SAT Practice Test 3, Section 8: Questions 11  16
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:
To find:
The possible values of n
Solution:
Topic(s): Symbol problems
We then test the given statements for the values of n:
Answer: (A) I only
12. Correct answer: (B)
Given:
20% of x = 80% of y
To find:
y in terms of x
Solution:
Topic(s): Percent
Translate ‘of” as ‘×’
Convert between percent and decimal.
Answer: (B) y = 25%x
13. Correct answer: (C)
Given:
x + y is even
(x + y) 2 + x + z is odd
x, y and z are positive integers
To find:
The statement that is true
Solution:
Topic(s): Odd and even numbers
You were given that x + y is even.
Applying the rule: Even × Even = Even
(x + y)^{2} = (x + y) × (x + y) = Even
You were also given that (x + y)^{2} + x + z is odd.
Applying the rule: Even + Odd = Odd
Since (x + y)^{2} is even, so, x + z is odd
Applying the same rule again: Even + Odd = Odd
If z is even, then x must be odd.
Answer: (C) If z is even, then x must be odd.
14. Correct answer: (E)
Given:
0 < x < 1
To find:
The statements that must be true
Solution:
Topic(s): Fractions
Given 0 < x < 1, we can say the x is a positive fraction with a value less than 1.
If a positive fraction with a value less than 1 is raised to a positive integer exponent then the larger the exponent the smaller the result.
This means that conditions I. x 2 > x 3 and III. x > x 3 are true.
Half of a positive integer is less than the original integer.
This means that condition II. is true.
Answer: (E) I, II and III
15. Correct answer: (A)
Given:
A scatter plot
To find:
The function that models the relationship between t, the number of seconds to complete the maze and p, the number of practices.
Solution:
If we were to draw a line to reflect the approximate values of the data on the graph, we would get a horizontal line that intersects the yaxis between 40 and 50.
A horizontal line would have an equation of the form t(p) = c, where c is a constant.
Out of all the answers given only (A) t(p) = 40, satisfies that condition.
Answer: (A) t(p) = 40
16. Correct answer: (E)
Given:
The pattern consisting of 5 L by W rectangles
To find:
The number of L by W rectangles needed to cover a region 12L by 10L
Solution:
Since the region to be covered is given is in terms of L, we would want to get the width and length of the above pattern to be in terms of L as well.
The above pattern forms a rectangle.
From the two vertical sides, we know that:
The width of the rectangle is then
The above pattern is a rectangle with dimensions:
In order to cover the region without any leftovers, we need to place the width of the rectangle along the side that is 10L. The number of rectangles that we can place along the side 10L is:
The length of the rectangle is 2L. The number of rectangles that can be placed along the side 12L is 12L ÷ 2L = 6.
So, we would need 6 × 6 = 36 of rectangles with the above pattern.
Be careful! The question wants the number of rectangles of dimensions L by W.
The above pattern has 5 rectangles of dimensions L by W.
So, the answer is 36 × 5 = 180
Answer: (E) 180
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