Question Explanations For

SAT Practice Test 2 (Math Test: Calculator Section)

1.

The Correct Answer is (A) — Subtracting 2x and 4 from each side of the equation gives us -10 = 2x. Dividing each side by 2 gives us x = -5.

2.

The Correct Answer is (B) — Since a and b are both even integers, we know that: (a + 1) is odd, (b + 1) is odd, (b +2) is even, and (a -1) is odd. So I. is a product of two odd integers, which is also odd. II. is a product of an even and odd integer, which is even. III. is the product of two odd integers, which is odd. B is the correct answer.

3.

The Correct Answer is (D) — Since the growth of the tree is linear, we expect our graph to be a line. This eliminates choices A and B. We are also told that the tree is initially 3 feet tall, meaning that the height when time = 0 is not zero. This eliminates choice C. The correct answer is D.

4.

The Correct Answer is (C) — If we set x =1, y can be 1, 2, 3, or 4 to satisfy the inequality. If we set x = 2, then y can only be equal to 1. We cannot set x equal to any higher integers since that would immediately violate the inequality. Counting up all the (x,y) pairs gives us 5.

5.

The Correct Answer is (B) — The average daily increase in the number of Monarch butterflies is the slope of the fitted line. We can estimate that there were approximately 10 butterflies at day 0, giving us the point (0, 10). We can then estimate that there were approximately 50 butterflies on day 20, giving us the point (20, 50). Calculating the slope gives us

6.

The Correct Answer is (B) — We are told that b is 150% greater than c, which means b = c + 1.5c. Plugging in c = 20, we get b = 20 + (1.5)(20) = 50. a is 8% of b so a = (0.08)b. Plugging in b = 50, we get a = (0.08)(50) = 4.

7.

The Correct Answer is (B) — First, we count all the people who showed symptoms: 216 + 584 = 800 people. Of these 800 people, 216 were vaccinated. So the percentage of patients who showed symptoms who were also vaccinated is 216/800 x 100 = 27%.

8.

The Correct Answer is (D) — When we divide each side of the equation by 3, we get x = (1/6)y. We want to find (1/3)y so we can multiply both sides of the equation by 2 to get 2x = (1/3)y. The answer is D.

9.

The Correct Answer is (D) — We calculate p(2) by p(2) = |2(2) - 5| = |-1| = 1. We calculate p(-2) by p(-2) = |-2(2) - 5| = |-9| = 9. So p(2) + p(-2) = 1 + 9 = 10.

10.

The Correct Answer is (B) — We are told that the circumference of circle E is 6π. Because circumference = 2πr, we can calculate that the circle E has a radius of 3. The two sides of rectangle CDEH are the radii, so the area of CDEH is 3 x 3 = 9. We are shown in the diagram that line ED and line DF are equal lengths, so the area of CDFG must also be 9. So the total area of rectangle EFGH is 9 + 9 = 18.

11.

The Correct Answer is (D) — We can find the length of a line given its points by drawing a right triangle where the legs are the difference in x and y-coordinates of the two points. The hypotenuse of this right triangle is the length of the line. The difference in y for the two points is 7 -3 = 4. The difference in x is 1 - (-2) = 3. At this point, we can recognize that this is a 3-4-5 triangle and choose answer choice D.

12.

The Correct Answer is (B) — First, we count the total number of students in Class A: 1+ 6 + 4. Then we count the number of students that speak more than 2 languages, which is the number of students that speak 3 languages. The chart shows that 4 students speak 3 languages. We calculate the percentage by 4/21 x 100 = 19%.

13.

The Correct Answer is (A) — In class A, if all the students were lined up in increasing order of number of languages spoken, the middle student would speak 1 language. This makes the median of class A 1. The category that has the most number of students is 1 language spoken, making the mode of class A 1. Similarly, the median of class B is 2 and the mode is 1. This means that class A has a median smaller than class B, and both classes have the same mode.

14.

The Correct Answer is (C) — When we factor a 2 out of the expression, we get . We can further factor this term to get 2(x + 3)(x -2). From this, we can eliminate choices A and B. We can then notice that the product of 2 and (x + 3) equals 2x + 6, making this term also a factor. The correct answer is C.

15.

The Correct Answer is (A) — If c is the original price of the car, then c x 1.2 = 36,000 giving us c = 30,000. The final price of the car is 5% less than $36,000, giving us (0.95)(36,000) = 34,200. We can then subtract the original price from this final price to get the profit, giving us 34,200 - 30,000 = $4200.

16.

The Correct Answer is (B) — Distributing in the 4 on the left side and the negative sign of the right side of the equation, we get . Cross-multiplying then gives us 20x + 15 = 9 + 3x. Subtracting each side by 3x and 15 gives us 17x = -6. Then dividing each side by 17 gives us x = -6/17.

17.

The Correct Answer is (D) — First, we add up all the percentages of red, yellow, and blue umbrellas to get 60%. We are told that the total number of umbrellas is 1800, so we multiply this term by 0.60 to get 1080 umbrellas.

18.

The Correct Answer is (C) — 12√2 can be factored into 3 × 4 × √2. Bringing the 4 under the radical gives us 3√(2×16) =3 √32. This eliminates answer choice A. 6√8 can be factored into 2 × 3 × √(8.) Bringing the 2 under the radical gives us 3√(4×8) = 3√32. This eliminates answer choice B. We can factor 2 × 2√(2×2×3). There is no way to bring a number of in or out of the radical to produce 3√32. The correct answer is C.

19.

The Correct Answer is (D) — Macey’s savings can be expressed as 100 + 10y, where y is the number of years. Sam’s savings can be expressed as . After five years Macey will have 100 + 10(5) = $150. Sam will have . Subtracting Macey’s savings from Sam’s savings gives us 161.05 - 150 = 11.05. So after 5 years, Macey will have saved $11.05 less than Sam.

20.

The Correct Answer is (C) — Substituting 2 and -2 for answer choice A gives us 3/2 < 3/(-2), which is not a true statement. When we try answer choice B, we get 15 < 15, which is also untrue. When we try answer choice C, we get -5 < 11, which is a true statement. The answer is C.

21.

The Correct Answer is (B) — We first find the volume of the pool by taking the product of the dimensions, which gives us 2 × 10 × 10 = 200. When we convert this value to gallons we get 52,800 gallons. We are only interested in half the pool, so we divide this value by 2 to get 26,400 gallons. We can divide this value by 55 gallons to find how many minutes it would take to fill half the pool, which gives us 26,400/55 = 480 minutes. Converting this to hours gives us 8 hours.

22.

The Correct Answer is (B) — When we add x to both sides of the equation, we get y = -2x. Dividing each side of the equation by -2 and y gives us -1/2 = x/y. The correct answer is B.

23.

The Correct Answer is (D) — We are told that the wolf population increases by 5% each year. This means that after 1 year, the wolf population is 20(1.05). After 2 years, the wolf population is 20(1.05)(1.05). If we continue this pattern, we can see that the wolf population at any given year can be expressed as .

24.

The Correct Answer is (C) — When we halve both q and r, we get , which can be simplified to , which can be further simplified to . This is twice as large as , so C is the correct answer.

25.

The Correct Answer is (B) — We can divide the value found in the None column by the value in the Total column for each age group to the find the percentage of people who did not own a vehicle. Doing this we get:

18-29 Age Group
Percentage 498/26,955×100 = 13%

30-49 Age Group
Percentage 2309/35,520×100 = 6.5%

50-69 Age Group
Percentage 2004/29,597×100 = 6.8%

70+ Age Group
Percentage 5377/29,492×100 = 18%

From this list, we can see that the 30-49 age group has the smallest percentage.

26.

The Correct Answer is (C) — We can find the number of people 50 or more years with an electric or hybrid car by 1068 + 792 = 1860. We can divide this number by the total number of electric or hybrid car owners, giving us 1860/9396 × 100 = 20%.

27.

The Correct Answer is (C) — sin(π) = 0, and squaring this value also gives us 0, so A is not the correct answer. sin(π/2) = 1, and squaring this value also gives us 1, so B is not the correct answer. sin(-π/2) = -1, and squaring this value gives us 1 so sin(-π/2) ≠ (-π/2). C is the correct answer.

28.

The Correct Answer is (D) — Graphs for answer choices A and B imply that the area of this rectangle can be 800 or greater. These values are not possible with only 40ft of fencing material. Similarly, the graph for answer choice C says that the area can be as large as 400, but this value is also impossible with only 40ft of fencing material. The correct answer is D.

29.

The Correct Answer is (B) — When we multiply the two terms together we get 10 + 30i - 2i - 6. Because =-1, the last term is equal to 6, giving us 10 + 28i + 6 = 16 + 28i.

30.

The Correct Answer is (A) — We are dealing with the equation . Subtracting from both sides of the equation gives us , which can be simplified to . Factoring the numerator using difference of squares gives us . Cancelling gives us

31.

The Correct Answer is (150) — We can divide 75 miles by 30 miles per hour to find the number of hours it will take to make this trip, which gives us 75/30 = 2.5 hours. When we convert this value to minutes, we get 150 minutes.

32.

The Correct Answer is (80) — If 2/5 of n is 48, then (2/5)n = 48. Solving for n gives us n = 120. We can multiply this n by 2/3 to find 2/3 of n, which gives us (2/3)(120) = 80.

33.

The Correct Answer is (32) — Plugging in -3 into f(x) gives us

34.

The Correct Answer is (33) — We can divide the number of miles traveled by the average speed to find the number of hours it took to make a particular trip. From this we can calculate that the 3 mile trip with Bus A took 3/20 = 0.15 hours. The 6 miles trip with Bus B took 6/15 = 0.4 hours. Consequently, the whole trip took 0.15 + 0.4 = 0.55 hours. Converting this value to minutes gives us 33 minutes.

35.

The Correct Answer is (18) — To get a common denominator for the two terms on the left side, we multiply the first term by and the second term by

This gives us

We can simplify this to

Cross-multiplying gives us Moving all the terms to the left side gives us We can then factor the left side into Solving for the roots gives us a = -1 or 18. Since the question asks for the positive value, the correct answer is 18.

36.

The Correct Answer is (87) — The sides of the box are equal to 3 diameters of the cans, which tells us that the dimensions of the box are 9 × 9 × 5. From this we calculate the volume which is 9 × 9 × 5 = 405. Next we can find the volume of one can. Each can has a radius of 1.5, which means that the area of the top of a can is × 3.14. We then multiply this value by 5 to get the volume of the can, which is (1.5)(1.5)(3.14)(5) = 35.325. We then multiply this value by 9 to find the total volume of all the cans together, which is (35.325)(9) = 317.925. Subtracting this value from the volume of the box gives us 405 - 317.925 = 87.

37.

The Correct Answer is (8833) — After the first year, Mia’s debt is 2000(1.04) = 2080. Adding 2000 to this value and multiplying by the total gives us (2080+2000)(1.04) = 4243.2, which is Mia’s total debt after the second year. When we repeat this process for the third year, we get (4243.2+2000)(1.04) = 6492.93. When we repeat this one last time for the fourth year, we get (6492.93+2000)(1.04) = $8833.

38.

The Correct Answer is (1553) — Right after graduation, Mia’s debt is $8833. Since this amount accrues an interest of 4% for the next two years, Mia’s debt 2 years after graduation is (8833) = 9553. After paying a lump sum of $8000, Mia’s debt will be 9553 - 8000 = $1553.