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GMAT Club Math Book 2024 v8_p1_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 1 | 1 | general | GMAT Club
Math Book
8th Edition
May 2024 |
GMAT Club Math Book 2024 v8_p2_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 2 | 2 | word_problems | Table of Contents:
Number Theory ………………………………………………… 2
Remainders ..…………………………………………………….18
Algebra …………………………………………………………….25
Sequences and Progressions ……………………………… 33
Functions / Coordinate Geometry ……………………….. 39
Word Problems………………………………………….……….59
Work Problems………………………………………….……….64
Distance Rate Time Pr... |
GMAT Club Math Book 2024 v8_p3_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 3 | 3 | number_theory | GMAT Club Math Book
NUMBER THEORY
Definition
Number Theory is concerned with the properties of numbers in general, and in particular integers.
As this is a huge issue we decided to divide it into smaller topics. Below is the list of Number Theory topics.
GMAT Number Types
GMAT deals with only Real Numbers: Integers, F... |
GMAT Club Math Book 2024 v8_p4_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 4 | 4 | fractions_decimals_percents | 2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2
without a remainder and as zero is evenly divisible by 2 then it must be even.
3. 0 is neither positive nor negative integer (the only one of this kind).
4. 0 is divisible by EVERY integer.
IRRATIONAL NUMBERS
Fra... |
GMAT Club Math Book 2024 v8_p5_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 5 | 5 | number_theory | Prime Numbers
A Prime number is a natural number with exactly two distinct natural number divisors: 1 and itself. Otherwise
a number is called a composite number. Therefore, 1 is not a prime, since it only has one divisor, namely 1.
A number is prime if it cannot be written as a product of two factors and , both of whi... |
GMAT Club Math Book 2024 v8_p6_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 6 | 6 | number_theory | Factors
A divisor of an integer , also called a factor of , is an integer which evenly divides without leaving a
remainder. In general, it is said is a factor of , for non-zero integers and , if there exists an integer
such that .
• 1 (and -1) are divisors of every integer.
• Every integer is a divisor of itself.
• Ev... |
GMAT Club Math Book 2024 v8_p7_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 7 | 7 | number_theory | power of the common factors).
• Every common divisor of a and b is a divisor of gcd(a, b).
• a*b=gcd(a, b)*lcm(a, b)
Lowest Common Multiple - LCM
The lowest common multiple or lowest common multiple (lcm) or smallest common multiple of two integers a
and b is the smallest positive integer that is a multiple both of a a... |
GMAT Club Math Book 2024 v8_p8_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 8 | 8 | number_theory | • Note: 0!=1.
• Note: factorial of negative numbers is undefined.
Trailing zeros:
Trailing z
eros are a sequence of 0's in the decimal representation (or more generally, in any positional
representation) of a number, after which no other digits follow.
125000 has 3 trailing zeros;
The number of trailing zeros in the de... |
GMAT Club Math Book 2024 v8_p9_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 9 | 9 | number_theory | =
We need all the prime {2,3,5} to be represented twice in 900, 5 can provide us with only 6 pairs, thus there is
900 in the power of 6 in 50!.
Consecutive Integers
Consecutive integers are integers that follow one another, without skipping any integers. 7, 8, 9, and -2, -1,
0, 1, are consecutive integers.
• Sum of con... |
GMAT Club Math Book 2024 v8_p10_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 10 | 10 | fractions_decimals_percents | middle term multiplied by number of terms. There are five terms in the set {1, 7, 13, 19, 25}, middle term is
13, so the sum is 13*5 =65.
FRACTIONS
Definition
Fractional numbers are ratios (divisions) of integers. In other words, a fraction is formed by dividing one
integer by another integer. Set of Fraction is a subs... |
GMAT Club Math Book 2024 v8_p11_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 11 | 11 | fractions_decimals_percents | Reciprocal
Reciprocal for a number , denoted by or , is a number which when multiplied by yields . The
reciprocal of a fraction is . To get the reciprocal of a number, divide 1 by the number. For example
reciprocal of is , reciprocal of is .
Operation on Fractions
• Adding/Subtracting fractions:
To add/subtract fractio... |
GMAT Club Math Book 2024 v8_p12_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 12 | 12 | fractions_decimals_percents | 1: The recurring number is .
2: , the number is of length so we have added two nines.
3: Reducing it to lowest terms: .
• To convert a mixed-recurring decimal to fraction:
1. Write down the number consisting with non-repeating digits and r
epeating digits.
2. Subtract non-repeating number from above.
3. Divide 1-2 by t... |
GMAT Club Math Book 2024 v8_p13_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 13 | 13 | word_problems | EXPONENTS
Exponents are a "shortcut" method of showing a number that was multiplied by itself several times. For
instance, number multiplied times can be written as , where represents the base, the number that is
multiplied by itself times and represents the exponent. The exponent indicates how many times to
multiple t... |
GMAT Club Math Book 2024 v8_p14_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 14 | 14 | sequences_patterns | For instance , the two possible solutions are and .
When solving equations with odd exponents, we'll have only one solution.
For instance for , solution is and for , solution is .
Exponents and divisibility:
is ALWAYS divisible by .
is divisible by if is even.
is divisible by if is odd, and not divisible by a+b if n... |
GMAT Club Math Book 2024 v8_p15_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 15 | 15 | fractions_decimals_percents | General rules:
• and .
•
•
•
•
• , when , then and when , then
• When the GMAT provides the square root sign for an even root, such as or , then the only accepted
answer is the positive root.
That is, , NOT +5 or -5. In contrast, the equation has TWO solutions, +5 and -5. Even
roots have only a positive value on t... |
GMAT Club Math Book 2024 v8_p16_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 16 | 16 | word_problems | , so the royalties decreased by 60%.
• Simple Interest
Simple interest = principal * interest rate * time
Example: If $15,000 is invested at 10% simple annual interest, how much interest is earned after 9 months?
Solution: $15,000*0.1*9/12 = $1125
• Compound Interest
, where C = the number of times compounded annually.... |
GMAT Club Math Book 2024 v8_p16_c2 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 16 | 16 | word_problems | n
the exponent applies to the entire power.
• If exponentiation is indicated by stacked symbols, the rule is to work from the top down, thus:
and not
Percent = ∗ 100 =Change
Original
= ∗ 100 = 60
−2
10
8
100
2
10
Balance(final) = principal∗ (1 + interest
C )time∗C
Balance(final) = principal∗ (1 + interest)time
Balanc... |
GMAT Club Math Book 2024 v8_p17_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 17 | 17 | number_theory | PRACTICE QUESTIONS
Easy:
1. https://gmatclub.com/forum/if-n-is-a-pr ... 22490.html
2. https://gmatclub.com/forum/if-x-is-an-i ... 68233.html
3. https://gmatclub.com/forum/how-many-two ... 91802.html
4. https://gmatclub.com/forum/if-n-is-an-i ... 96084.html
5. https://gmatclub.com/forum/root-80-root-139868.html
6. https... |
GMAT Club Math Book 2024 v8_p17_c2 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 17 | 17 | general | forum/if-each-expr ... 87153.html
9. https://gmatclub.com/forum/what-is-the- ... 51159.html
10. https://gmatclub.com/forum/sqrt-7-sqrt- ... 68800.html
GMAT Club Math Book
17 |
GMAT Club Math Book 2024 v8_p18_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 18 | 18 | number_theory | GMAT Club Forum
Remainders
https://gmatclub.com/forum/remainders-144665.html
REMAINDERS
created by: Bunuel
Definition
If and are positive integers, there exist unique integers and , called the
quotient and remainder, respectively, such that
and .
For example, when 15 is divided by 6, the quotient is 2 and the remaind... |
GMAT Club Math Book 2024 v8_p19_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 19 | 19 | number_theory | If a number is divided by 10, its remainder is the last digit of that number. If it is
divided by 100 then the remainder is the last two digits and so on.
For example, 123 divided by 10 has the remainder 3 and 123 divided by 100 has
the remainder of 23.
Example #1 (easy)
If the remainder is 7 when positive integer n is... |
GMAT Club Math Book 2024 v8_p20_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 20 | 20 | statistics | Example #3 (easy)
What is the tens digit of positive integer x ?
(1) x divided by 100 has a remainder of 30.
(2) x divided by 110 has a remainder of 30.
(1) x divided by 100 has a remainder of 30. We have that : 30, 130, 230,
... as you can see every such number has 3 as the tens digit. Sufficient.
(2) x divided by 110... |
GMAT Club Math Book 2024 v8_p21_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 21 | 21 | number_theory | Example #6 (medium)
Positive integer n leaves a remainder of 4 after division by 6 and a remainder of
3 after division by 5. If n is greater than 30, what is the remainder that n leaves
after division by 30?
A. 3
B. 12
C. 18
D. 22
E. 28
Positive integer n leaves a remainder of 4 after division by 6: . Thus n could
be: ... |
GMAT Club Math Book 2024 v8_p22_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 22 | 22 | algebra | Answer: D. Discuss this question HERE.
Example #8 (hard)
When 51^25 is divided by 13, the remainder obtained is:
A. 12
B. 10
C. 2
D. 1
E. 0
, now if we expand this expression all terms but the last one will have
in them, thus will leave no remainder upon division by 13, the last term will
be . Thus the question become... |
GMAT Club Math Book 2024 v8_p23_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 23 | 23 | number_theory | Answer: E. Discuss this question HERE.
Example #10 (hard)
If p, x, and y are positive integers, y is odd, and p = x^2 + y^2, is x divisible by
4?
(1) When p is divided by 8, the remainder is 5
(2) x – y = 3
(1) When p is divided by 8, the remainder is 5. This implies that .
Since given that , then -->
.
So, . Now, if t... |
GMAT Club Math Book 2024 v8_p24_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 24 | 24 | number_theory | (2) The remainder of is --> is: 2, 5, 8, 11, ... so we have the third case. Which
means that the remainder of is 0. Now, the question asks whether the remainder
of , which is 0, greater than the reminder of , which is 0, 1, or 2.
Obviously it cannot be greater, it can be less than or equal to. So, the answer to the
que... |
GMAT Club Math Book 2024 v8_p25_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 25 | 25 | algebra | GMAT Club Math Book
Algebra
https://gmatclub.com/forum/algebra-101576.html
Algebra 101
Scope
Manipulation of various algebraic expressions
Equations in 1 & more variables
Dealing with non-linear equations
Algebraic identities
Notation & Assumptions
In this document, lower case roman alphabets will be used to denote va... |
GMAT Club Math Book 2024 v8_p26_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 26 | 26 | algebra | questions.
Degree of an expression
The degree of an algebraic expression is defined as the highest power of the variables present in the expression.
Degree 1 : Linear
Degree 2 : Quadratic
Degree 3 : Cubic
Degree 4 : Bi-quadratic
Egs : the degree is 1
the degree is 3
the degree of x is 3, degree of z is 5, degree of t... |
GMAT Club Math Book 2024 v8_p27_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 27 | 27 | algebra | Solving equations of degree 2 : QUADRATIC
The general form of a quadratic equation is
The equation has no solution if
The equation has exactly one solution if
This equation has 2 solutions given by if
The sum of roots is
The product of roots is
If the roots are and , the equation can be written as
A quick way to... |
GMAT Club Math Book 2024 v8_p28_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 28 | 28 | number_theory | So the solution is y=1 or 2 or x^3=1 or 2 or x=1 or
Other tricks
Sometimes we are given conditions such as the variables being integers which make the solutions much easier to
find. When we know that the solutions are integral, often times solutions are easy to find using just brute force.
Eg. and we know a,b are inte... |
GMAT Club Math Book 2024 v8_p29_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 29 | 29 | algebra | ABSOLUTE VALUE
(Modulus)
Definition
The absolute value (or modulus) of a real number x is x's numerical value without regard to its sign.
For example, ; ;
Graph:
Important properties:
How to approach equations with moduli
It's not easy to manipulate with moduli in equations. There are two basic approaches that will h... |
GMAT Club Math Book 2024 v8_p30_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 30 | 30 | algebra | For example,
a) Positive: if , we can rewrite the equation as:
b) Negative: if , we can rewrite the equation as:
We can also think about conditions like graphics. is a key point in which the expression under modulus
equals zero. All points right are the first condition and all points left are second condition .
2. S... |
GMAT Club Math Book 2024 v8_p31_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 31 | 31 | word_problems | b) --> . --> . x e { , } and both solutions satisfy the
condition.
(Optional) The following illustration may help you understand how to open modulus at different conditions.
Answer: , , ,
Tip & Tricks
The 3-steps method works in almost all cases. At the same time, often there are shortcuts and tricks that allow
you to... |
GMAT Club Math Book 2024 v8_p32_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 32 | 32 | coordinate_geometry | Practice Questions
Easy:
1. https://gmatclub.com/forum/which-of-the ... 44267.html
2. https://gmatclub.com/forum/if-y-is-an-i ... 39867.html
3. https://gmatclub.com/forum/on-the-numbe ... 16027.html
4. https://gmatclub.com/forum/if-k-2-m-2-w ... 07128.html
5. https://gmatclub.com/forum/if-y-0-which ... 09621.html
6. ht... |
GMAT Club Math Book 2024 v8_p33_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 33 | 33 | sequences_patterns | GMAT Club Math Book
Algebra: Sequences and Progressions
https://gmatclub.com/forum/algebra-sequences-and-progressions-101891.html
Sequences & Progressions
created by: shrouded1
Definition
Sequence : It is an ordered list of objects. It can be finite or infinite. The elements may
repeat themselves more than once in the... |
GMAT Club Math Book 2024 v8_p34_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 34 | 34 | sequences_patterns | Examples
1. All odd positive integers : {1,3,5,7,...}
2. All positive multiples of 23 : {23,46,69,92,...}
3. All negative reals with decimal part 0.1 : {-0.1,-1.1,-2.1,-3.1,...}
Geometric Progressions
Definition
It is a special type of sequence in which the ratio of consequetive terms is constant
General Term
is the... |
GMAT Club Math Book 2024 v8_p35_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 35 | 35 | sequences_patterns | Important Properties
Of any three consecutive terms of a HP, the middle one is always the harmonic mean of
the other two, where the harmonic mean (HM) is defined as :
Or in other words :
APs, GPs, HPs : Linkage
Each progression provides us a definition of "mean" :
Arithmetic Mean : OR
Geometric Mean : OR
Harmonic Mea... |
GMAT Club Math Book 2024 v8_p36_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 36 | 36 | sequences_patterns | For Example : Consider the GP with {1,2,4,8,16,32,...}, so b_n=2^(n-1)
Pick out the subsequence of terms
New sequence is {4,16,64,...} which is a GP with and
The special sequence in which each term is the sum of previous two terms is known as
the fibonacci sequence. It is neither an AP nor a GP. The first two terms a... |
GMAT Club Math Book 2024 v8_p37_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 37 | 37 | sequences_patterns | Example 4
For every integer k from 1 to 10, inclusive, the kth term of a certain sequence is given by
(-1)^(k+1) *(1/2^k). If T is the sum of the first 10 terms in the sequence then T is
a)greater than 2
b)between 1 and 2
c)between 1/2 and 1
d)between 1/4 and 1/2
e)less than 1/4.
Solution
The sequence given has first t... |
GMAT Club Math Book 2024 v8_p38_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 38 | 38 | sequences_patterns | Practice Questions
Easy:
1. https://gmatclub.com/forum/the-infinite ... 00090.html
2. https://gmatclub.com/forum/in-an-increa ... 43749.html
3. https://gmatclub.com/forum/the-sequence ... 46630.html
4. https://gmatclub.com/forum/the-sequence ... 34498.html
5. https://gmatclub.com/forum/in-a-certain ... 44376.html
6. ht... |
GMAT Club Math Book 2024 v8_p39_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 39 | 39 | coordinate_geometry | GMAT Club Math Book
Algebra Functions & Coordinate Geometry
https://gmatclub.com/forum/algebra-functions-87652.html
FUNCTIONS & COORDINATE GEOMETRY
Definition
Coordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate
system and the principles of algebra and analysis.
The Coordinate Plane
I... |
GMAT Club Math Book 2024 v8_p40_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 40 | 40 | coordinate_geometry | "rectangular coordinates".
X axis
The horizontal scale is called the x-axis and is usually drawn with the zero point in the
middle. Values to the right are positive and those to the left are negative.
Y axis
The vertical scale is called the y-axis and is also usually drawn with the zero point in the
middle. Values abov... |
GMAT Club Math Book 2024 v8_p41_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 41 | 41 | coordinate_geometry | up (y). Negative numbers mean to go left (x) or down (y).
Distance between two points
Given coordinates of two points, distance D between two points is given by:
(where is the difference between the x-coordinates and is the
difference between the y-coordinates of the points)
As you can see, the distance formula on the... |
GMAT Club Math Book 2024 v8_p42_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 42 | 42 | coordinate_geometry | Midpoint of a Line Segment
A line segment on the coordinate plane is defined by two endpoints whose coordinates are
known. The midpoint of this line is exactly halfway between these endpoints and it's
location can be found using the Midpoint Theorem, which states:
• The x-coordinate of the midpoint is the average of th... |
GMAT Club Math Book 2024 v8_p43_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 43 | 43 | coordinate_geometry | There are several approaches commonly used in coordinate geometry. It does not matter
whether we are talking about a line, ray or line segment. In all cases any of the below
methods will provide enough information to define the line exactly.
1. General form.
The general form of the equation of a straight line is
Where ... |
GMAT Club Math Book 2024 v8_p44_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 44 | 44 | algebra | The equation of a straight line passing through points and is:
Example #1
Q: Find the equation of a line passing through the points A (17,4) and B (9,9).
Solution: Substituting the values in equation we'll get:
--> --> OR if we want to write
the equation in the slope-intercept form:
4. Using one point and the slope
... |
GMAT Club Math Book 2024 v8_p45_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 45 | 45 | algebra | The equation of a straight line that passes through a point with a
slope m is:
Example #2
Q: Find the equation of a line passing through the point A (14,23) and the slope 2.
Solution: Substituting the values in equation we'll get
-->
4. Intercept form.
The equation of a straight line whose x and y intercepts are a an... |
GMAT Club Math Book 2024 v8_p46_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 46 | 46 | algebra | Given two points and on a line, the slope of the line is:
If the equation of the line is given in the Point-intercept form: , then is
the slope. This form of a line's equation is called the slope-intercept form, because can
be interpreted as the y-intercept of the line, the y-coordinate where the line intersects the
y-... |
GMAT Club Math Book 2024 v8_p47_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 47 | 47 | algebra | Positive slope
Here, y increases as x increases, so the line slopes upwards to the right. The slope will be
a positive number. The line below has a slope of about +0.3, it goes up about 0.3 for
every step of 1 along the x-axis.
Negative slope
Here, y decreases as x increases, so the line slopes downwards to the right. ... |
GMAT Club Math Book 2024 v8_p48_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 48 | 48 | algebra | 7. If the slope is 1 the angle formed by the line is degrees.
8. Given a point and slope, equation of a line can be found. The equation of a
straight line that passes through a point with a slope is:
Vertical and horizontal lines
A vertical line is parallel to the y-axis of the coordinate plane. All points on the line... |
GMAT Club Math Book 2024 v8_p49_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 49 | 49 | algebra | A horizontal line has a slope of zero.
The equation of a horizontal line is:
Where: y is the coordinate of any point on the line; b is where the line crosses the y-axis
(y intercept). Notice that the equation is independent of x. Any point on the horizontal line
satisfies the equation.
Parallel lines
Parallel lines hav... |
GMAT Club Math Book 2024 v8_p50_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 50 | 50 | algebra | From two given points on the line.
From the equation of the line in slope-intercept form
From the equation of the line in point-slope form
The equation of a line through the point and parallel to line
is:
Distance between two parallel lines and can be found by
the formula:
Example #1
Q:There are two lines. One line is... |
GMAT Club Math Book 2024 v8_p51_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 51 | 51 | algebra | Solution: We first find the slope of the line AB using the same method as in the example
above.
For the line to be parallel to AB it will have the same slope, and will pass through a given
point, C(12,10). We therefore have enough information to define the line by it's equation
in point-slope form form:
-->
Perpendic... |
GMAT Club Math Book 2024 v8_p52_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 52 | 52 | algebra | The two lines and are perpendicular if
.
The equation of a line passing through the point ) and perpendicular to line
is:
Example #1:
Q: Are the two lines below perpendicular?
Solution:
To answer, we must find the slope of each line and then check to see if one slope is the
negative reciprocal of the other or if their... |
GMAT Club Math Book 2024 v8_p53_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 53 | 53 | algebra | If the lines are perpendicular, each will be the negative reciprocal of the other. It doesn't
matter which line we start with, so we will pick AB:
Negative reciprocal of 0.358 is
So, the slope of CD is -2.22, and the negative reciprocal of the slope of AB is -2.79. These
are not the same, so the lines are not perpendi... |
GMAT Club Math Book 2024 v8_p54_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 54 | 54 | algebra | To find the intersection of two straight lines:
1. First we need their equations
2. Then, since at the point of intersection, the two equations will share a point and thus
have the same values of x and y, we set the two equations equal to each other. This gives
an equation that we can solve for x
3. We substitute the x... |
GMAT Club Math Book 2024 v8_p55_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 55 | 55 | coordinate_geometry | intercept form): and (A vertical line)
Solution: When one of the lines is vertical, it has no defined slope. We find the
intersection slightly differently.
On the vertical line, all points on it have an x-coordinate of 12 (the definition of a vertical
line), so we simply set x equal to 12 in the first equation and solv... |
GMAT Club Math Book 2024 v8_p56_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 56 | 56 | geometry | This equation of the circle follows from the Pythagorean theorem applied to any point on
the circle: as shown in the diagram above, the radius is the hypotenuse of a right-angled
triangle whose other sides are of length x-a and y-b.
If the circle is centered at the origin (0, 0), then the equation simplifies to:
Number... |
GMAT Club Math Book 2024 v8_p57_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 57 | 57 | coordinate_geometry | .
The general or standard form of a quadratic function is , or in function
form, , where is the independent variable, is the dependent
variable, and , , and are constants.
The larger the absolute value of , the steeper (or thinner) the parabola is, since
the value of y is increased more quickly.
If is positive, the par... |
GMAT Club Math Book 2024 v8_p58_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 58 | 58 | coordinate_geometry | The vertex of the parabola is located at point .
Note: typically just is calculated and plugged in for x to find y.
Practice Questions
Easy:
1. https://gmatclub.com/forum/which-of-the ... 29938.html
2. https://gmatclub.com/forum/in-the-recta ... 65534.html
3. https://gmatclub.com/forum/in-a-rectang ... 94392.html
4. h... |
GMAT Club Math Book 2024 v8_p59_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 59 | 59 | word_problems | GMAT Club Math Book
Word Problems Made Easy
https://gmatclub.com/forum/word-problems-made-easy-87346.html
Word Problems Made Easy
created by: sriharimurthy
edited by: bb, walker, Bunuel
This is an introductory post to word problems.
It deals primarily with the translation of word problems into equations.
Discussions r... |
GMAT Club Math Book 2024 v8_p60_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 60 | 60 | word_problems | 7) Once you have the equations written down it's time to do the math! This is usually
quite simple. Be very careful so as not to make any silly mistakes in calculations.
8) Lastly, after solving, cross check to see that the answer you have obtained
corresponds to what was asked. The makers of these GMAT questions love ... |
GMAT Club Math Book 2024 v8_p61_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 61 | 61 | word_problems | The ‘how much is left’ construction
Sometimes, the question will give you a total amount that is made up of a number of
smaller amounts of unspecified sizes. In this case, just assign a variable to the unknown
amounts and the remaining amount will be what is left after deducting this named amount
from the total.
Consid... |
GMAT Club Math Book 2024 v8_p62_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 62 | 62 | fractions_decimals_percents | Length = 2*width
Example 4.
The ratio of the length of a rectangular garden to its width is 2. Express its length in terms
of its width.
Solution:
Key words: ratio of (implies division); is (implies equal to)
Thus, the phrase ‘ratio of length to width is 2’ becomes:
Length/width = 2 → Length = 2*width
Example 5.
The le... |
GMAT Club Math Book 2024 v8_p63_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 63 | 63 | algebra | Now let’s see what the question gives us.
‘Garden with width 6 meters’ translates to:
Width of garden = 6
W – 2x = 6
Thus, if we know W we can find x.
‘Length of a rectangular garden surrounded by walkway is twice its width’ translates to:
Length of garden + length of walkway = 2*(width of garden + width of walkway)
L ... |
GMAT Club Math Book 2024 v8_p64_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 64 | 64 | word_problems | GMAT Club Math Book
Work Problems
https://gmatclub.com/forum/work-problems-87357.html
‘Work’ Word Problems Made Easy
created by: sriharimurthy
edited by: bb, walker, Bunuel
NOTE: In case you are not familiar with translating word problems into equations please
go through THIS POST FIRST.
What is a ‘Work’ Word Problem?... |
GMAT Club Math Book 2024 v8_p65_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 65 | 65 | word_problems | completed will be (1*1)/5
STEP 2: Add up the amount of work done by each person/machine in that one
unit of time.
This would give us the total amount of work completed by both of them in one hour. For
example, if A completes of the work in one hour and B completes of the work in
one hour, then TOGETHER, they can comple... |
GMAT Club Math Book 2024 v8_p66_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 66 | 66 | word_problems | Example 2.
Working, independently X takes 12 hours to finish a certain work. He finishes 2/3 of the
work. The rest of the work is finished by Y whose rate is 1/10 of X. In how much time
does Y finish his work?
Solution:
Now the only reason this is trickier than the first problem is because the sequence of
events are sl... |
GMAT Club Math Book 2024 v8_p67_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 67 | 67 | word_problems | calculate the rate at which B works: Rate at which B works = .
‘B prints 5 pages a minute more than printer A’ This means that the difference between
the amount of work B and A complete in one minute corresponds to 5 pages. So, let us
calculate that difference. It will be
‘How many pages does the task contain?’ If of ... |
GMAT Club Math Book 2024 v8_p67_c2 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 67 | 67 | algebra | age
to form the equations, they are really not all that tough.
And as far as the concept of ‘work’ word problems is concerned – it is always the
same!
− =1
24
1
60
1
40
− =1
40
1
60
1
120
1
120
= 600(5∗1)
1
120
660
t+10
660
t
∗ 1.1 =660
t+10
660
t
t = 100 = 6660
t+10
GMAT Club Math Book
67 |
GMAT Club Math Book 2024 v8_p68_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 68 | 68 | word_problems | GMAT Club Math Book
Distance, Speed Time
https://gmatclub.com/forum/distance-speed-time-87481.html
'Distance/Speed/Time' Word Problems Made Easy
created by: sriharimurthy
edited by: bb, walker, Bunuel
NOTE: In case you are not familiar with translating word problems into equations please
go through this post first : h... |
GMAT Club Math Book 2024 v8_p69_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 69 | 69 | word_problems | travel for 2 hours at that speed, you would have traveled 100 miles. 3 hours would
be 150 miles, etc.
If you were to double the speed, then you would have traveled 100 miles in the first
hour and 200 miles at the end of the second hour.
We can figure out any one of the components by knowing the other two.
For example, ... |
GMAT Club Math Book 2024 v8_p70_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 70 | 70 | word_problems | about how to use the formula.
So the trick is to be able to understand EXACTLY what they are giving you and
EXACTLY what it is that is missing, but you do that from thinking, not from the
formula, because the formula only works for the COMPONENTS of any trip
where you are going an average speed for a certain amount of ... |
GMAT Club Math Book 2024 v8_p71_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 71 | 71 | word_problems | In the next section we will learn how to do just that.
Resolving the Components
When you first start out with these problems, the best way to approach
them is by organizing the data in a tabular form.
Use a separate column each for distance, speed and time and a separate row for the
different components involved (2 par... |
GMAT Club Math Book 2024 v8_p72_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 72 | 72 | word_problems | Warning: Make sure that the units for time and distance agree with the units for the rate.
For instance, if they give you a rate of feet per second, then your time must be in seconds
and your distance must be in feet. Sometimes they try to trick you by using the wrong
units, and you have to catch this and convert to th... |
GMAT Club Math Book 2024 v8_p73_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 73 | 73 | word_problems | In the first row, we are given the distance and the speed. Thus it is possible to calculate
the time.
Time(1) = Distance(1)/Speed(1) = 1/30
In the second row, we are given just the distance. Since we have to calculate speed, let
us give it a variable 'x'. Now, by using the 'D/S/T' relationship, time can also be express... |
GMAT Club Math Book 2024 v8_p74_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 74 | 74 | word_problems | Thus, the distance he spent driving will be '150 - x'
Now, in the first row, we have the distance in terms of 'x' and we have been given the
speed. Thus we can calculate the time he spent driving in terms of 'x'.
Time(1) = Distance(1)/Speed(1) = (150 - x)/30
Similarly, in the second row, we again have the distance in t... |
GMAT Club Math Book 2024 v8_p75_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 75 | 75 | word_problems | From the second row, we can form the following equation :
Distance(2) = Speed(2) * Time(2) = (x - 20)*5
Now, equating the distances because they are equal we get the following equation :
3*x = 5*(x - 20) --> x = 50 mph.
Answer : 50 mph.
Example 4.
Two cyclists start at the same time from opposite ends of a course that ... |
GMAT Club Math Book 2024 v8_p76_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 76 | 76 | word_problems | In the first row, we have the speed of the boat in terms of 'b' and we are given the time.
Thus we can get the following equation :
Distance(1) = Speed(1) * Time(1) = (b + 3)*3
In the second row, we again have the speed in terms of 'b' and we are given the time.
Thus we can get the following equation :
Distance(2) = Sp... |
GMAT Club Math Book 2024 v8_p77_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 77 | 77 | sets_probability_counting | GMAT Club Math Book
Overlapping Sets
https://gmatclub.com/forum/overlapping-sets-144260.html
ADVANCED OVERLAPPING SETS
Some hard GMAT quantitative questions will require you to know and understand the formulas for set theory, presenting three sets and
asking various questions about them. There are two main formulas to ... |
GMAT Club Math Book 2024 v8_p78_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 78 | 78 | geometry | Again: when we add three groups A, B, and C some sections are counted more than once. For instance: sections d, e, and f are
counted twice and section g thrice. Hence we need to subtract sections d, e, and f ONCE (to count section g only once) and
subtract section g TWICE (again to count section g only once).
When we s... |
GMAT Club Math Book 2024 v8_p79_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 79 | 79 | statistics | Example 3:
Of 20 Adults, 5 belong to A, 7 belong to B, and 9 belong to C. If 2 belong to all three organizations and 3 belong to exactly
2 organizations, how many belong to none of these organizations?
Translating:
"20 Adults": Total=20;
"5 belong to A, 7 belong to B, and 9 belong to C": A=5, B=7, and C=9;
"2 belong to... |
GMAT Club Math Book 2024 v8_p80_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 80 | 80 | fractions_decimals_percents | "4 names were on all 3 rosters": EnMnS=g=4;
Question:: Total=?
Apply first formula: -->
--> .
Answer: 50. Discuss this question HERE.
Example 7:
There are 50 employees in the office of ABC Company. Of these, 22 have taken an accounting course, 15 have taken a
course in finance and 14 have taken a marketing course. Nin... |
GMAT Club Math Book 2024 v8_p81_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 81 | 81 | fractions_decimals_percents | Question:: how many students play exactly two of these sports?
Apply first formula:
{Total}={Hockey}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither}
50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2;
Those who play ONLY Hockey and Cricket are 7-2=5;
Those who play ONLY Cricket and Football are 4-2=2;
Those who... |
GMAT Club Math Book 2024 v8_p82_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 82 | 82 | sets_probability_counting | Answer: C.
P.S. Notice that max range for the original question is not limited when the max # of people in all 3 groups for revised question is
17+28+35 (in case there is 0 overlap between the 3 groups).
Answer: C. Discuss this question HERE.
_____________________________________________________________________________... |
GMAT Club Math Book 2024 v8_p83_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 83 | 83 | sets_probability_counting | GMAT Club Math Book
Probability
https://gmatclub.com/forum/probability-87244.html
PROBABILITY
Definition
A number expressing the probability (p) that a specific event will occur, expressed as the
ratio of the number of actual occurrences (n) to the number of possible occurrences (N).
A number expressing the probabilit... |
GMAT Club Math Book 2024 v8_p84_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 84 | 84 | sets_probability_counting | There are 6 equally possible outcomes when we roll a die. The probability of getting any
number out of 1-6 is .
All possibilities: {1,2,3,4,5,6}
Marbles, Balls, Cards...
Let's assume we have a jar with 10 green and 90 white marbles. If we randomly choose a
marble, what is the probability of getting a green marble?
The ... |
GMAT Club Math Book 2024 v8_p85_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 85 | 85 | sets_probability_counting | Example #1
Q:There is a coin and a die. After one flip and one toss, what is the probability of getting
heads and a "4"?
Solution: Tossing a coin and rolling a die are independent events. The probability of
getting heads is and probability of getting a "4" is . Therefore, the probability of
getting heads and a "4" is:
... |
GMAT Club Math Book 2024 v8_p86_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 86 | 86 | sets_probability_counting | Combination of independent and mutually exclusive
events
Many probability problems contain combination of both independent and mutually
exclusive events. To solve those problems it is important to identify all events and their
types. One of the typical problems can be presented in a following general form:
Q: If the pr... |
GMAT Club Math Book 2024 v8_p87_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 87 | 87 | sets_probability_counting | 1) combinatorial approach: The total number of possible committees is . The
number of possible committee that includes both Bob and Rachel is .
2) reversal combinatorial approach: Instead of counting probability of occurrence of
certain event, sometimes it is better to calculate the probability of the opposite and then... |
GMAT Club Math Book 2024 v8_p88_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 88 | 88 | sets_probability_counting | and faster.
- we choose 1 couple out of 5 couples.
- we chose one person out of remaining 8 people.
- the total number of combinations to choose 3 people out of 10 people.
3) probability approach:
1st person: - we choose any person out of 10.
2nd person: - we choose any person out of 8=10-2(one couple from previous ... |
GMAT Club Math Book 2024 v8_p89_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 89 | 89 | word_problems | Tips and Tricks: Symmetry
Symmetry sometimes lets you solve seemingly complex probability problem in a few
seconds. Let's consider an example:
Example #1
Q: There are 5 chairs. Bob and Rachel want to sit such that Bob is always left to Rachel.
How many ways it can be done ?
Solution: Because of symmetry, the number of ... |
GMAT Club Math Book 2024 v8_p90_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 90 | 90 | number_theory | Practice Questions
Easy:
1. https://gmatclub.com/forum/in-a-box-of- ... 07395.html
2. https://gmatclub.com/forum/among-a-grou ... 34499.html
3. https://gmatclub.com/forum/the-probabil ... 44730.html
4. https://gmatclub.com/forum/xavier-yvonn ... 65822.html
5. https://gmatclub.com/forum/carol-purcha ... 21728.html
6. ht... |
GMAT Club Math Book 2024 v8_p91_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 91 | 91 | sets_probability_counting | GMAT Club Math Book
Combinations
https://gmatclub.com/forum/combinations-87345.html
COMBINATORICS
created by: walker
edited by: bb, Bunuel
Definition
Combinatorics is the branch of mathematics studying the enumeration, combination, and
permutation of sets of elements and the mathematical relations that characterize th... |
GMAT Club Math Book 2024 v8_p92_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 92 | 92 | statistics | to arrange marbles in a row if blue and green marbles have to be next to each other?
Solution: Let's write out all possible ways to arrange marbles in a row and then find only
arrangements that satisfy question's condition:
Answer is 4.
Example #3
Q:. There are three marbles: 1 blue, 1 gray and 1 green. In how many way... |
GMAT Club Math Book 2024 v8_p93_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 93 | 93 | sets_probability_counting | Combination
A combination is an unordered collection of k objects taken from a set of n distinct
objects. The number of ways how we can choose k objects out of n distinct objects is
denoted as:
knowing how to find the number of arrangements of n distinct objects we can easily find
formula for combination:
1. The total ... |
GMAT Club Math Book 2024 v8_p94_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 94 | 94 | statistics | Circular arrangements
Let's say we have 6 distinct objects, how many relatively different arrangements do we
have if those objects should be placed in a circle.
The difference between placement in a row and that in a circle is following: if we shift all
object by one position, we will get different arrangement in a row... |
GMAT Club Math Book 2024 v8_p95_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 95 | 95 | general | Practice Questions
Easy:
1. https://gmatclub.com/forum/there-are-8- ... 34582.html
2. https://gmatclub.com/forum/there-are-5- ... 88100.html
3. https://gmatclub.com/forum/a-certain-un ... 68638.html
4. https://gmatclub.com/forum/the-diagram- ... 44271.html
5. https://gmatclub.com/forum/in-a-tournam ... 55939.html
6. ht... |
GMAT Club Math Book 2024 v8_p95_c2 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 95 | 95 | word_problems | forum/how-many-dif ... 71774.html
9. https://gmatclub.com/forum/a-committee- ... 04966.html
10. https://gmatclub.com/forum/in-how-many- ... 56400.html
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GMAT Club Math Book
95 |
GMAT Club Math Book 2024 v8_p96_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 96 | 96 | statistics | GMAT Club Math Book
Standard Deviation
https://gmatclub.com/forum/standard-deviation-87905.html
STANDARD DEVIATION
Definition
Standard Deviation (SD, or STD or ) - a measure of the dispersion or variation in a
distribution, equal to the square root of variance or the arithmetic mean (average) of
squares of deviations ... |
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