GMAT Quant (Correct Answers)
2^2Correct Answers4
1^2Correct Answers1
3^2Correct Answers9
4^2Correct Answers16
5^2Correct Answers25
6^2Correct Answers36
7^2Correct Answers49
8^2Correct Answers64
9^2Correct Answers81
10^2Correct Answers100
11^2Correct Answers121
12^2Correct Answers144
13^2Correct Answers169
14^2Correct Answers196
15^2Correct Answers225
25^2Correct Answers625
√2Correct Answers1.414
√3Correct Answers1.732
√5Correct Answers2.236
2^0Correct Answers1
2^1Correct Answers2
2^3Correct Answers8
2^4Correct Answers16
2^5Correct Answers32
2^6Correct Answers64
2^7Correct Answers128
2^8Correct Answers256
2^9Correct Answers512
prime #Correct Answers2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 43,47
ODD+ODDCorrect AnswersEVEN
ODD+EVENCorrect AnswersODD +
EVEN+EVENCorrect AnswersEVEN
ODD*ODDCorrect AnswersODD*
ODD*EVENCorrect AnswersEVEN *
EVEN*EVENCorrect AnswersEVEN2
Area of a circleCorrect Answersπ * r^2
CircumferenceCorrect Answers2 * π * radius
Volume of CylinderCorrect Answersheight * π *r^2
Volume of sphereCorrect Answers4/3 * π *r^3
Area of a TriangleCorrect Answers1/2 base * height
Right Triangle Frequent CombosCorrect Answers3 4 5 and 6 8 10 and 5 12 13
Height in Equil TriangleCorrect Answers√3/2 * side
Area of TrapezoidCorrect Answers1/2 (long base+short base) * height
,Length of diagonal for squareCorrect Answers√2 * side
Rate ProblemCorrect AnswersHow far we have to go/ how fast we are getting there
Even and Odd Numbers: Addition / SubtractionCorrect Answerseven +/- even = even;
even +/- odd = odd;
odd +/- odd = even.
Even and Odd Numbers: MultiplicationCorrect Answerseven * even = even;
even * odd = even;
odd * odd = odd.
POSITIVE AND NEGATIVE NUMBERS: MultiplicationCorrect Answerspositive *
positive = positive
positive * negative = negative
negative * negative = positive
POSITIVE AND NEGATIVE NUMBERS: DivisionCorrect Answerspositive / positive =
positive
positive / negative = negative
negative / negative = positive
The first twenty-six prime numbers areCorrect Answers2, 3, 5, 7, 11, 13, 17, 19, 23, 29,
31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,
101
Note: only positive numbers can be primes
all prime numbers above 3 are of the formCorrect Answers6n - 1 or 6n + 1
If is a positive integer greater than 1, then there is always a prime numberCorrect
AnswersP whth N<P<2N
If a number equals the sum of its proper divisors, it is said to be a perfect
number.Correct AnswersExample: The proper divisors of 6 are 1, 2, and 3: 1+2+3=6,
hence 6 is a perfect number.
If P is a prime number and P is a factor of AB thenCorrect AnswersP is a factor of A or
P is a factor of B.
Finding the Number of Factors of an IntegerCorrect Answers(p+1)(q+1)(r+1)....(z+1)
Finding the Sum of the Factors of an IntegerCorrect Answers(a^(p+1) - 1)*(b^(q+1) -
1)*(c^(r+1) - 1) / (a-1)(b-1)(c-1)
Greatest Common Factor (Divisior) - GCF (GCD)Correct AnswersThe greatest common
divisor (gcd), also known as the greatest common factor (gcf), or
highest common factor (hcf), of two or more non-zero integers, is the largest positive
integer that divides the numbers without a remainder.
Every common divisor of a and b is a divisor ofCorrect Answersgcd(a, b).
gcd(a, b)*lcm(a, b)Correct Answersa*b
Lowest Common Multiple - LCMCorrect AnswersThe 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
and of b. Since it is a multiple, it can be divided by a and b without a remainder. If either
a or b is 0, so that there is no such positive integer, then lcm(a, b) is defined to be zero.
To find the LCM, you will need to do prime-factorization. Then multiply all the factors
(pick the highest power of the common factors).
, Perfect SquareCorrect AnswersA perfect square, is an integer that can be written as the
square of some other integer. For
example 16=4^2, is an perfect square.
There are some tips about the perfect square:
• The number of distinct factors of a perfect square is ALWAYS ODD.
• The sum of distinct factors of a perfect square is ALWAYS ODD.
• A perfect square ALWAYS has an ODD number of Odd-factors, and EVEN number of
Even-factors.
• Perfect square always has even number of powers of prime factors.
Divisibility Rules - 2Correct Answers2 - If the last digit is even, the number is divisible by
2.
Divisibility Rules - 3Correct Answers3 - If the sum of the digits is divisible by 3, the
number is also.
Divisibility Rules - 4Correct Answers4 - If the last two digits form a number divisible by
4, the number is also
Divisibility Rules - 5Correct Answers5 - If the last digit is a 5 or a 0, the number is
divisible by 5.
Divisibility Rules - 6Correct Answers6 - If the number is divisible by both 3 and 2, it is
also divisible by 6.
Divisibility Rules - 7Correct Answers7 - Take the last digit, double it, and subtract it from
the rest of the number, if the answer
is divisible by 7 (including 0), then the number is divisible by 7.
Divisibility Rules - 8Correct Answers8 - If the last three digits of a number are divisible
by 8, then so is the whole number
Divisibility Rules - 9Correct Answers9 - If the sum of the digits is divisible by 9, so is the
number
Divisibility Rules - 10Correct Answers10 - If the number ends in 0, it is divisible by 10.
Divisibility Rules - 11Correct Answers11 - If you sum every second digit and then
subtract all other digits and the answer is: 0,
or is divisible by 11, then the number is divisible by 11.
Example: to see whether 9,488,699 is divisible by 11, sum every second digit:
4+8+9=21, then subtract the sum of other digits: 21-(9+8+6+9)=-11, -11 is divisible by
11, hence 9,488,699 is divisible by 11.
Divisibility Rules - 12Correct Answers12 - If the number is divisible by both 3 and 4, it is
also divisible by 12.
Divisibility Rules - 25Correct Answers25 - Numbers ending with 00, 25, 50, or 75
represent numbers divisible by 25.
The number of trailing zeros in the decimal representation of n!, the factorial of a
nonnegative
integer n, can be determined with this formula:Correct Answersn/5 + n/5^2 + n/5^3 + ...
+ n/5^k
Finding the number of powers of a prime number P, in the N!.Correct Answersn/p +
n/p^2 + n/p^3... till p^x < n
Sum of n consecutive integers equalsCorrect Answersthe mean multiplied by the
number of terms,
If n is odd, the sum of consecutive integers is always divisibleCorrect Answersby n
2^2Correct Answers4
1^2Correct Answers1
3^2Correct Answers9
4^2Correct Answers16
5^2Correct Answers25
6^2Correct Answers36
7^2Correct Answers49
8^2Correct Answers64
9^2Correct Answers81
10^2Correct Answers100
11^2Correct Answers121
12^2Correct Answers144
13^2Correct Answers169
14^2Correct Answers196
15^2Correct Answers225
25^2Correct Answers625
√2Correct Answers1.414
√3Correct Answers1.732
√5Correct Answers2.236
2^0Correct Answers1
2^1Correct Answers2
2^3Correct Answers8
2^4Correct Answers16
2^5Correct Answers32
2^6Correct Answers64
2^7Correct Answers128
2^8Correct Answers256
2^9Correct Answers512
prime #Correct Answers2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 43,47
ODD+ODDCorrect AnswersEVEN
ODD+EVENCorrect AnswersODD +
EVEN+EVENCorrect AnswersEVEN
ODD*ODDCorrect AnswersODD*
ODD*EVENCorrect AnswersEVEN *
EVEN*EVENCorrect AnswersEVEN2
Area of a circleCorrect Answersπ * r^2
CircumferenceCorrect Answers2 * π * radius
Volume of CylinderCorrect Answersheight * π *r^2
Volume of sphereCorrect Answers4/3 * π *r^3
Area of a TriangleCorrect Answers1/2 base * height
Right Triangle Frequent CombosCorrect Answers3 4 5 and 6 8 10 and 5 12 13
Height in Equil TriangleCorrect Answers√3/2 * side
Area of TrapezoidCorrect Answers1/2 (long base+short base) * height
,Length of diagonal for squareCorrect Answers√2 * side
Rate ProblemCorrect AnswersHow far we have to go/ how fast we are getting there
Even and Odd Numbers: Addition / SubtractionCorrect Answerseven +/- even = even;
even +/- odd = odd;
odd +/- odd = even.
Even and Odd Numbers: MultiplicationCorrect Answerseven * even = even;
even * odd = even;
odd * odd = odd.
POSITIVE AND NEGATIVE NUMBERS: MultiplicationCorrect Answerspositive *
positive = positive
positive * negative = negative
negative * negative = positive
POSITIVE AND NEGATIVE NUMBERS: DivisionCorrect Answerspositive / positive =
positive
positive / negative = negative
negative / negative = positive
The first twenty-six prime numbers areCorrect Answers2, 3, 5, 7, 11, 13, 17, 19, 23, 29,
31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,
101
Note: only positive numbers can be primes
all prime numbers above 3 are of the formCorrect Answers6n - 1 or 6n + 1
If is a positive integer greater than 1, then there is always a prime numberCorrect
AnswersP whth N<P<2N
If a number equals the sum of its proper divisors, it is said to be a perfect
number.Correct AnswersExample: The proper divisors of 6 are 1, 2, and 3: 1+2+3=6,
hence 6 is a perfect number.
If P is a prime number and P is a factor of AB thenCorrect AnswersP is a factor of A or
P is a factor of B.
Finding the Number of Factors of an IntegerCorrect Answers(p+1)(q+1)(r+1)....(z+1)
Finding the Sum of the Factors of an IntegerCorrect Answers(a^(p+1) - 1)*(b^(q+1) -
1)*(c^(r+1) - 1) / (a-1)(b-1)(c-1)
Greatest Common Factor (Divisior) - GCF (GCD)Correct AnswersThe greatest common
divisor (gcd), also known as the greatest common factor (gcf), or
highest common factor (hcf), of two or more non-zero integers, is the largest positive
integer that divides the numbers without a remainder.
Every common divisor of a and b is a divisor ofCorrect Answersgcd(a, b).
gcd(a, b)*lcm(a, b)Correct Answersa*b
Lowest Common Multiple - LCMCorrect AnswersThe 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
and of b. Since it is a multiple, it can be divided by a and b without a remainder. If either
a or b is 0, so that there is no such positive integer, then lcm(a, b) is defined to be zero.
To find the LCM, you will need to do prime-factorization. Then multiply all the factors
(pick the highest power of the common factors).
, Perfect SquareCorrect AnswersA perfect square, is an integer that can be written as the
square of some other integer. For
example 16=4^2, is an perfect square.
There are some tips about the perfect square:
• The number of distinct factors of a perfect square is ALWAYS ODD.
• The sum of distinct factors of a perfect square is ALWAYS ODD.
• A perfect square ALWAYS has an ODD number of Odd-factors, and EVEN number of
Even-factors.
• Perfect square always has even number of powers of prime factors.
Divisibility Rules - 2Correct Answers2 - If the last digit is even, the number is divisible by
2.
Divisibility Rules - 3Correct Answers3 - If the sum of the digits is divisible by 3, the
number is also.
Divisibility Rules - 4Correct Answers4 - If the last two digits form a number divisible by
4, the number is also
Divisibility Rules - 5Correct Answers5 - If the last digit is a 5 or a 0, the number is
divisible by 5.
Divisibility Rules - 6Correct Answers6 - If the number is divisible by both 3 and 2, it is
also divisible by 6.
Divisibility Rules - 7Correct Answers7 - Take the last digit, double it, and subtract it from
the rest of the number, if the answer
is divisible by 7 (including 0), then the number is divisible by 7.
Divisibility Rules - 8Correct Answers8 - If the last three digits of a number are divisible
by 8, then so is the whole number
Divisibility Rules - 9Correct Answers9 - If the sum of the digits is divisible by 9, so is the
number
Divisibility Rules - 10Correct Answers10 - If the number ends in 0, it is divisible by 10.
Divisibility Rules - 11Correct Answers11 - If you sum every second digit and then
subtract all other digits and the answer is: 0,
or is divisible by 11, then the number is divisible by 11.
Example: to see whether 9,488,699 is divisible by 11, sum every second digit:
4+8+9=21, then subtract the sum of other digits: 21-(9+8+6+9)=-11, -11 is divisible by
11, hence 9,488,699 is divisible by 11.
Divisibility Rules - 12Correct Answers12 - If the number is divisible by both 3 and 4, it is
also divisible by 12.
Divisibility Rules - 25Correct Answers25 - Numbers ending with 00, 25, 50, or 75
represent numbers divisible by 25.
The number of trailing zeros in the decimal representation of n!, the factorial of a
nonnegative
integer n, can be determined with this formula:Correct Answersn/5 + n/5^2 + n/5^3 + ...
+ n/5^k
Finding the number of powers of a prime number P, in the N!.Correct Answersn/p +
n/p^2 + n/p^3... till p^x < n
Sum of n consecutive integers equalsCorrect Answersthe mean multiplied by the
number of terms,
If n is odd, the sum of consecutive integers is always divisibleCorrect Answersby n
