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1 An art gallery owner is hanging paintings for a new show Of the six paintings she has to choose
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from, she can only hang three on the main wall of the gallery Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings A 18 B 30 C 64 D 120 E 216
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2 A composer s guild is planning its spring concert, and ten pieces have been submitted
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for consideration The director of the guild knows that they will only have time to present four of them If the pieces can be played in any order, how many combinations of pieces are possible A 40 B 210
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C 1090 D 5040 E 10000
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3 If x and y are odd integers, which of the following must always be a non-integer
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A xy B x y
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C x D xy 2
E xy
4 Dan has a membership at a local gym that also gives classes three nights a week On any given
class night, Dan has the option of taking yoga, weight training, or kickboxing classes If Dan decides to go to either one or two classes per week, how many different combinations of classes are available A 3 B 6 C 7 D 9 E 12
5 Terry is having lunch at a salad bar There are two types of lettuce to choose from, as well as
three types of tomatoes, and four types of olives He must also choose whether or not to have one of the two types of soup on the side If Terry has decided to have the salad and soup combo and he picks one type of lettuce, one type of tomato, and one type of olive for his salad, how many total options does he have for his lunch combo A 9 B 11 C 24 D 48 E 54
6 If r is negative and s is positive, which of the following cannot be negative
A B
r s s r
110#
THE QUANTITATIVE SECTION
C r2+s D r2s2 E r s
Solutions
1 D
This problem asks for us to arrange the paintings, so it is a permutation Using the
n! 6 5 4 3 2 1 (n k )! formula and using 6 as our n and 3 as our k, we get the following: 3 2 1
P = n k
When we cancel out, we get 6 5 4, which is 120
2 B
This problem is a combination, so we would use the formula
Ck =
n! k !(n k )! Since 10 is
our n and 4 is our k, the equation works out to multiplying gives us 210 combinations
3 D
10 9 8 7 6 5 4 3 2 1 Simplifying and 4 3 2 1 6 5 4 3 2 1
xy Since we know that x and y are odd, xy ust always be odd Therefore, 2 will always be a non-integer None of the other answer choices has this relationship; in all of the other cases, it is possible to have values of x and y that would yield integer results
4 D
This problem is best done by brute force First, we must establish that Dan has the option
of taking one or two classes per week If he only takes one class, the three possibilities are Y, W, and K If he takes two classes per week, the six possibilities are YY, KK, WW, YK, YW, and WK (because the problem is looking for combinations, not arrangements) So that adds up to nine possible combinations
5 D
This is a relatively simple problem if you know the process and you read carefully All you
have to do is multiply the number of options: 2 types of lettuce, 3 types of tomatoes, 4 types of olives, and 2 soup options (You did remember the soup, didn t you ) 2 3 4 2 = 48, so 48 is our answer
6 B
Based on the rules of positive and negative numbers, the only answer choice that must be
negative is B, since it takes a positive and divides it by a negative All other manipulations end up positive
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PART TWO
The Verbal and Writing Sections
Copyright 2007 by The McGraw-Hill Companies, Inc Click here for terms of use
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Critical Reasoning
INTRODUCTION
Many people find the GMAT Critical Reasoning section to be one of the more difficult parts of the test, mostly because the questions look different from any type of problem they have seen before In casual reading you might come across something that looks like a Reading Comprehension passage, and you might notice grammatical errors like those in Sentence Correction questions, but you are not likely to encounter something that looks like a Critical Reasoning question Don t worry, though Critical Reasoning questions test the same thought processes you use every day Critical Reasoning questions test your skills in evaluating the strengths and weaknesses of arguments This is something you do all the time, without necessarily realizing it When you re buying a car, do you accept the salesperson s claim that this is the car for you, or do you examine the argument for potential weaknesses If a coworker approaches you with an idea about a new business direction, do you just stand there nodding, or do you consider the potential benefits and pitfalls of the idea Obviously, in both cases you take the critical approach You evaluate arguments every day of your life Now, you must apply those same critical reasoning skills to the very specific format tested by the GMAT Approximately 12 of the 41 verbal questions you will see on the GMAT will be Critical Reasoning questions Answering this type of question generally takes longer than the other types of verbal question, so ACT gives you a slightly smaller number of these questions When you receive your first Critical Reasoning question, the instructions will look like this: For this question, select the best of the answer choices given To review these directions for subsequent questions of this type, click on HELP These directions, obviously, don t tell you very much about what to expect Here s what you can expect: You will see a brief reading passage, usually around 50 words long, that will present some form of argument (ACT refers to these passages as a stimulus ) Immediately after the passage will be a short question (the question stem ) that asks you to examine some aspect of the reasoning in the passage As with all other GMAT question types, these questions give you five answer choices, of which only one is correct Critical Reasoning questions require you to quickly change gears between different topics and different kinds of convoluted logic ACT will try to trip you up in logical traps and
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