698 MCGRAW-HILL’S SAT
4.B If you have the patience, you can write out a
quick calendar for yourself to track the days:
Or you can use the simple fact that successive Tues-
days (like any other days) are always 7 days apart.
Therefore, if the 1st of the month is a Tuesday, so are
the 8th, the 15th, the 22nd, and the 29th. Therefore, the
30th is a Wednesday and the 31st is a Thursday.
(Chapter 9, Lesson 3: Numerical Reasoning Problems)
5.A From the given information: m= 8 n
0 < m+n< 50
Substitute for m: 0 < 8n+n< 50
Combine like terms: 0 < 9n< 50
Divide by 9: 0 < n< 5^5 ⁄ 9Since nmust be an integer, ncan be 1, 2, 3, 4, or 5.
(Chapter 8, Lesson 6: Inequalities, Absolute Values,
and Plugging In)
6.D First find the value of y: y% of 50 is 32.Simplify:
Cross-multiply: 50 y=3,200
Divide by 50: y= 64What is 200% of 64?
Interpret: 2.00 × 64 = 128
(Chapter 7, Lesson 5: Percents)
7.B g(x) =x+x1/2
Plug in 16 for x: g(16) = 16 + 16 1/2
Take square root of 16: g(16) = 16 + 4
Combine like terms: g(16) = 20(Chapter 11, Lesson 2: Functions)
8.C The slope of the line is −^3 ⁄ 4 , so use the slope
equation and the coordinates of point A (0, 12) to find
the coordinates of point B (x,0):
Cross-multiply: 4(−12) =−3(x)
Simplify: − 48 =− 3 x
Divide by −3: 16 =xThe base of the triangle is 16, and its height is 12.
Area =^1 ⁄ 2 (base)(height)
Substitute: Area =^1 ⁄ 2 (16)(12)
Simplify: Area = 96
(Chapter 10, Lesson 4: Coordinate Geometry)
m
yy
xx x x=
−
−
=
−
−
=
−
(^21) =−
21
012
0
12 3
4
y
100×=50 32
9.A Find the sum of each repetition of the pattern:
− 1 + 1 + 2 = 2
Next, determine how many times the pattern
repeats in the first 25 terms: 25 ÷ 3 = 8 with a
remainder of 1.
Multiply the sum of the pattern by 8 to obtain the sum
of the first 24 terms: 2 × 8 = 16
The 25th term is −1, which makes the sum 16 +− 1 =15.
(Chapter 11, Lesson 1: Sequences)10.D The ratio of white marbles to blue marbles is
4 to b.The probability of randomly selecting a white
marble from the jar is^1 ⁄ 4. This means that one out of
every four marbles in the jar is white and three out of
every four marbles are blue. If there are four white
marbles, then there are 4 × 3 =12 blue marbles.
(Chapter 7, Lesson 4: Ratios and Proportions)11.B Area =^1 ⁄ 2 (base)(height)
Substitute: 10 =^1 ⁄ 2 (base)(height)
Divide by^1 ⁄ 2 : 20 =(base)(height)
The base and the height are both integers. Find all the
“factor pairs” of 20: 1, 20; 2, 10; and 4, 5
Plug each pair into the Pythagorean theorem to find
the least possible length of the hypotenuse:
a^2 +b^2 =c^2
42 + 52 =c^2
Combine like terms: 41 =c^2
Take square root:
a^2 +b^2 =c^2
22 + 102 =c^2
Combine like terms: 104 =c^2
Take square root:
a^2 +b^2 =c^2
12 + 202 =c^2
Combine like terms: 401 =c^2
Take square root:
is the shortest possible hypotenuse.
(Chapter 10, Lesson 5: Areas and Perimeters)
(Chapter 10, Lesson 3: The Pythagorean Theorem)12.B −1 < y< 0
This means that yis a negative decimal fraction.
Answer choices (A), (C), and (E) will all be negative num-
bers. Answer choices (B) and (D) are positive numbers.
When you raise a simple fraction to a positive number
larger than 1, it gets smaller. y^4 < y^2 , which makes (B) the
greatest value. Pick a value like y=−^1 ⁄ 2 and see.
(Chapter 9, Lesson 3: Numerical Reasoning Problems)41
401 =c104 =c41 =cSu M T W Th FSa
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