Sat math Essentials

10.
510
If 32% of the students have left the audito-
rium, then 100 – 32 = 68% of the students are
still in the auditorium; 68% of 750 =
(0.68)(750) = 510 students.
11.
15
Use the distance formula to find the distance
from (–1,2) to (11,–7):
Distance = 
(
x
2
– 
x
1
)
2
+ (
y
2
– 
y
1
)
2
Distance = 
(11 – (
–1))
2
+
((–7)
– 2)
2
Distance = 
(12)
2
+
(–9)
2
Distance = 
144 + 8
1
Distance = 
225
Distance = 15 units
12.
17.6
If Robert averages 16.3 feet for five jumps,
then he jumps a total of (16.3)(5) = 81.5 feet.
The sum of Robert’s first four jumps is 12.4 ft
+ 18.9 ft + 17.3 ft + 15.3 ft = 63.9 ft. There-
fore, the measure of his fifth jump is equal to
81.5 ft – 63.9 ft = 17.6 ft.
13.
35
The order of the four students chosen does
not matter. This is a “seven-choose-four”
combination problem—be sure to divide to
avoid counting duplicates:
(
(
7
4
)
)
(
(
6
3
)
)
(
(
5
2
)
)
(
(
4
1
)
)
= 
8
2
4
4
0
=
35. There are 35 different groups of four stu-
dents that Mr. Randall could form.
14.
4,000
The Greenvale sales, represented by the light
bars, for the months of January through May
respectively were $22,000, $36,000, $16,000,
$12,000, and $36,000, for a total of $122,000.
The Smithtown sales, represented by the dark
bars, for the months of January through May
respectively were $26,000, $32,000, $16,000,
$30,000, and $22,000, for a total of $126,000.
The Smithtown branch grossed $126,000 –
$122,000 = $4,000 more than the Greenvale
branch.