SAT Practice Test 2, Section 3: Questions 11  15
The following are worked solutions for the questions in the math sections of the SAT Practice Tests found in the Official SAT Study Guide.
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11. Correct answer: (A)
Given:
The figure
To find:
The true statement
Solution:
Topic(s): supplementary angles
x and y are supplementary angles
x + y = 180. If x > 90 the y < 90
Answer: (A) y < 90
12. Correct answer: (D)
Given:
The line with equation y = 5x – 10
The line crosses the xaxis at point (a, b)
To find:
The value of a
Solution:
Topic(s): Coordinate geometry
At the point where the line crosses the xaxis the value of y will be 0.
Substitute y = 0, and x = a, into y = 5x – 10.
0 = 5a – 10 ⇒ 5a = 10 ⇒ a = 2
Answer: (D) 2
13. Correct answer: (E)
Given:
The noon temperature for 7 cities
The median temperature is 40
To find:
The temperature (t) that city D cannot be
Solution:
Topic(s): Statistics
Write out the numbers in increasing order.
27 33 40 44 50 68
In order for 40 to be the median i.e. in the middle, t needs to on the left of 40. This means that t < 40.
We are required to find the answer that does not fit the criteria.
Only (E) 42 is greater than 40.
Answer: (E) 42
14. Correct answer: (D)
Given:
The figure
To find:
Perimeter of the figure
Solution:
Topic(s): complementary angles, equilateral triangle, perimeter
To get the perimeter of the figure, we need to know the lengths of PC and PD.
Given the right angles and the lengths of the three sides, we can deduce that ABCD is a square. So, we know that the length of CD is 6.
Angles ACP and PCD are complementary angles.
So, angle PCD = 90º – angle ACP = 90º – 30º = 60º.
In the same way, angles BDP and PDC are complementary angles.
So, angle PDC = 90º – angle BDP = 90º – 30º = 60º.
Triangle PCD has two angles that are 60º. When a triangle has two 60º angles, it must be an equilateral triangle that has three equal sides. Since the length of CD is 6. We can deduce that the lengths of PC and PD are also 6.
Now, we can calculate the perimeter of the figure = 6 + 6 + 6 + 6 + 6 = 30
Answer: (D) 30
15. Correct answer: (C)
Given:
m is the greatest prime factor of 38
n is the greatest prime factor of 100
To find:
m + n
Solution:
Topic(s): Factors
The factors of 38 are: 1 × 38, 2 × 19.
The greatest prime factor of 38 is 19 = m.
The factors of 100 are: 1 × 100, 2 × 50, 4 × 24, 5 × 20, 10 ×10.
The greatest prime factor of 100 is 5 = n.
m + n = 19 + 5 = 24
Answer: (C) 24
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