SAT Practice Test Solutions:
2014–15 SAT Practice Test
2013–14 SAT Practice Test
The Official SAT Study Guide, second edition
 Practice Test 1: Sections
3,
7,
8.
 Practice Test 2: Sections
2,
5,
8.
 Practice Test 3: Sections
2,
5,
8.
 Practice Test 4: Sections
3,
6,
9.
 Practice Test 5: Sections
2,
4,
8.
 Practice Test 6: Sections
2,
4,
8.
 Practice Test 7: Sections
3,
7,
9.
 Practice Test 8: Sections
3,
7,
9.
 Practice Test 9: Sections
2,
5,
8.
 Practice Test 10: Sections
2,
5,
8.
Here are solutions for section 8 of practice test #9 in The Official SAT Study Guide, second edition, found on pages 914–919. The solutions below demonstrate faster, more informal methods that might work better for you on a fastpaced test such as the SAT. To learn more about these methods, see my ebook Succeeding in SAT Math or the SAT math tips page.
 If 6,700 = 100(6k + 7), then 6,700 = 600k + 700, or 6,000 = 600k. So, k = 10. Select (C) 10.
 Convert the sentence into an equation: Convert the first half of the sentence into an equation (to be precise, inequality):
3  3

more than  +

n  n

is a negative number  < 0

 Convert the sentence into an equation: Similarly, convert the second half of the sentence into an inequality:
5  5

more than  +

n  n

is a positive number  > 0

 So, we now have, 3 + n < 0 and 5 + n > 0. So, n has to be between −3 and −5 (but not −3 or −5).
 Look at the answer choices: The only answer between −3 and −5 is (B) −4. Select that answer.
 Since the dotted lines bisect the angles with measures x° and y°, then z = ½x + ½y = ½(70) + ½(40) = 55. Select (E) 55.
 Guess and check: Try each answer until you find one that does not fit:
 For (A), if there are 20 pieces of fruit in the basket, then there are 8 apples, so eliminate that answer.
 For (B), if there are 35 pieces of fruit, then there are 14 apples. Eliminate that answer.
 For (C), if there are 52 pieces of fruit, then there are 20.4 apples. It doesn't make sense to have a fractional number of apples, so this must be our answer. Select (C) 52.
 Draw a diagram: You may find it helpful to draw a square and an equilateral triangle to picture the problem.
 Estimate the answer: If the two shapes have equal perimeters, and the square has more sides thant the triangle, then the sides of the triangle must be a bit bigger than 3, perhaps 4 or so.
 Look at the answer choices: We can definitely eliminate answers (A) and (B). (C) seems the best guess, but it's probably a good idea to spend a bit more time confirming it.
 If the square has sides of length 3, its perimeter is 12. If the equilateral triangle has a perimeter of 12, then each side must be 12 ÷ 3 = 4. Select (C) 4.
 If x = −1, then x, x³, and x^{5} will equal −1, so the expressions containing these terms will all be negative. We can eliminate answers (A), (C), and (E).
 Answer (B) is equal to 4k(−1)² = 4k. Answer (D) is equal to 8k(−1)^{4} = 8k. As k is positive, (D) has the greater value. Select (D) 8kx^{4}.
 If Josephine cycles the fastest, then the steepest part of the graph should be in the middle. Using that, we can eliminate choices (A), (C), and (D).
 Since Josephine runs faster than she swims, the third part of the graph should be steeper than the first part of the graph. We can eliminate choice (B). Select (E).
 Draw a diagram: You may find it useful to draw a graph of the situation.
 When x = √6, then, from the first equation, y = 6 − 7 = −1. So, k = −1.
 Substitute x = √6, y = −1 into the second equation:
−1 = −6 + j
j = 5
Select (A) 5.
 Guess and check: Starting with the smallest value, check to see whether it makes the equation true. For (A), 2 − 4 = 2, which is < 3. Select (A) 4. Note: If it turned out the smallest value didn't work, you should try the largest value next.

 Solution 1:
 Estimate the answer: The angle labelled x° appears to definitely be more than 60° and less than 90°. Perhaps it it somewhere around 75° or so.
 Look at the answer choices: There are a few answers close to 75°, including (C) 72° and (D) 80°. We can definitely eliminate answer (A), though.
 Draw a diagram: Draw lines from one vertex to two opposite vertices.
 The lines that were drawn divide the pentagon into three triangles. Since, from the Reference Information, the sum of the measures in degrees of the angles of a triangle is 180, and the pentagon is made up of three triangles, the sum of the measures of degrees of the angles of the pentagon is 540°.
 As the pentagon has five interior angles, and the question tells us that all interior angles of that pentagon are congruent, then each angle measures 540/5 = 108°.
 Since x is the supplement of a 108° angle, it measures 180 − 108 = 72°. Select (C) 72.
 Solution 2: You might recall that the sum of the interior angles of a polygon with n sides is 180(n − 2). So, the sum of the interior angles of the pentagon in the diagram, which has 5 sides, is 180(5 − 2) = 180 · 3 = 540. Since the question states that all interior angles of the polygon are congruent, then each angle must be 540/5 = 108 degrees. Now, since the angle labelled x° is supplementary with one of the angles of the pentagon, the measure of x is 180 − 108 = 72. Select (C) 72.
 Estimate the answer: If the length of the drawing of the tool is 3/8 of its actual length, and the drawing is 6 inches long, then the actual length of the tool will be more than twice that length and less than three times that length (keep in mind that 3/8 is between ½ and ⅓). So, the length will be somewhere between 12 and 18 inches.
 Look at the answer choices: The only answer between 12 and 18 is (C) 16. Select that answer.
 Solution 1: Say that (x + 3)/2 = y, where y is an integer. Then:
x + 3 = 2y
x = 3 + 2y
Now, since y is an integer, 2y is an even integer. So, x must be 3 more than an even integer. An integer 3 more than an even integer is an odd integer. Select (E) an odd integer.
 Solution 2: Guess and check: Select values for x such that (x + 3)/2 is not an integer, and eliminate all answers that correspond to the value chosen. To start with, if x = 2, (x + 3)/2 is not an integer. So, we can eliminate (B) a positive integer and (D) an even integer. (x + 3)/2 is not an integer if x = 6, so we can eliminate (C) a multiple of 3. Finally, (x + 3)/2 is not an integer if x = −2, so we can eliminate (A) a negative integer. Select (E) an odd integer.
 Draw a diagram: Draw line QS on the diagram.
 Estimate the answer: For comparison purposes, draw line PR on the diagram. Line QS appears to have half the slop of line PR. The slope of PR is (10 − 6)/(11 − 3) = ½, so the slope of QS appears to be around ¼.
 Look at the answer choices: The only answer that makes sense based on our estimate is (B) ¼. Select that answer.
 If p is a factor of n + 3, then kp = n + 3, for some k. Now, n + 10 = n + 3 + 7 = kp + 7. Now, since p is a factor of n + 10, p is a factor of kp + 7. Since p is a factor of kp, then p must be a factor of 7 if p is a factor of kp + 7. If p is a factor of 7, then p = 1 or p = 7, since 7 is prime. We are told that p is greater than 1, so p = 7. Select (B) 7.
 Draw a diagram: Note that YB < YA < YC < YD and YC = YE. Mentally rotate all of the angles onto a plane and draw a diagram as follows:
 From the diagram, it's not too hard to see that angle D is smallest. Select (D) ∠XDY.
 When you see a problem like this, it's usually easiest to try to turn the expression that you have to evaluate into something resembling the givens. We can do that by factoring the expression:
x²y − xy²
= xy(x − y)
= 7(5)
= 35
Select (D) 35.