What is the highest number of high school students who will not be assigned
to the team they prefer?
A) 30
B) 35
C) 40
D) 45
E) 50
A taxi leaves the Point A 5 hours after a bus left the same spot. The bus
is traveling 30 mph slower than the taxi. Find the speed of the
taxi, if it overtakes the bus in three hours.
A)
36
B)
38
C)
40
D)
42
E)
44
Two cars start at the same time from opposite ends of a
highway that is 45 miles long. One car is riding at 14 mph
and the second cyclist is riding at 16 mph. How long after
they begin will they meet?
A)
1
B)
1.2
C)
1.25
D)
1.35
E)
1.5
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49
50
51
52
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Exponents
Venn Diagram
Answer Key:
1) E
2) A
3) C
4) A
5) E
53
54
6) E
7) E
8) C
9) B
10) D
11) D
12) E
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Page 91
Isosceles
Isosceles
If angle a = c, then
side length D = E
When this condition is met, the triangle
is called an isosceles
If angle a = c, then
side length D = E
When this condition is met, the triangle
is called an isosceles
b
c
a
D
E
F
Right Isosceles
Right Isosceles
A right isosceles is a specific type of
isosceles triangle where the angles
are 45-45-90 as shown.
A right isosceles is a specific type of
isosceles triangle where the angles
are 45-45-90 as shown.
x
x
2
x
Right Isosceles
Right Isosceles
Hypotenuse = ?
Hypotenuse =
Hypotenuse = ?
Hypotenuse =
a
b
h
y
p
o
t
e
n
u
s
2
2
b
a
45
˚
45
˚
90
˚
Circle
Circle
Area =
π
r
2
Circumference =
π
*diameter (Rhymes: “pi”
“di”)
Area =
π
r
2
Circumference =
π
*diameter (Rhymes: “pi”
“di”)
r
Triangle Area =
Triangle Area =
height
base
*
2
1
Cylinder/Sphere
Cylinder/Sphere
Volume of cylinder = Area of circle * how far that circle extends
Volume of cylinder =
π
r
2
* height
Volume sphere =
Volume of cylinder = Area of circle * how far that circle extends
Volume of cylinder =
π
r
2
* height
Volume sphere =
3
3
4
r
2 miles
1 mile
30
˚
60
˚
90
˚
Triangle
Right
3
2
x
x
x
3
4
5
5
12
13
Know these triangle
ratios!
2
2
2
c
b
a
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GMAT Quant: Problem Solving

Page 92
GMAT Quant: Problem Solving

Page 93
Sum of Sequences
Sequences:
Sum, Average, # of terms
Sum:
What is sum of all multiples of 3
from 1 to 100?
Average:
What is the average of all these
multiples of 3?
# of Terms:
How many numbers are
multiples of 3 between 1 and 100?
Sequences:
Sum, Average, # of terms
Sum:
What is sum of all multiples of 3
from 1 to 100?
Average:
What is the average of all these
multiples of 3?
# of Terms: