# The New Official Guide Companion

by , May 10, 2010 We have some exciting news this week: the launch of a new book and online resource called the Official Guide Companion by ManhattanGMAT (copyright 2010). Were calling it the OGC for short.

We all know (and love!) the great questions given to us in the Official Guide books. Less well-beloved are the explanations given for the problems. Weve gone through The Official Guide 12th Edition and written our own explanations for every single quant problem. The OGC also includes Horacios Hot List (Horacio is one of our ace instructors!); Horacio compiled a list of the OG12 questions that our students ask about most frequently in office hours, and weve added extra pointers for these Hot Button questions.

The material comes in two forms: a physical book and an online database in which you can look up the explanations.

As part of the OGC launch, you can sign up for a free trial period starting today, May 10th. You can use the online OGC for free for this entire week! The free trial period ends May 17th. (After that, the book and online database will be available for purchase.)

To give you an idea of what to expect, excerpts from the new OGC are below. (Note: for copyright reasons, the full text of the OG problems is NOT included in the OGC or in this article; you can use your own copy of OG12 to read the full text of the problems.)

Okay, without further ado, heres excerpt #1, an explanation for OG12 Diagnostic Test problem #15.

## Excerpt #1

From Official Guide Companion, copyright 2010 ManhattanGMAT; duplication or further distribution requires permission

D 15. Number Properties: Divisibility & Primes

Difficulty: 700800*

OG Page: 22

*Note: we have estimated the difficulty levels for all of the problems.

The problem first requires us to identify all of the Prime Numbers less than 20. They are 2, 3, 5, 7, 11, 13, 17, and 19.

The problem next asks us to find the answer choice closest to the product of these prime numbers. As a result, we know that we can use Estimation on this problem. Our decision to estimate is further reinforced by the fact that the answer choices are very far apart. (If you have difficulty visualizing this, try writing out the numbers with all of the zeroes. For instance, [pmath]10^5[/pmath]= 100,000 and [pmath]10^6[/pmath] = 1,000,000.)

Since the answer choices are in Powers of Ten, the key is to group the numbers so that the products are close to powers, or multiples, of ten.

Given 2, 3, 5, 7, 11, 13, 17, and 19:

2 5 = 10

3 7 = 21 20

11 19 10 20 200

13 17 10 20 200

Notice that we have rounded in both directions to get more accurate estimates. For instance, we have rounded 11 down and 19 up. The true product of 11 and 19 is 209, which is very close to (10)(20) = 200. There is less than a 5% difference.

Multiply the rounded numbers together:

10 20 200 200 = 8 [pmath]10^6[/pmath]

Round this result once again:

8 [pmath]10^6[/pmath] 10 [pmath]10^6[/pmath] 1 [pmath]10^7[/pmath]

Notice that we have to round 8 up to 10. The 8 came from the three 2s, which we should not have simply dropped or rounded down to 1.

Depending upon how we chose to group the numbers, we may have arrived at this answer differently. However, grouping and rounding is a far more efficient approach than multiplying all of the individual numbers.

<end of excerpt>

The previous problem is on Horacios Hot List. Heres what Horacio has to say about it:

From Official Guide Companion, copyright 2010 ManhattanGMAT; duplication or further distribution requires permission

Focus on the phrase "closest to" and the large spread in the answer choices. You only need to estimate the product. Find ways to round off your computations. You'll save lots of time.

The OG says that you should go ahead and multiply all the numbers up and get 9,699,690. Thats downright insane. Do not do this.

## Excerpt #2

The second excerpt, below, is an explanation for OG12 Diagnostic Test problem #30.

From Official Guide Companion, copyright 2010 ManhattanGMAT; duplication or further distribution requires permission

EIVs: Inequalities

Difficulty: 600700

OG Page: 25

This Inequalities problem also involves Algebraic Translation from words to math.

Lets begin by Naming Variables for the two unknowns. Let h represent the number of hundred-dollar certificates sold, and let t represent the number of ten-dollar certificates sold. (Notice that there is a Hidden Constraint here: h and t must be integers, since we use them to count physical objects.) We can create two equations:

h + t = 20 (The store sold 20 certificates.)

100h + 10t = Total Value

Notice that for the second equation, we have multiplied the monetary value of each type of certificate by the number of such certificates sold. (Some people confuse this step by thinking of the variables as equal to 100 and 10. This is incorrect, since our variables represent the number of such certificates, not their monetary value.)

The question asks us for the value of t.

(1): SUFFICIENT. This statement seems insufficient at first glance. After all, it does not give us an exact amount for the Total Value but only a range: the Total Value is between 1,650 and 1,800. Thus:

1,650 100h + 10t 1,800

For this information to be sufficient, we must be left with only one solution for t. So lets Test Possible Values to see whether we can find two or more solutions. Given the lower boundary, we can start by testing h = 16 and t = 4. (We have to try values that sum to 20.) This set of test numbers yields (100)(16) + 10(4) = 1,640, which is too low.

Next, try h = 17 and t = 3. This yields (100)(17) + 10(3) = 1,730, which works. But is 1,730 the only value that works?

Lets also try h = 18 and t = 2. This yields (100)(18) + 10(2) = 1,820, which is too high.

Thus, 1,730 is the only possible Total Value between 1,650 and 1,800. As a result, we can say with certainty that t = 3 and that this information is sufficient. Notice that the integer constraint on h and t is crucial. Otherwise, there would be more than one possible Total Value in the given range.

(2): INSUFFICIENT. This statement tells us that h > 15.

This leaves multiple possible values for h (16, 17, 18, 19, or 20), and thus multiple corresponding values for t (4, 3, 2, 1, or 0).

The correct answer is (A): Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

<end of excerpt>

### Blast from the Past: How to get the free e-book The GMAT Uncovered

FYI if you havent already gotten a copy of our free e-book, The GMAT Uncovered, follow this link to the original article discussing how to get it and how to use it.

If you have any feedback about our new Official Guide Companion (or any of our other materials), please dont hesitate to let us know!