Math Flashcards
(177 cards)
1
Q
1 - What is the most important question to ask before evaluating the statements?
A
1 - What would be sufficient to answer this question? The biggest mistake people make on Data Sufficiency question is doing more work than they have to. Taking the time to figure out what is needed before looking at the statements helps prevent that.
2
Q
2 - What does 12TEN stand for?
A
2 - 12TEN is a mnemonic to remember the order of answer choices in Data Sufficiency questions. It stands for: 1 alone is sufficient 2 alone is sufficient Together the statements are sufficient Either statement is sufficient Neither statement is sufficien
3
Q
3 - What is the Kaplan Method for Data Sufficiency questions?
A
3 - 1) Analyze the question stem. 2) Evaluate the statements using 12TEN.
4
Q
4 - What is the Kaplan Method for Problem Solving?
A
4 - 1) Analyze the question. 2) Identify the task. 3) Approach strategically 4) Confirm your answer
5
Q
5 - What are the major topics tested on the quantitative section?
A
5 - Algebra, Proportions, Number Properties, and Geometry
6
Q
6 - What is the approximate mix of questions on the quantitative section?
A
6 - 15 Data Sufficiency questions 22 Problem solving questions
7
Q
7 - True or False: An answer of “no” to a yes/no Data Sufficiency question means that statement is insufficient.
A
7 - False. A statement is insufficient when it leads to the answer being “sometimes yes/sometimes no.” As long as the statement leads to a single answer, it is sufficient.
8
Q
8 - When should you combine the statements in Data Sufficiency?
A
8 - Combine the statements only if both of them have been proven insufficient. Once that is the case, you have to determine whether the answer is (C ) or (E).
9
Q
9 - What is the best way to combines statements in Data Sufficiency?
A
9 - Treat them as if they are one long statement.
10
Q
10 - True or False: A statement in a value question is sufficient only if it leads to a singular value.
A
10 - True. If, for example, a statement leads to x = [-2,2] it is not sufficient. It must lead to a single value.
11
Q
11 - What are the two criteria that must be remembered when Picking Numbers?
A
11 - The numbers must be permissible and manageable. You get to pick the numbers you work with, to make them as easy to work with as possible, remembering any rules that the question has given you. Remember that this doesn’t mean the numbers need to be re
12
Q
12 - What are the clues that you can look for to help you pick numbers?
A
12 - If there are fractions in the answer choices, try to pick numbers that work with the denominators of the fractions. If there are percents in the question, 100 is usually the easiest number to work with. If you need to divide one variable by anoth
13
Q
13 - Can you pick numbers on Data Sufficiency questions?
A
13 - Yes, but only to prove insufficiency. Even if you pick multiple sets of numbers, you’re only making it more likely that an answer is sufficient, not proving it sufficient.
14
Q
14 - What answer choices are more likely to be correct when the question asks “Which of the following ….?”
A
14 - (D) or (E)
15
Q
15 - What is Backsolving?
A
15 - Backsolving is a form of Picking Numbers, only you pick the numbers given to you in the answer choices. Because one of those numbers must be correct, Backsolving can often get you the right answer quickly, and with little extra work.
16
Q
16 - When should you think about using Backsolving?
A
16 - Whenever there are numbers but no variables in the answer choices, especially with word problems.
17
Q
17 - Which answer choice do you want to test first when Backsolving?
A
17 - Test either (B) or (D) first. There’s usually some hint as to whether the answer is more likely to be high or low; if not, just pick whichever seems easier. If you pick (D) and that works, great. If it’s too low, then (E) must be the answer. If it’s
18
Q
18 - What are the two ways to solve a system of linear equations?
A
18 - Substitution - Isolate one variable in one equation, then substitute for all instances of that variable in the other equation. Combination - Add or subtract whole equations. Use this when it will allow you to eliminate a variable or get directly to
19
Q
19 - If a question asks you what CANNOT be true, what does that mean about the incorrect answers?
A
19 - It means they could be true. It’s important to note that it doesn’t mean the wrong answers MUST be true.
20
Q
20 - What are the four Core Competencies that the GMAT tests?
A
20 - 1) Critical Thinking 2) Pattern Recognition 3) Paraphrasing 4) Attention to the right detail
21
Q
21 - What are the two types of Data Sufficiency questions?
A
21 - Value - The question is asking for a specific value for a variable. Yes/No - The question is asking whether or not a statement is true. Value questions make up about two-thirds of the Data Sufficiency questions you’ll see.
22
Q
22 - when two objects are heading in opposite directions, how do you find their combined speed? How do you find it when they are heading in the same direction?
A
22 - When objects move in opposite directions, add their speeds. When objects move in the same direction, subtract their speeds.
23
Q
23 - [(32)(34)]5
A
23 - First, the two exponents of the same base (3) are multiplied, so add the exponents: 2 + 4 = 6, so you have 3(2+4) = 36. Then you raise an exponent to an exponent, so the values are multiplied, and the final value is 3(6 * 5) = 330.
24
Q
24 - For what values of x is x2 < x?
A
24 - x2 when 0 < x < 1. At 1 or 0, x2 - x, and squaring any positive number greater than 1 will result in an even larger value. All negative values of x will become positive when squared. Only Fractions between 0 and 1 get smaller when squared.
25
25 - Of addition, subtraction, multiplication, and division, with which two can radicals be combined or split? With which two can the radicals not be combined or split?
25 - Radicals can be combined or split when the operations are multiplication and division. They cannot be combined or split when the operations are addition and subtraction.
26
26 - √(a2)
26 - On the GMAT, the square root sign always designates the positive square root. So √(a2) = a is positive, and √(a2) = -a when a is negative.
27
27 - How many solutions do absolute value problems normally have?
27 - Absolute value problems normally have two solutions. However, there will only be one correct answer choice, so only one of these solutions will appear in the answer choices of a GMAT question.
28
28 - True or False: The value inside an absolute value sign must be positive.
28 - False. The final result of an absolute value must be positive, but any number or variables inside the absolute value sign can be positive or negative. Watch out for this common Test Day trap.
29
29 - In inequalities, what must you know in order to multiply or divide by variables?
29 - In inequalities, you cannot multiply or divide by the variables unless you know whether they are positive or negative. Dividing by a negative will change the sign of the inequality.
30
30 - True or False: One is a prime number.
30 - False. A Prime number is divisible only by "1 and itself" - in the case of the number "1 and itself" are the same number. Thus, the smallest prime is 2.
31
31 - When variables are in the powers of an equation with exponents, how can you equate the exponents?
31 - You can equate the exponents by setting the bases of the exponents equal to one another, then canceling the common base.
32
32 - What is the formula for overlapping sets?
32 - Total = Group 1 + Group 2 - Both + Neither
33
33 - What fraction is used in all probability questions?
33 - Every probability question can be solved by finding (Desired)/(Total).
34
34 - Many radicals can be simplified by factoring out what?
34 - Many radicals can be simplified by factoring out perfect squares.
35
35 - What is absolute value on a number line?
35 - Absolute value is the distance from zero on the number line.
36
36 - What is an integer?
36 - An integer is a positive whole number, a negative whole number, or zero.
37
37 - To find the factors of a number, what do you start with and count up?
37 - To find the factors of a number, start with 1 and count up, noting which factors go evenly into the number.
38
38 - True or False: All prime number are odd.
38 - False. There is one even prime number: 2.
39
39 - What is the smallest prime number?
39 - 2
40
40 - How can you Pick Numbers for a number with a remainder n when divided by k?
40 - To Pick Number for a number with a remainder n when divided by k, take a multiple of k and add n. Because every number is a multiple of itself, k + n is often the easiest number to pick.
41
41 - What is the sum of the differences of each term on a list from the average of that list?
41 - The sum of the differences of each term on a list from the average of that list is 0.
42
42 - True or False: It is sometimes possible to determine the average without knowing the exact number of terms.
42 - True. You can use the weighted average formula if you have averages for proportions or the population, even if you don't have an example of the population. Weighted average = (Avg. of A)(Percent that are A) + (Avg of B)(Percent that are B) ….. (Avg
43
43 - True or False: Many complex multiplication and division problems can be simplified by reducing the terms to primes.
43 - True. On the GMAT, test-takers are rarely expected to do complex arithmetic. Most scary-looking division and multiplication will end up reducing to a simpler form one the prime factors of the elements are identified and canceled out.
44
44 - What is the prime factorization of 210?
44 - 2 \* 105 2 \* 5 \* 21 2 \* 5 \* 3 \* 7
45
45 - What is the average speed formula?
45 - Average speed = Total distance / Total time
46
46 - True or False: An easy shortcut to average-speed problems is to simply take the average of the speeds.
46 - False. Averaging the speeds is, in fact, a common wrong-answer trap; test-takers who make this error are failing to account for the different times spent at each speed.
47
47 - What are the steps for isolating a variable?
47 - 1) Eliminate any fractions by multiplying both sides or eliminate radicals by squaring both sides. 2) Put all terms with the variable you're solving for on one side by adding or subtracting on both sides. 3) Combine like terms. 4) Factor out the d
48
48 - What does an represent in a sequence? an-1? an+1?
48 - an represents any term in a sequence. an-1 is the term before it, and an+1 is the term after.
49
49 - How can you rapidly eliminate answer choices on average speed questions?
49 - You can rapidly eliminate answer choices by recognizing which way the speeds are weighted. If a problem involves more time at a fast speed than at a slower speed, the average speed will be higher, and vice versa.
50
50 - What is the combined work formula for two workers?
50 - The combined work formula is T = (AB) / (A + B). T is the total time it will take to complete one task if the two workers work together, and A and B are the times it takes each worker to complete the task alone.
51
51 - What is the combined work formula for three of more workers?
51 - For three or more workers, the combined work formula is (1/T) = 1/A + 1/B + ….. + 1/n. T is the total time it will take all the workers working together to complete one task, and A, B, …. N are the times it will take the individual workers to complet
52
52 - What is the difference between simple and compound interest?
52 - In simple interest, money is paid only on the principal. In compound interest, interest is paid both on the principal and on any previously accrued interest.
53
53 - What is the compound interest formula?
53 - (Total of principal and interest) = Principal\*(1+rate)time, where time is the number of times the interest is compounded and rate is the interest rate per time period, expressed as a decimal.
54
54 - What are perpendicular lines?
54 - Perpendicular lines are linear that meet at a 90° angle. Their slopes are negative reciprocals of one another.
55
55 - What do the interior angles of a triangle sum up to? For every additional side, what must you add? For example, what will the angles total in a five-sided figure?
55 - The interior angles of a triangle sum to 180°. For every side beyond three, add another 180°. For example, a five-sided figure will have angles totaling 180° + 2 (180) = 540°.
56
56 - The are of a circle is 36p and the circumference of that circle is 12p. If you take a 30° slice from the center, what will be the area of that slice? What will be the length of the arc formed by that slice?
56 - You know 30° is 1/12 of 360°, so the are of a 30° slice (or, as the GMAT will call it, "sector") will be 1/12 of the area of the circle, or 3p and the length of the arc will be 1/12 of the circumference of the circle, or p.
57
57 - True or False: 1) You can determine the ratio from two quantities. 2) You need at least one quantity in a ratio to determine the other quantities.
57 - 1) True. Any two quantities form a ratio. 2) True. A ratio can have an number of numerical values. You need at least one value to determine the other values.
58
58 - What is the percent formula?
58 - Percent = (New Value/Old Value) x 100% Do not confuse this formula with the percent change formula.
59
59 - What is the formula for percent change?
59 - Percent change = ((New Value - Old Value)/ Old Value) \* 100% The percent change between the new value and the old value will always be exactly 100% less than the new value as a percentage of the old value. On the GMAT, beware of answers exactly 100%
60
60 - What is standard deviation, and how is it tested?
60 - Standard deviation is the spread of numbers around the average. You will almost never be required to calculate standard deviation on the GMAT. To calculate the standard deviation of a set of numbers: 1) Find the mean. 2) Find the differences between
61
61 - To combine mutually exclusive probabilities, do you add or subtract the probabilities? To combine independent probabilities, do you multiply or divide the probabilities?
61 - To combine mutually exclusive probabilities, add the probabilities. To combine independent probabilities, multiply the probabilities.
62
62 - What are consecutive numbers?
62 - Consecutive numbers are numbers of a certain type, following one another without interruption. Numbers may be consecutive in ascending or descending order. The GMAT prefers to test consecutive integers (e.g., -2, -1, 0, 1, 2, 3, ….) but you may encou
63
63 - What is a cube root?
63 - The cube root of x is the number that multiplied by itself 3 times (i.e. cubed) give you x. Both positive and negative numbers have one and only one cube root, denoted by the symbol cube(), and the cube root of a number is always the same sign as the
64
64 - What is division by zero?
64 - Division by zero is undefined. For GMAT purposes that translates as "it can't be done." Because fractions are essential division (that is, 1/4 means 1 divided by 4), any fraction with a zero in the denominator is also undefined. So when you are given
65
65 - What is an isosceles triangle and how can you recognize one?
65 - An isosceles triangle is any triangle in which two sides are equal and the two angles opposite those two sides are also equal. Either the angles or the side-lengths are enough to recognize an isosceles triangle; equal angles will always be opposite t
66
66 - True or False: In a list of consecutive integers, the mean equals the median.
66 - TRUE
67
67 - There are 220 ways to select a committee of 3 members from a board of 12 members. How many ways are there to select the committee if it is expanded to 9 members?
67 - 220 For unordered subgroups, the existence of 220 possible groups of 3 committee members that there are 220 possible groups of 9 who could sit out. In the question, you are simply swapping the roles of the three-member groups and the nine-member gr
68
68 - What is the least common multiple of 6 and 8?
68 - Start by finding the prime factors of 6 and 8: 6 = (2)(3) 8 = (2)(2)(2) You see 2 appears as a factor three times in the prime factorization of 8, while 3 appears as only a single factor of 6. So the least common multiple of 6 and 8 will be (2)(2)
69
69 - Rules for Odds and Evens: Odd + Odd = Even + Even = Odd + Even = Odd x Odd = Even x Even = Odd x Even =
69 - Odd + Odd = Even Even + Even = Even Odd + Even = Odd Odd x Odd = Odd Even x Even = Even Odd x Even = Even Note that multiplying any number by an integer always produces another even number.
70
70 - What are the factors of 36?
70 - Thirty six has nine factors: 1, 2, 3, 4, 6, 9, 12, 18, 36. You can group these factors in pairs: (1)(36) = (2)(18) = (3)(12) = (4)(9) = (6)(6)
71
71 - When n is divided by 7, the remainder is 5. What is the remainder when 2n is divided by 7?
71 - Find a number that leaves a remainder of 5 when divided by 7. A good choice would be 12, which is simply 5 more than 7, of 7/1 plus a remainder of 5. If n= 12 then 2n= 24, which, when divided by 7, leaves a remainder of 3.
72
72 - 30 =
72 - 30 = 1 Any nonzero number raised to the exponent 0 equals 1. The lone exception is 0 raised to the 0 power, which is undefined.
73
73 - Does raising a fraction between zero and one to a power produce a result that is smaller or larger than the original fraction?
73 - Raising a fraction between zero and one to a power produces a result that is smaller than the original. Example: (1/2)2 = (1/2)(1/2) = 1/4
74
74 - 5^(-3) =
74 - A number raised to the exponent -x is the reciprocal of that number raised to the exponent x. Example: 5(-3) = 1/(53) = 1/(5 \* 5 \* 5) = 1/125
75
75 - What do fractional exponents relate to?
75 - Fractional exponents relate to roots. Example: x(1/2) = √(x) x(1/3) = cube(x) x(2/3) = cube(x2)
76
76 - When 10 is raised to an exponent that is a positive integer, what does that exponent tell you the number would contain if it were written out?
76 - When 10 is raised to an exponent that is a positive integer, that exponent tells how many zeros the number would contain if it were written out. For example, if asked to write 106 in ordinary notation, the exponent 106 indicates that you will need
77
77 - 5.6 \* 106 =
77 - 5.6 \* 106 = 5,600,000, or 5.6 million
78
78 - What is the value of x? 1) x = √(16) 2) x2 = 16
78 - When applying the four basic arithmetic operations, radicals (roots written with the radical symbol) are treated in much the same way as variables. The first statement is sufficient, because there is only one possible value for √(16), positive 4. T
79
79 - (2√(3))(7√(5) = (10√(21))/5√(3) =
79 - To multiple/divide roots, deal with what's inside the √() and outside the √() separately. (2√(3))(7√(5) = (2 \* 7)(√(3 \* 5) = 14√(5) (10√(21))/5√(3) = (10/5)(√(21/3) = 2√(7)
80
80 - If the number inside the radical is a multiple of a perfect square, what will you accomplish by factoring out the perfect square?
80 - If the number inside the radical is a multiple of a perfect square, the expression can be simplified by factoring out the perfect square. For example, √(72) = (√(36)√(2) = 6√(2)
81
81 - Simplify: √(48) = √(180) =
81 - Look for perfect squares (4, 9, 16, 25, 36, ….) inside the √(). Factor them out and unsquare them. √(48) = √(16) \* √(3) = 4√(3) √(180) = √(36) \* √(5) = 6√(5)
82
82 - What are most fractions on the GMAT (meaning that the numerator and denominator have no common factor greater than1?)
82 - Most fractions on the GMAT are in lowest terms. That means that the numerator and denominator have no common factor great than 1. The fastest way to reduce a fraction that has very large numbers in both the numerator and denominator is to find the
83
83 - √(2) + 3√(2) = √(2) - 3√(2) =
83 - √(2) + 3√(2) = 4√(2) √(2) - 3√(2) = -2√(2) You can add or subtract roots only when the parts inside the √() are identical; √(2) + √(3) cannot be combined.
84
84 - To multiply or divide one radical by another, in what order do you multiply or divide the numbers inside and outside the radical signs?
84 - To multiply or divide one radical by another, multiply or divide the number outside the radical signs, then the numbers inside the radical signs. For example, multiply this equation: (6√(3))(2√(5) = (6)(2)(√(3))(√(5)= 12√(15) Divide this equation:
85
85 - (10/9)(3/4)(8/15) =
85 - First, cancel a 5 out of the 10 and the 15, a 3 out of the 3 and the 9, and a 4 our of the 8 and the 4. Then multiply numerators together and dominators together: (2/3)(1/1)(2/3) = 4/9
86
86 - How many ways are there to arrange the letters in the word COAT? What about BOOK?
86 - There are n! ways to arrange n objects. Thus there are 4! = 24 ways to arrange the letters COAT. When elements repeat, divide by the factorial of the number of each repeated element. B and K appear once each in BOOK, but O appears twice, so: (4!)/(1
87
87 - Fifteen is 3/5 percent of what number?
87 - Find the whole: 15 = (3/5)(1/100) \* whole 15 = (3/500) \* whole Whole = 15(500/3) = 5(500) = 2,500
88
88 - What are the formulas for percent increase and percent decrease?
88 - % increase = ((increase)(100%))/(original) % decrease = ((decrease)(100%)/(original)
89
89 - What is compound interest?
89 - In compound interest, the money earned as interest is reinvested. The principal grows after every interest payment received.
90
90 - The ratio of boys to girls is 3 to 4. It there are 135 boys, how many girls are there?
90 - When using a ratio to determine an actual number, set up a proportion: 3/4 = 135/x 3 \* x = 4 \* 135 x = 180
91
91 - The ratio of domestic sales revenues to foreign sales revenues of a certain produce is 3:5. What fraction of total sales revenues comes from domestic sales?
91 - You have to convert from a part: part ratio to a part: whole ratio (the ratio of domestic sales revenues to total sales revenues), and you're not given actual dollar figures for domestic or foreign sales. But because all sales are either foreign or d
92
92 - The ratio of x to y is 5:4. The ratio of y to x is 1:2. What is the ratio of x to z?
92 - You want the y's in the two ratio's to equal each other, because then you can combine the x:y ratio and the y:z ratio to form x:y:z ratio that you need to answer this question. To make the y's equal, you can multiply the second ratio by 4. When you d
93
93 - The average annual rainfall in Boynton for 1976-1979 was 26 inches per year. Boynton received 24 inches of rain in 1976, 30 inches in 1977 and 19 inches in 1978. How many inches of rainfall did Boynton receive in 1979?
93 - If you're given the average, the total number of terms, and all but one of the actual numbers, you can find the missing number. You know that total rainfall equals 24 + 30 + 19 + (number of inches of rain in 1979) You know the average rainfall wa
94
94 - The average of 63, 64, 65, and x is 80. What is the value of x?
94 - When finding a average, the combined distance of the numbers above the average from the mean must be balanced with the combined distance of the numbers below the average from the mean. Think of each value in terms of its position relative to the av
95
95 - If 4x - 7 = 2x + 5, what is the value of x?
95 - 4x - 7 = 2x + 5 4x = 2x + 12 2x = 12 x = 6
96
96 - Let x\* be defined by the equation: x\* = (x2)/(1-x2) Evaluate (1/2)\*
96 - Symbolism problems usually require nothing more than substitution. Read the question stem carefully from a definition of the symbols and for any examples of how to use them. Then, just follow the give model, substituting the numbers that are in the
97
97 - Factor the expression 9x2 -1.
97 - A common factorable expression on the FMAT is the difference of two squares. Once you recognize a polynomial as the difference of two squares, you'll be able to factor it automatically, because any polynomial of the form a2 - b2 can be factored into
98
98 - The ratio of a to b is 7:3. The ratio of b to c is 2:5. What is the ratio of a to c?
98 - To solve combined ratios, multiply one or both ratios by whatever you need to in order to get the terms they have in common to match. Multiply each member of a:b by 2 and multiply each member of b:c by 3 and you get a:b = 14:6 and b:c = 6:15. Now t
99
99 - What is an algebraic expression?
99 - An algebraic expression is an expression containing one or more variables, one or more constants, and possibly one or more operation symbols. In the case of the expression, x there is an implied coefficient of 1. An expression does not contain an equ
100
100 - Factor the expression 2a + 6ac.
100 - Factoring a polynomial means expressing it as a product of two or more simpler expressions. Common factors can be factored out by suing the distributive law. The greatest common factor of 2a + 6ac is 2a. Using the distributive law, you can factor
101
101 - Simplify (3x2 + 5x)(x - 1).
101 - To simplify this equation, multiply using FOIL: First terms: (3x2)(x) = 3x3 Outer terms: (3x2)(-1)= -3x2 Inner terms: (5x)(x) = 5x2 Last terms: (5x)(-1) = -5x Now combine like terms: 3x3 - 3x2 + 5x2 - 5x = 3
102
102 - Factor the polynomial x2 + 6x + 9.
102 - x2 and 9 are both perfect squares, and 6x is twice the product of x and 3, so this polynomial is of the form a2 + 2ab + b2 with a = x and b = 3. Since there is a plus sign in front of the 6x, x2 + 6x + 9 = (x + 3)2. Any polynomial of this form is t
103
103 - Rewrite 7 - 3x \> 2 in its simplest form.
103 - Treat this inequality much like an equation - adding, subtracting, multiplying, and dividing both sides by the same thing. Just remember to reverse the inequality sign if you multiply or divide by a negative quantity. 7 - 3x \> 2 -3x \> -5 x \< 5/3
104
104 - What is the value of a number in a sequence related to?
104 - The value of a number in a sequence is related to its position in the list. Sequences are often represented on the GMAT as follows: S1, S2, S2,….Sn,…. The subscript part of each number gives you the position of each element in the series. S1 is the
105
105 - 8!/(6! \* 2!)
105 - 8!/(6! \* 2!) = (8 \* 7 \* 6!)/(6! \* 2 \* 1) = 28 Also note: 6! = 6 \* 5! = 6 \* 5 \* 4!, etc. Most GMAT factorial problems test your ability to factor and/or cancel.
106
106 - How many three-digit numbers can be formed with the digits 1, 3, and 5 using each only once?
106 - In number of possibility questions, you won't need to apply the combination and permutation formulas on the GMAT. The number of possibilities is generally so small that the best approach is just to write them out systematically and count them. Wri
107
107 - What is the probability formula?
107 - The probability formula is expressed as a ratio of the number of desired outcomes to the total number of possible outcomes. Probability is usually expressed as a fraction (for example "the probability of event A occurring is 1/3), but it can also be
108
108 - Name three classic quadratics.
108 - a2 + 2ab + b2 = (a + b)2 a2 - 2ab + b2 = (a - b)2 a2 - b2 = (a - b)(a + b)
109
109 - If x - 15 = 2y and 6y + 2x = -10, what is the value of y?
109 - One method of solving simultaneous equations is through substitution. The first step is to solve one equation for one variable in terms of the second. The second step is to substitute the result back in to the other equation and solve. Solve the
110
110 - Solve for x: (x2 + 6 = 5x)
110 - Manipulate the equation (if necessary) into the "\_\_\_\_\_\_" = 0 form, factor the left side, and break the quadratic into two simple equations. x2 + 6 = 5x x2 - 5x + 6 = 0 (x - 2)(x - 3) = 0 (x - 2) = 0 or (x - 3) = 0 x = 2 or 3
111
111 - What is a polygon?
111 - A polygon is a closed figure whose sides are straight line segments. Families or classes of polygons are named according to the number of sides: Triangle, quadrilateral, pentagon, hexagon (6 sides). Triangles and quadrilaterals are by far the mo
112
112 - What is the perimeter or a polygon?
112 - The perimeter is the distance around a polygon or the sum of the lengths of its sides.
113
113 - What is a combination question?
113 - A combination question asks you how many unordered subgroups can be formed from a larger group.
114
114 - What is the combination formula?
114 - Some combination questions use numbers that make quick, noncomputational solving difficult. In these cases, use the combination formula (n!)/(k!(n-k)!), where n is the number of items in the group as a whole, and k is the number of items in each sub
115
115 - What are permutations?
115 - Within any group of items or people, there are multiple arrangements, or permutations, possible. For instance, within a group of three items A, B, and C, there are six permutations: ABC, ACB, BAC, BCA, CAB and CBA. Permutations differ from combina
116
116 - What is the formula for permutations?
116 - If you're asked to find the number of ways to arrange a smaller group that's being drawn from a larger group, you can either apply logic or use the permutation formula: (n!)/(n - k)! Where groups of k entities are formed from n total entities.
117
117 - Restaurant A has 5 appetizers, 20 main courses, and 4 desserts. If a meal consists of 1 appetizer, 1 main course, and 1 dessert, how many different meals can be ordered at Restaurant A?
117 - Because you're only choosing one of each item, the number of possible outcomes from each set is the number of items in that set. There are 5 possible appetizers, 20 possible main courses, and 4 possible desserts. The number of different meals that c
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118 - If 2 students are chosen at random to run an errand from a class with 5 girls and 5 boys, what is the probability that both students chosen will be girls?
118 - The probability that the first student chosen will be a girl is 5/10 = 1/2, and because there would be 4 girls and 5 boys left out of 9 students, the probability that the second student chosen will be a girl (given that the first student chose is a
119
119 - What is an angle bisector?
119 - A line or line segment bisects an angle it is splits the angle in to two smaller, equal angles. Line segment BD below bisects (ang)ABC, and (ang)ABD has the same measure of (ang)DBC. The two smaller angles are each half the size of (ang)ABC. BD bi
120
120 - Factor the polynomial x2 - 3x + 2
120 - Many of the polynomials that you'll see on the GMAT can be factored into the product of the two binomials by using the FOIL method backward, factoring the given polynomial into two binomials, each containing an x term. Start by writing down what y
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121 - What is the vertex of a polygon?
121 - The vertex of a polygon (plural: vertices) of a polygon is a point where two sides intersect. Polygons are named by assigning each vertex a letter and listing them in order, as in pentagon ABCDE below.
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122 - What is a regular polygon?
122 - A regular polygon is a polygon with sides of equal length and interior angles of equal measure.
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123 - What is the formula for finding the degree measure of one angle in a regular polygon?
123 - n sides ((n - 2) \* 180) / n
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124 - How do you find the minimum or maximum lengths for a side of a triangle?
124 - If you know the lengths of two sides of a triangle, you know that the third side is between their positive difference and their sum. For example, the lengths of two of the sides or a triangle are 7 and 3. What is the range of possible lengths for t
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125 - In the diagram above, the base has length 4 and the height has length 3. What is the area of the triangle?
125 - Area = (1/2)(b \* h) = (bh)/2 = (4 \* 3)/2 = 6 Because the lengths of the base and height were not given in specific units, such as centimeters or feet, the area of the triangle is simply said to be 6 square units.
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126 - What is the area of right triangle ABC? 1) AB = 5 2) BC = 4
126 - In this data sufficiency example, neither statement alone is sufficient. You may think at first that together the two statements are enough, because it looks like ABS is a 3-4-5 right triangle. Not so fast! You're given two sides, but you don't know
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127 - What do you call an arc that is exactly half the circumference of its circle?
127 - An arc that is exactly half the circumference of its circle is called a semicircle.
128
128 - What is coordinate geometry?
128 - In coordinate geometry, the locations of points in a plane are indicated by ordered pairs of real numbers.
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129 - What is the distance from (2,3) to (-7,3)?
129 - If two points have the same x's or the same y's - that is, they make a line segment that is parallel to an axis- all you have to do is subtract the numbers that are different. The y's are the same, so just subtract the x's: (2 - (-7)) = 9
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130 - What is the distance from (2,3) to (-1,-1)?
130 - If the points have different x's and different y's, make a right triangle and use the Pythagorean theorem. It's a 3-4-5 triangle! PQ = 5
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131 - If the coordinates of point A are (3,4) and the coordinates of point B are (6,8), what is the distance between points A and B?
131 - Plot points A and B, and draw in line segment AB. The length of AB is the distance between the two points. Now draw a right triangle, with AB as its hypotenuse. The missing vertex will be the intersection of a line segment drawn through point A para
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132 - Line r is a straight line as shown above. Which of the following points lies on line r?
132 - Line r intercepts the y-axis at (0,-2), so you can plug -2 in for b in the slope-intercept form of a linear equation. Line r has a rise (delta)y of 2 and a run (delta)x of 5, so its slope is 2/5. That makes the slope-intercept form y = (2/5)x - 2
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133 - How do you find the volume of a cylinder? How do you find the surface area of a cylinder?
133 - To find the volume or surface area of a cylinder, you need two pieces of information - the height of the cylinder and the radius of its base. Volume of a cylinder = (area of base)(height) = p(r2)(h) Lateral surface area of a cylinder = (circumfere
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134 - The area of a square circumscribed about a circle is 36. What is the circumference of the circle?
134 - Look for the connection. Is the diameter the same as a side or a diagonal? To get the circumference, you need the diameter or radius. In this case the circle's diameter is also the square's edge. Circumference = p(diameter) = 6p
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135 - How do you multiply square roots?
135 - The product of more than one square root is equal to the square root of their total product. Example: √(3) \* √(5) = √(3\*5) = √(15)
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136 - Hos do you divide square roots?
136 - The quotient of more than one square root is equal to the square root of their total quotient. Example: (√(6)/√(3)) = (√(6/3)) = √(2)
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137 - What are isosceles triangles?
137 - Isosceles triangles are triangles that have two equal sides. The angles opposite these sides, or base angles, are also equal.
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138 - Translate 1/4, 1/5, 1/6, and 1/8 into their decimal equivalents.
138 - 1/4 = .25 1/5 = .20 1/6 = .166 1/8 = .125
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139 - What is the probability of throwing a 2, a 5, and a 3, in no particular order, on a fair six-sided die?
139 - There are 3 dependent trials, each with 6 possible outcomes - one for each side of the die. The probability of the first trial is 3/6 (3 desired outcomes, 2, 5, 3, out of the 6 possible outcomes). The probability of the second trial is 2/6 ( the two
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140 - 0! =
140 - 0! = 1
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141 - What is a standard deviation?
141 - A standard deviation is a standardized distance from the average of a group, based on a weighted average of all points' distances from the average.
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142 - Does a prime number multiplied by another prime number always equal an odd number?
142 - Usually this is true, because all prime numbers greater than 2 are odd, but 2 is also a prime number (the smallest, and only prime). Thus a prime number multiplied with 2 (another prime) would be even.
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143 - An isosceles right triangle has a base of 2n and a hypotenuse x. What is the area of the triangle?
143 - The area of a triangle is equal to (1/2)bh. Here, you are given the base, 2n. You are also given that the triangle is isosceles, so you know the remaining side (height) will also be 2n. (1/2)(2n \* 2n) = (1/2)(4n2) = 2n2
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144 - Right triangle ABC is inscribed in circle O, with segment BC intersecting the center of O. If segment AB = 3, what is the circumference of circle O?
144 - Because you know ABC is an inscribed right triangle, you know it is an isosceles triangle, with sides x : x : x(√(2)). You are given AB = 3, which means the hypotenuse (BC) will be 3√(2), which is also the diameter of the circle. The formula for the
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145 - x0
145 - Any number to the 0th power equals 1
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146 - What is the surface area of a rectangular prism with the dimension 4 \* 3 \* 2?
146 - A uniform rectangular prism has three pairs of equal, rectangular sides. The total surface area is the summation of these six sides. Therefore, the total surface area would be: 2(4 \* 3 + 4 \* 2 + 3 \* 2) = 2(12 + 8 + 6)= 2(26)= 52
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147 - What is the mean, median, and mod of the following set of numbers (5, 8, 23, 47, 47, 62)
147 - The mean is the average: 32 The median is the set's middle most number. When a set has an even number of integers, the median is the average of the two middle-most number. This set's median is (23 + 47)/2 or 35 The mode of a set is the most freque
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148 - A bus travels from Station B to Station A at 50 mph, and returns from Station A to Station B at 30mph along the same path. What is the average speed of the bus in mph?
148 - To find the average of two speeds, you cannot simply average the two numbers, but rather you must calculate the weighted average of the two legs of the journey. To do this you must find the total distance traveled, and divide that by the total time
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149 - If the ratio of sparrows to the total number of birds in an aviary is 3:12, and there are 12 sparrows in the aviary, how many total birds does the aviary contain, not including sparrows?
149 - The aviary contains 48 total birds. Excluding the 12 sparrows, the aviary contains 36 birds.
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150 - A right triangle has sides with lengths of 20 and 25. What is the length of the third side?
150 - This is a classic Pythagorean triplet (3:4:5). The sides given represent the 4 and 5 in this triplet (4 \* 5 = 20, and 5 \* 5 = 25), so the third side would be represented by the 3, and is thus 3\* 5, or 15.
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151 - A pair of intersecting lines make an angle of 37°. What is the measurement of its vertical angle?
151 - Vertical angles are always equal. Thus the vertical angle of 37° angle would be 37°.
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152 - What is the formula used to calculate simple interest?
152 - Total of Principal and Interest = Principal \* (1 + rt), where r is the interest rate (expressed as a decimal), and t is the total number of time periods considered.
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153 - What is the formula used to calculate compound interest?
153 - Total of Principal and Interest = Principal \* (1 + r)t, where r is the interest rate (expressed as a decimal), and t is the total number of time periods considered.
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154 - How can you determine if a number is divisible by 2? 3? 4? 5? 6? 9? 10?
154 - A number is divisible by 2 if the number is even; by 3: if the sum of the digits is divisible by 3; by 4: if the two-digit number formed by the last two digits is divisible by 4; by 5: if the last digit is 0 or 5; by 6: if the number is divisible by
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155 - If 5x \* 55x = 125, what is the value of x?
155 - When multiplying exponentials with the same base, you can eliminate the base and deal solely with the exponents. In order to do that here, first find the common base throughout the expression. Both 5x and 55x have a common base of 5, and 125 can be
156
156 - √(2\*1/2) \* √(10)
156 - √(2\*1/2) \* √(10) = 5
157
157 - What is the order of operations represented by PEMDAS?
157 - P- Parentheses E- Exponents M- Multiplication D- Division A- Addition S- Subtraction
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158 - What are the angle measurements of a triangle with side lengths x: x(√(3)): 2x?
158 - This is a right triangle with angle measurements 30:60:90?
159
159 - What is the sum of the angles of a polygon with 7 sides?
159 - The sum of the angles of a polygon with n sides is equal to (n-2)(180). For a polygon with 7 sides you have: (7 -2)(180) = 5\*180 = 900
160
160 - A customer wants to buy three different fruits. If there are seven different fruits available at the grocer's, how many different ways can he pick his fruit?
160 - This is a combination, so use your combinations formula: (n!)/(k!(n-k)!), where n = the number of fruits available, and k is the number of fruit being picked. 7!/(3!(7-3)!) = (7 \* 6 \*5 \* 4!)/((3 \* 2 \* 1)(4 \* 3 \* 2 \* 1)) = (7 \* 6 \* 5)/(3 \* 2 \* 1)
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161 - What is the sum of the integers 105 through 225 inclusive?
161 - The average of the given range is 165, and there are 121 terms. The sum of the integers is thus 165 \* 121, or 19,965.
162
162 - A circle has an inscribed angle of 60°, with a corresponding arc of 3p. What is the area of the circle?
162 - Because the arc of 3p corresponds to 60° inscribed angle, you know that 3p is 1/6 of the circumference (as 60° is 1/6 of the total 360° in the circle). This gives you a circumference of 18p, which then tells you the diameter is 18. If the diameter i
163
163 - A right triangle has side lengths 20 and 52. What is the length of the third side?
163 - This is a 5:12:13 Pythagorean triplet. The two sides given reflective of the 5 and 13 lengths so the third side would be 48.
164
164 - To find the number of unordered subgroups of k members from a group of n, what is the combination/permutation formula you would use?
164 - To find the number of unordered subgroups of k members from a group of n, use the combination formula, which is: nCk = (n!)/(k!(n-k)!)
165
165 - To find the number of ordered groups of k members from a group n, what is the combination/permutation formula you would use?
165 - To find the number of ordered groups of k members from a group of n, use the permutation formula, which is: nPk = (n!)/(n-k)!
166
166 - What is the formula for the odds of at least one of events A and B occurring?
166 - P(A or B) = P(A) + P(B) - P(A and B) This formula is similar to the overlapping sets formula; you count the overlap twice, so must subtract it once to get a correct total. Note that P(A and B) = P(A) \* P(B)
167
I1 - In the diagram above, Line L1 is parallel to line L2. What is the value of x?
I1 - The angle marked x° corresponds to the angel adjacent to the left of the 70° angle on line L1. Therefore it must be supplementary to the 70° angle. If 70° + x° = 180°, x must equal 110°.
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I2 - (ang)A of triangle ABC is a right angle. Is side BC longer or shorter than side AB?
I2 - This question seems very abstract until you draw a diagram of a right triangle, labeling the vertex with the 90° angle as point A. To find the shortest distance from a point to a line, draw a line segment from the point to the line, such that the l
169
I3 - What is the height of a triangle?
I3 - The height of a triangle is the perpendicular distance from a vertex to the side opposite the vertex. The height may fall inside or outside the triangle, or it may coincide with on of the sides. In the diagrams above, AD, LK, EH, are altitudes.
170
I4 - What is the length of AG?
I4 - To find the diagonal of a rectangular solid, use the Pythagorean theorem twice, unless you spot "special" triangles. Draw diagonal AC: ABC is 3-4-5 triangle, so AC = 5. Now look at triangle ACG: ACG is another special triangle so you don't need to
171
I5 - If all the vertices of a polygon lie on a circle, then what do you know about the polygon in relation to the circle? If the all the sides of a polygon are tangent to the circle, then what?
I5 - A polygon is inscribed in a circle if all the vertices of the polygon lie on the circle. A polygon is circumscribed about a circle if all the sides of the polygon are tangent to the circle. Square ABCD, below, is inscribed in circle O. You can also
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