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

### Solving GMAT Questions with two linear equations and two unknowns

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

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.