(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


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 GMAT Scoring Algorithm Works?

Categories : GMAT Score

GMAT AlgorithmThe 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?

Categories : GMAT Study Plan

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...


Categories : Ratio and Proportion

A proportion is represented by two ratios which are equated to each other. In GMAT Quant questions, we would be presented with one variable and three values for proportions. Reduce the ratio in either side to the lowest possible value before cross-multiplying.

For example , a proportion can be presented as a/b = c/d or a:b = c:d

So as per our strategy reduce a/b to the smallest possible fraction

ex: 24/10 should be translated to 12/5

GMAT Proportion: A football field is 9600 square yards.  If 1200 pounds of fertilizer are spread evenly across the entire field, how many pounds of fertilizer were spread over an area of the field totaling 3600 square yards?

A. 450
B. 600
C. 750
D. 2400
E. 3200

The key word here is “spread evenly”. This implies that the relationship of fertilizer per square foot is uniform, and you can set equal the relationship of the wholes to the relationship of the parts.

A/F = 9600/1200 = 3600/x

Clearly, we can eliminate the zeros on the left side:

9600/1200 = 3600/x

96/12 = 3600/x

Then we can divide 96/12:

8 = 3600/x

Here, we can still reduce left-to-right, by canceling 4 in both:

2 = 900/x

Oh wait! There’s more! Both 2 and 900 are divisible by 2!

Three Types of GMAT Profit and Loss Problems

You will encounter the following three types of Profit/Loss problems in the GMAT:

Profit/loss as percentage of Cost Price

In this case you will be given the cost price and sales price, and will be asked to simply calculate the profit/loss incurred by the seller by entering into the given transaction. This will be done by dividing the difference between the Sales Price and the Cost Price by the Cost Price. To convert the decimal into a percentage, you will multiply it by 100.

Profit Percentage = ((Sales Price - Cost Price)/Cost Price) x 100

Selling price = Z x (Cost price)

Where Z is any positive number. When Z < 1 we have a loss. When Z = 1 we have neither profit nor loss. When Z > 1 we have a profit.

Profit or Loss % = (Z - 1) x 100.

Selling price = [(Y / 100) + 1]x (Cost price)

Where Y is the profit or loss percentage. When Y < 0 we have a loss. When Y = 0 we have neither profit nor loss. When Y > 0 we have a profit.

Profit/loss as percentage of Sales Price

Sometimes the problem will be worded differently and will require the test taker to calculate...

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.  

Area of Triangle

(GMAT 800) If n and a are positive integers, what is the units digit

If n and a are positive integers, what is the units digit of n^(4a+2) – n^(8a)?

(1) n = 3
(2) a is odd

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
B)    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
C)    BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient;
D)    EACH statement ALONE is sufficient to answer the question asked;
E)    Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

BONUS QUESTION: What actually is the units digit (assuming the answer is not E)?


One important thing to note about exponents is that, by definition, they indicate “repetitive multiplication” – the multiplication of the same number over and over again.  Accordingly, they lend themselves nicely to patterns, as when you perform the  same action over and over again you’ll tend to get similar results.  When you consider statement 1, that n = 3, look at how 3 multiplies to different exponents:...

Top 10 GMAT Verbal tips for Non-native speakers

Categories : GMAT Verbal

Top Verbal Tips for Non-Native GMAT Test TakerEven if English isn’t your first language, you can still achieve an excellent score on the GMAT Verbal section. Here are a few tips to get you started!

1. Build your grammar skills first. You can ignore most of the challenging vocabulary on sentence corrections as long as you identify what part of speech each word is, and how it functions within the sentence. To do this, you’ll need to spend some time with a solid English grammar review book. I recommend pairing a heavy-duty review book, like the Oxford Guide or those published by McGraw-Hill or...

GMAT Formal Logic Basics: And, or, neither, nor…

GMAT LogicWe’ve covered, in an earlier blog post, how to deal with the simplest formal logic statement: If X, then Y.  But what happens when our necessary or sufficient factors become more complicated?  Let’s look at a couple of examples, using the idea of a vegetable salad.  The simplest statement and its contrapositive might look like this:

If the salad has lettuce, then it has tomatoes.
If the salad has no tomatoes, then it has no lettuce.

Now let’s add more vegetables (and more complicated logic):

If the salad has lettuce or spinach, then it has tomatoes and peppers.

Here’s an important idea: when you are forming a contrapositive, you already know that the necessary and sufficient factors are switched around and negated.  But now you also have to remember that “and” becomes “or,” and vice versa.  So the statement above becomes:

If the salad has no tomatoes or no peppers, then it has no lettuce and no spinach.

I find it extremely helpful to individually negate each element of the statement; otherwise, it’s easy to get confused. ...

GMAT Data Sufficiency Strategy - The Obvious Answer Trap

Categories : Data Sufficiency

GMAT DS Obvious Answer TrapData Sufficiency questions are supposed to be hard; more so than any other question type they tend to represent a chess match between you and the author, as the author has two chances to get you to make a mistake.  She won’t likely waste either statement giving you an easy pass – the questions have to elicit something from you in terms of efficiency or ingenuity in order to answer them correctly, so if an answer choice seems obvious within 15-20 seconds and you can’t spot a trap, well, you just fell into the trap.  Consider the question:

What is the value of x?

1) 3x + 2y = 15

2)  y = (-3/2) (x – 5)

This should pretty obviously be C. 

Two equations, two variables, neither works alone but both work together, right? 

But that is too easy, and the GMAT won’t often give you the answer that quickly.  Much as though the author had moved a pawn...

How can I raise my Verbal score?

GMAT Verbal ScoreThere are many who might feel that, while quantitative questions are clear-cut and objective, verbal questions are shrouded in the ambiguity of language and that, as a result, achieving a high score on the verbal section is to some degree a matter of luck that is determined by the whims of the little evil verbal GMAT goblins.

This could not be farther from the truth.  The language and communication skills that the GMAT tests are as straight-forward as any algebra problem.  So let's look at how you can take control of your score on the verbal section.

Test Strategy

As you probably already know, the GMAT is an adaptive exam.  This means that whether you answer the question presented correctly determines the level of the next question.  For example, say you are given a critical-reasoning question at a 600 level.  If you answer the question correctly, the next question will be at approximately a 650 level.  (These figures are not precise, for the exact calculations are not disclosed.)  If you get the question wrong, however, the next question might be a 550-level question.  ...

5 Reasons why you should Take the GMAT During or Right After College

Categories : GMAT Preparation

In case you didn't knew, your GMAT Score is valid for five years. Not many MBA Aspirants think about this. But it is always better to take the GMAT just after or while you are still in a college.

1. Time

Sure, you’re busy now — but chances are you’ll be even busier once you’re out in the real world working 40-60+ hours a week. With that kind of schedule, it will be difficult to section off time to study for the GMAT. Also, beginning your prep now — when you know that you’ll still have ample time to retake the exam should it not go too smoothly — will allow you take the pressure off yourself on test day.

2. Study zone

It may take some practice to master complex Data Sufficiency problems and dense Reading Comprehension passages. Since you are already digesting complex information and working under pressure to complete academic tasks in college, it shouldn’t be too hard to add a little GMAT preparation to your daily studying regime. That way, it feels like just an extra class, rather than an unfamiliar burden.

3.Math and Verbal Skills

We hear this constantly: after several years away from day-to-day practice, it may be hard to work with formulas or remember your grammar fundamentals. Given that you had to take that last...

Using Possessive Pronouns in GMAT Sentence Correction

GMAT Possessive PronounPossessive pronouns aren’t one of the biggest issues tested on the GMAT, but they do appear sometimes, and understanding them can not only potentially boost your Verbal score but can also make you a better writer, which will help in your AWA and your business school application process.

Just like other pronouns, possessive pronouns must have a clear antecedent, and must agree with that antecedent in gender and in number. There are a few tricky rules that come into play with possessive pronouns that you don’t see elsewhere, however.

1.No apostrophes needed

Turning a singular noun into a possessive noun usually involves the use of an apostrophe.  For example, you might say “my neighbor’s car.”  “Neighbor” is the noun, and to make it clear that the car belongs to your neighbor, you add an apostrophe and an “s”.  If we replace “neighbor’s” with “his,” though, we don’t need an apostrophe to indicate possession.  People often become particularly confused by the possessive form of one specific pronoun: it. The rule is...

3 Crucial GMAT Sentence Correction Strategies

Categories : Sentence Correction

GMAT SC StrategiesOf all the question types on the GMAT, a global exam for which the pool of test takers includes more than half of its examinees from outside the United States, Sentence Correction may seem the most arbitrary to prospective examinees.  Math we get: nearly all MBA graduates will have to make decisions using numbers and nearly all MBA programs require coursework in areas like finance and accounting for which some baseline math skills are important.   But English grammar?  Why would schools like INSEAD and ESADE, located in countries where English is not an official language and attracting students from all corners of the globe, be concerned with English grammar subtleties?  Especially when, as about 1/3 of the verbal section, sentence correction counts for about 17% of someone’s GMAT score.  It’s probably nice to know that everyone can speak the same language, but 17% of someone’s entry value?  Isn’t that overkill?

That should be a clue to you that Sentence...

Never actually understood Absolute Values ? Here is your chance!

Categories : Absolute Value

GMAT Absolute ValuesAbsolute 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.