Mode: Let’s say that you are given a set of numbers, such as {4,3,7,9,9,11,10}. In order to find the mode, you have to arrange the numbers in ascending...


GMAT Data Sufficiency Strategy - Don’t Contradict Yourself


Categories : Data Sufficiency

GMAT Don't Contradict YourselfTrue to their name, Data Sufficiency questions ask you to determine when you will have enough information to make a conclusive decision.  In doing so, these questions can assess your ability to plan ahead for a task; to elicit an effective return-on-investment (remember, you can’t use both statements if one of them is, alone, sufficient), to find flaws with conventional wisdom, and to think flexibly. Data Sufficiency questions also strike fear and loathing in the hearts of many GMAT examinees, but hold a special place in the hearts of a select few who love the nuance that these questions permit.  

There’s a hard-and-fast rule regarding Data Sufficiency that people don’t know and use as much as they should: the statements can never contradict each other.  Knowing this, if your answers for statement 1 and statement 2 are different, you must go back and reconsider your math; as Boston GMAT tutor David says, that’s an “answer choice F”, meaning that you just effed up the math somehow.

Consider the question:

Is x...


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 (...


(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...


GMAT Sentence Correction Strategies - Focus on Testable sections



Sentence Correction questions can include up to 54 words, making for incredibly long sentences and time consuming reading.  But similar to GMAT SC - Spot Decision Points, knowing what is likely to be a testable section of a sentence and what is not, you can break apart the sentence into the parts that matter to you as a test-taker.  Proper nouns, correctly-applied modifiers, adjectives and adverbs can all be streamlined to make for shorter sentences

For example, in the sentence:

Originally called BackRub, Google was founded by two Stanford PhD students, Larry Page, whose father, Dr. Carl Victor Page, was a computer science professor at Michigan State University, and Sergey Brin.

The proper nouns and excessive adjectives can be eliminated or condensed, bringing you down to:

Originally called BackRub, Google was founded by two students, Larry, whose father, Carl, was a...


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 GMAT Problem Solving Tips


Categories : GMAT Tips, Problem Solving

GMAT Problem Solving TipsThe 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...


Using Venn Diagrams to solve GMAT Set Questions


Categories : Venn Diagrams, Sets

On your GMAT, you will encounter 1-3 questions that contain overlapping groups with specific characteristics. You will almost never see more than two characteristics (since you can’t draw 3D on your scratch paper). For illustration, let’s take a look at the following Data Sufficiency example:

Q) Of the 70 children who visited a certain doctor last week, how many had neither a cold nor a cough?

(1) 40 of the 70 children had a cold but not a cough.
(2) 20 of the 70 children had both a cold and a cough.

There are two characteristics (cough and cold) and two categories for each (yes and no), so there are four total categories, as indicated by this matrix:
 
Four Total Categories
I’ve filled in the given information from both statements, and the parenthetical information is inferred. This clearly lays out the 4 combinations of options. If we sum vertically, we can infer that there are 60 total children with colds. Because there are 70 total children, this also means that 10 do NOT have colds. The bottom-right quadrant cannot be found because we do not know how those 10 children get divided between the two empty boxes. Choice E – together the statements are insufficient...


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...