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