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

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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?

**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...

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**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

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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!

...

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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...

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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.

...

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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)?

ANSWER BELOW

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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.

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Of 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...

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2. Think of Absolute Values as distances from zero

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...