QUANTITATIVE REASONING
ANSWER KEY: SECTION 3
14. 21.93 Miles.
This problem tests your ability to calculate the sides of a triangle. The easiest way to answer this problem is to
sketch out the course of the boat.
END
c
30
h
30°
120°
30°
b
8
30°
START
30
Now use your knowledge of a 30-60-
90 triangle to work out the measurements for
h
and
b
. First write down the
relationships:
short leg
12
hypotenuse
√3
long leg
2
hypotenuse
tarting ith the s all
triangle or ed a ter the first turn ou see the h potenuse is . he ne t turn
happens to or another
triangle in the opposite direction ith a h potenuse o . o find
h
you then get:
h
8 30
2
2
o find
b
you use:
√3
√3
b
2
8 – 2
√3
Now use the Pythagorean Theorem, plugging in the values for
h
and
b
:
distance
√(192
√3)2
.
Enter 21.93 miles in the text box.
297
PRACTICE TEST 2
ARGOPREP.COM/GRE
QUANTITATIVE REASONING
ANSWER KEY: SECTION 3
15. 91.
This problem tests your ability to use the Pythagorean Theorem. You are given:
s
= 6 and
r
= 7. From this you need to find the area o rectangle
ABCD
. o start ou ill find it help ul to add a couple o labels to the diagra
A
B
r
s
h
x
D
C
You start by calculating
h
and
x
using the Pythagorean theorem:
h
2
r
2
r x
)2
Pythagorean Theorem for base of triangle opposite
x
h
2
s
2
x
2
Pythagorean Theorem for
x
s
2
x
2
r
2
r x
)2
Substitute
s
2
x
2
r
2
r
2
rx x
2
Expand the exponent
62
x
2
2
2
x x
2
Substitute values
x
Simplify
x
36
Solve for
x
14
e t find
h
using the simplest equation:
h
2
2
36
14
h
36 – 36
13
√
14
√ 1 – 1
14
√ 14
Now relate the area of the triangle to the dimension that you know:
Area of the
rectangle BC CD
irst find a calculable e pression or
CD
:
CD
2
r
2
BC
2
Pythagorean Theorem
CD
√4
r
2
BC
2
Take the square root
CD
√4
r
2
h
)2
Substitute
298
ARGOPREP.COM/GRE
QUANTITATIVE REASONING
ANSWER KEY: SECTION 3
Now substitute the known values into the area formula:
Area of the rectangle
h
√4
r
2
h
2
Substitution
2
Area of the rectangle
6 13
4(72
6 13
ubstitute and calculate
√ 14
√
√ 14
Be sure to follow instructions and round to the nearest whole
number. Enter
91
in the text box.
16. A.
his proble tests our s ill ith calculating percentages. o find the percentage
decrease use the or ula
percent decrease = starting value – end value
starting value
Substituting the values from the chart you get:
280,000 – 240,000
40,000
.
280,000
280,000
The correct answer choice is
A
.
17. B.
This problem tests your understanding of median, and how to calculate an increase by percentage. First, create a
set of the data points on the chart using the salary value for each year:
{260,000, 280,000, 240,000, 230,000, 240,000}
Now sort the set by value:
{280,000, 260,000, 240,000, 240,000, 230,000}
The median is the center element: 240,000. Now calculate the 10% increase:
salary
.
The correct answer choice is
B
.
18. D.
This problem tests your ability to translate a word problem into a geometry problem and calculate a complex
area. ou are loo ing or the area enclosed b three ad acent circles each ith a radius o . he first thing to do
is s etch out a diagra o the figure description
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