GMAT Quant Exam Questions and
Answers
NEW FORMAT - correct answer-31 Q's
62 mins
2 mins per Q
Strat: First page 3 Q's, then seven pages of 4 Q's
Count down from 56 by 8's
Formula for sum of infinite geometric progression with common ratio |r| < 1 - correct
answer-b / (1-r)
b is first term
(Ex: 1/2, -1/4, 1/8, -1/16, ... => r = -1/2 and b = 1/2)
Circle - formulas, length of an arc trick - correct answer-Radius = r
Diameter = 2r
Area = πr²
Circumference (aka perimeter) = 2πr
360 total degrees
Can find arc length and sector area by multiplying the entire circle's area or
circumference by (central angle / 360)
Triangle inscribed in a circle - correct answer-If a triangle is inscribed in a circle so that
one of its sides is a diameter of the circle, then the triangle is a right triangle
Conversely, any right triangle inscribed in a circle means its hypotenuse is a diameter of
that circle
Triangle - types, area, properties - correct answer-Angles add up to 180˚
Sum of any 2 sides is always greater than the third length
Any side is greater than the difference between the other 2 lengths
If a triangle has sides of equal length, their corresponding angles are also equal (and
vice versa)
Equilateral = 3 equal sides and equal angles
Isosceles = 2 sides have equal length and equal angles
Scalene = no sides are the same
Acute = all angles are less than 90˚
Obtuse = has an angle above 90˚
,Area = (length of altitude • length of base) / 2
Can use Pythagorean Theorem for right triangle side lengths
Common right triangle triplets to memorize (can skip using Pythagorean Theorem and
save time) - correct answer-3-4-5
5-12-13
8-15-17
6-8-10 (this is double the 3-4-5)
10-24-26 (this is double the 5-12-13)
45-45-90 right triangle lengths ratio - correct answer-In 45-45-90 triangles, the lengths
of sides are in ratio 1:1:(√2) ( ex: 2:2:(2√2) )
(x:x:x√2)
30-60-90 right triangle lengths ratio - correct answer-In 30:60:90 triangles, the lengths of
sides are in ratio 1:(√3):2 ( ex: 3:(3√3):6 )
(x:x√3:2x)
Important note: An equilateral triangle (60-60-60) can be cut into two equal 30-60-90
triangles
Square inscribed in a circle - correct answer-Can use the circle's diameter to bisect the
rectangle into 2 equal triangles
Exponent rules - correct answer-(xʳ)(xˢ) = xʳ⁺ˢ
(xʳ)ˢ = xʳˢ = (xˢ)ʳ
xʳ/xˢ = xʳ⁻ˢ
x⁻ʳ = 1/xʳ
(xʳ)(yʳ) = (xy)ʳ
x⁰ = 1
(x/y)ʳ = xʳ/yʳ
xʳ/ˢ = ˢ√xʳ
Fundamental counting principle - correct answer-Ex: 3 different types of toppings for a
sandwich (5 types of bread, 8 types of meat, 6 types of cheese). How many types of
sandwiches can you make?
Answer: 5•8•6 = 240
Permutation - correct answer-The number (n) of ways to choose a sample of r elements
from a set of n distinct objects where order does matter and replacements are not
allowed.
nPr = (n!)/(n-r)!
, Combination - correct answer-The number of ways to choose a sample of r elements
from a set of n distinct objects where order does not matter and replacements are not
allowed.
nCr = (n!) / ( (n-r)! * r! )
Difference between permutation and combination - correct answer-Permutations are for
lists (order matters) and combinations are for groups (order doesn't matter)
Sphere - circumference, surface area and volume - correct answer-Circumference = 2πr
Surface area = 4πr²
V=(4/3)πr³
Integer - correct answer-Any whole number, can be positive negative or zero
What is 0 divisible by? - correct answer-Every integer except 0
Exponent Trick using factors - correct answer-Every number to a power is equal to the
multiplication of its factors by that power
Ex: 10⁵ = 5⁵ * 2⁵
Quadrilateral - correct answer-Polygon with 4 sides
area = (length of altitude) • (length of base)
Parallelogram - correct answer-Quadrilateral in which both pairs of opposite sides are
parallel
Opposite sides have equal length
Opposite angles are equal, adjacent angles (both on bottom or both on top) add up to
180
The diagonal will divide the parallelogram into 2 equal triangles
Area = (base)(height)
(area is NOT length*width be careful)
Trapezoid - correct answer-Quadrilateral with two sides that are parallel
area = (1/2)•(sum of the lengths of the bases)•(height)
Rectangular solids - correct answer-Surface area = sum of the areas of all the faces
(don't need to think too much about which face has what numbers associated with it,
just use formula SA=2lw+2lh+2wh )
Volume = (length)•(width)•(height)
in other words, (area of base)•(height)
Diagonal of a cube: (side length)•√3
Answers
NEW FORMAT - correct answer-31 Q's
62 mins
2 mins per Q
Strat: First page 3 Q's, then seven pages of 4 Q's
Count down from 56 by 8's
Formula for sum of infinite geometric progression with common ratio |r| < 1 - correct
answer-b / (1-r)
b is first term
(Ex: 1/2, -1/4, 1/8, -1/16, ... => r = -1/2 and b = 1/2)
Circle - formulas, length of an arc trick - correct answer-Radius = r
Diameter = 2r
Area = πr²
Circumference (aka perimeter) = 2πr
360 total degrees
Can find arc length and sector area by multiplying the entire circle's area or
circumference by (central angle / 360)
Triangle inscribed in a circle - correct answer-If a triangle is inscribed in a circle so that
one of its sides is a diameter of the circle, then the triangle is a right triangle
Conversely, any right triangle inscribed in a circle means its hypotenuse is a diameter of
that circle
Triangle - types, area, properties - correct answer-Angles add up to 180˚
Sum of any 2 sides is always greater than the third length
Any side is greater than the difference between the other 2 lengths
If a triangle has sides of equal length, their corresponding angles are also equal (and
vice versa)
Equilateral = 3 equal sides and equal angles
Isosceles = 2 sides have equal length and equal angles
Scalene = no sides are the same
Acute = all angles are less than 90˚
Obtuse = has an angle above 90˚
,Area = (length of altitude • length of base) / 2
Can use Pythagorean Theorem for right triangle side lengths
Common right triangle triplets to memorize (can skip using Pythagorean Theorem and
save time) - correct answer-3-4-5
5-12-13
8-15-17
6-8-10 (this is double the 3-4-5)
10-24-26 (this is double the 5-12-13)
45-45-90 right triangle lengths ratio - correct answer-In 45-45-90 triangles, the lengths
of sides are in ratio 1:1:(√2) ( ex: 2:2:(2√2) )
(x:x:x√2)
30-60-90 right triangle lengths ratio - correct answer-In 30:60:90 triangles, the lengths of
sides are in ratio 1:(√3):2 ( ex: 3:(3√3):6 )
(x:x√3:2x)
Important note: An equilateral triangle (60-60-60) can be cut into two equal 30-60-90
triangles
Square inscribed in a circle - correct answer-Can use the circle's diameter to bisect the
rectangle into 2 equal triangles
Exponent rules - correct answer-(xʳ)(xˢ) = xʳ⁺ˢ
(xʳ)ˢ = xʳˢ = (xˢ)ʳ
xʳ/xˢ = xʳ⁻ˢ
x⁻ʳ = 1/xʳ
(xʳ)(yʳ) = (xy)ʳ
x⁰ = 1
(x/y)ʳ = xʳ/yʳ
xʳ/ˢ = ˢ√xʳ
Fundamental counting principle - correct answer-Ex: 3 different types of toppings for a
sandwich (5 types of bread, 8 types of meat, 6 types of cheese). How many types of
sandwiches can you make?
Answer: 5•8•6 = 240
Permutation - correct answer-The number (n) of ways to choose a sample of r elements
from a set of n distinct objects where order does matter and replacements are not
allowed.
nPr = (n!)/(n-r)!
, Combination - correct answer-The number of ways to choose a sample of r elements
from a set of n distinct objects where order does not matter and replacements are not
allowed.
nCr = (n!) / ( (n-r)! * r! )
Difference between permutation and combination - correct answer-Permutations are for
lists (order matters) and combinations are for groups (order doesn't matter)
Sphere - circumference, surface area and volume - correct answer-Circumference = 2πr
Surface area = 4πr²
V=(4/3)πr³
Integer - correct answer-Any whole number, can be positive negative or zero
What is 0 divisible by? - correct answer-Every integer except 0
Exponent Trick using factors - correct answer-Every number to a power is equal to the
multiplication of its factors by that power
Ex: 10⁵ = 5⁵ * 2⁵
Quadrilateral - correct answer-Polygon with 4 sides
area = (length of altitude) • (length of base)
Parallelogram - correct answer-Quadrilateral in which both pairs of opposite sides are
parallel
Opposite sides have equal length
Opposite angles are equal, adjacent angles (both on bottom or both on top) add up to
180
The diagonal will divide the parallelogram into 2 equal triangles
Area = (base)(height)
(area is NOT length*width be careful)
Trapezoid - correct answer-Quadrilateral with two sides that are parallel
area = (1/2)•(sum of the lengths of the bases)•(height)
Rectangular solids - correct answer-Surface area = sum of the areas of all the faces
(don't need to think too much about which face has what numbers associated with it,
just use formula SA=2lw+2lh+2wh )
Volume = (length)•(width)•(height)
in other words, (area of base)•(height)
Diagonal of a cube: (side length)•√3
