GMAT Quant Exam with Complete
Solutions
2^2 - correct answer-4
1^2 - correct answer-1
3^2 - correct answer-9
4^2 - correct answer-16
5^2 - correct answer-25
6^2 - correct answer-36
7^2 - correct answer-49
8^2 - correct answer-64
9^2 - correct answer-81
10^2 - correct answer-100
11^2 - correct answer-121
12^2 - correct answer-144
13^2 - correct answer-169
14^2 - correct answer-196
15^2 - correct answer-225
25^2 - correct answer-625
√2 - correct answer-1.414
√3 - correct answer-1.732
√5 - correct answer-2.236
,2^0 - correct answer-1
2^1 - correct answer-2
2^3 - correct answer-8
2^4 - correct answer-16
2^5 - correct answer-32
2^6 - correct answer-64
2^7 - correct answer-128
2^8 - correct answer-256
2^9 - correct answer-512
prime # - correct answer-2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 43,47
ODD+ODD - correct answer-EVEN
ODD+EVEN - correct answer-ODD +
EVEN+EVEN - correct answer-EVEN
ODD*ODD - correct answer-ODD*
ODD*EVEN - correct answer-EVEN *
EVEN*EVEN - correct answer-EVEN2
Area of a circle - correct answer-π * r^2
Circumference - correct answer-2 * π * radius
Volume of Cylinder - correct answer-height * π *r^2
Volume of sphere - correct answer-4/3 * π *r^3
Area of a Triangle - correct answer-1/2 base * height
Right Triangle Frequent Combos - correct answer-3 4 5 and 6 8 10 and 5 12 13
Height in Equil Triangle - correct answer-√3/2 * side
,Area of Trapezoid - correct answer-1/2 (long base+short base) * height
Length of diagonal for square - correct answer-√2 * side
Rate Problem - correct answer-How far we have to go/ how fast we are getting there
Even and Odd Numbers: Addition / Subtraction - correct answer-even +/- even = even;
even +/- odd = odd;
odd +/- odd = even.
Even and Odd Numbers: Multiplication - correct answer-even * even = even;
even * odd = even;
odd * odd = odd.
POSITIVE AND NEGATIVE NUMBERS: Multiplication - correct answer-positive *
positive = positive
positive * negative = negative
negative * negative = positive
POSITIVE AND NEGATIVE NUMBERS: Division - correct answer-positive / positive =
positive
positive / negative = negative
negative / negative = positive
The first twenty-six prime numbers are - correct answer-2, 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 form - correct answer-6n - 1 or 6n + 1
If is a positive integer greater than 1, then there is always a prime number - correct
answer-P whth N<P<2N
If a number equals the sum of its proper divisors, it is said to be a perfect number. -
correct answer-Example: 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 then - correct answer-P is a factor of A or
P is a factor of B.
Finding the Number of Factors of an Integer - correct answer-(p+1)(q+1)(r+1)....(z+1)
Finding the Sum of the Factors of an Integer - correct answer-(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 answer-The 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 of - correct answer-gcd(a, b).
gcd(a, b)*lcm(a, b) - correct answer-a*b
Lowest Common Multiple - LCM - correct answer-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
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 Square - correct answer-A 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 - 2 - correct answer-2 - If the last digit is even, the number is divisible
by 2.
Divisibility Rules - 3 - correct answer-3 - If the sum of the digits is divisible by 3, the
number is also.
Divisibility Rules - 4 - correct answer-4 - If the last two digits form a number divisible by
4, the number is also
Divisibility Rules - 5 - correct answer-5 - If the last digit is a 5 or a 0, the number is
divisible by 5.
Divisibility Rules - 6 - correct answer-6 - If the number is divisible by both 3 and 2, it is
also divisible by 6.
Divisibility Rules - 7 - correct answer-7 - 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.
Solutions
2^2 - correct answer-4
1^2 - correct answer-1
3^2 - correct answer-9
4^2 - correct answer-16
5^2 - correct answer-25
6^2 - correct answer-36
7^2 - correct answer-49
8^2 - correct answer-64
9^2 - correct answer-81
10^2 - correct answer-100
11^2 - correct answer-121
12^2 - correct answer-144
13^2 - correct answer-169
14^2 - correct answer-196
15^2 - correct answer-225
25^2 - correct answer-625
√2 - correct answer-1.414
√3 - correct answer-1.732
√5 - correct answer-2.236
,2^0 - correct answer-1
2^1 - correct answer-2
2^3 - correct answer-8
2^4 - correct answer-16
2^5 - correct answer-32
2^6 - correct answer-64
2^7 - correct answer-128
2^8 - correct answer-256
2^9 - correct answer-512
prime # - correct answer-2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 43,47
ODD+ODD - correct answer-EVEN
ODD+EVEN - correct answer-ODD +
EVEN+EVEN - correct answer-EVEN
ODD*ODD - correct answer-ODD*
ODD*EVEN - correct answer-EVEN *
EVEN*EVEN - correct answer-EVEN2
Area of a circle - correct answer-π * r^2
Circumference - correct answer-2 * π * radius
Volume of Cylinder - correct answer-height * π *r^2
Volume of sphere - correct answer-4/3 * π *r^3
Area of a Triangle - correct answer-1/2 base * height
Right Triangle Frequent Combos - correct answer-3 4 5 and 6 8 10 and 5 12 13
Height in Equil Triangle - correct answer-√3/2 * side
,Area of Trapezoid - correct answer-1/2 (long base+short base) * height
Length of diagonal for square - correct answer-√2 * side
Rate Problem - correct answer-How far we have to go/ how fast we are getting there
Even and Odd Numbers: Addition / Subtraction - correct answer-even +/- even = even;
even +/- odd = odd;
odd +/- odd = even.
Even and Odd Numbers: Multiplication - correct answer-even * even = even;
even * odd = even;
odd * odd = odd.
POSITIVE AND NEGATIVE NUMBERS: Multiplication - correct answer-positive *
positive = positive
positive * negative = negative
negative * negative = positive
POSITIVE AND NEGATIVE NUMBERS: Division - correct answer-positive / positive =
positive
positive / negative = negative
negative / negative = positive
The first twenty-six prime numbers are - correct answer-2, 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 form - correct answer-6n - 1 or 6n + 1
If is a positive integer greater than 1, then there is always a prime number - correct
answer-P whth N<P<2N
If a number equals the sum of its proper divisors, it is said to be a perfect number. -
correct answer-Example: 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 then - correct answer-P is a factor of A or
P is a factor of B.
Finding the Number of Factors of an Integer - correct answer-(p+1)(q+1)(r+1)....(z+1)
Finding the Sum of the Factors of an Integer - correct answer-(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 answer-The 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 of - correct answer-gcd(a, b).
gcd(a, b)*lcm(a, b) - correct answer-a*b
Lowest Common Multiple - LCM - correct answer-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
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 Square - correct answer-A 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 - 2 - correct answer-2 - If the last digit is even, the number is divisible
by 2.
Divisibility Rules - 3 - correct answer-3 - If the sum of the digits is divisible by 3, the
number is also.
Divisibility Rules - 4 - correct answer-4 - If the last two digits form a number divisible by
4, the number is also
Divisibility Rules - 5 - correct answer-5 - If the last digit is a 5 or a 0, the number is
divisible by 5.
Divisibility Rules - 6 - correct answer-6 - If the number is divisible by both 3 and 2, it is
also divisible by 6.
Divisibility Rules - 7 - correct answer-7 - 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.
