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
- Practice Test 2: Sections
- Practice Test 3: Sections
- Practice Test 4: Sections
- Practice Test 5: Sections
- Practice Test 6: Sections
- Practice Test 7: Sections
- Practice Test 8: Sections
- Practice Test 9: Sections
- Practice Test 10: Sections
Here are solutions for section 6 of the fourth practice test in The Official SAT Study Guide, second edition, found on pages 581–586. The following solutions demonstrate faster, more informal methods that might work better for you on a fast-paced test such as the SAT. To learn more about these methods, see my e-book Succeeding in SAT Math or the SAT math tips page.
- Solution 1:
Solution 2: Guess and check. Try each answer, starting with the middle answer, to see if it works. Does (C) 9 work? (3 + 9)/2 = 6, which is not 7½. So, try a larger answer, say (D). (3 + 12)/2 = 15/2 = 7½, so this is the correct answer. Select (D) 12.
- First, convert the right-hand side to an improper fraction, namely 15/2.
- So, if (3 + ♢)/2 = 15/2, then
3 + ♢ = 15Select (D) 12.
♢ = 12
- Solution 1: From the diagram, angle 2 is an obtuse angle and angle 4 is another obtuse angle. So, look for two obtuse angles formed by m. Angles 6 and 8 are obtuse. Therefore, the answer is (D) 6 and 8.
Solution 2: Using Z, F, and C patterns (or however you remember congruent angles when a line intersects a pair of parallel lines), you can determine that angle 2 is congruent to angles 6 and 8, and angle 4 is congruent to angles 6 and 8. Based on this information, the only answer that makes sense is (D) 6 and 8. Select that answer.
- There are a few ways of solving this problem; I'll only illustrate the most direct route.
- Work backwards: We could determine the total number of unemployed women if we knew the number of employed women (since we know the total). We have the number of employed people and the number of employed men, so we can find the number of employed women.
- The number of employed women is equal to (total employed - total men employed), or 48,000 − 27,000 = 21,000. The number of unemployed women is equal to (total number of women - total number of women employed) or 21,500 − 21,000 = 500. Select (A) 500.
- Substitute k = 4 in A(k) = 4k − 30:
A(15) = 4(15) − 30
Select (E) $30.
A(15) = 30
- Solution 1: Substitute xr = v in v = kr:
xr = kr
So, x is equal to k. Select (D) x.
x = k
- Try a special case: Pick specific numbers for x and r (say x = 2 and r = 3). Since xr = v, then v = 2(3) = 6. Now:
v = kr
6 = 3k
k = 2
- Look at the answer choices: Substitute x = 2 in each of the answer choices and see which evaluates to 2, the value of k we found in the previous step. It's pretty obvious that the only such choice is (D) x. Select that answer.
- Read the question carefully and understand what it is asking: You have a basket of eggs. For every two eggs in the basket, there are three brown eggs. It is not possible to have every number of eggs in the basket; you are asked to find which of the choices represents a number you can't have.
- Draw a diagram: You may find it helpful to draw a diagram of a basket of eggs, with white and brown eggs in the ratio of 2 to 3.
- Look at the answer choices: If, for every two white eggs in the basket, there are three brown eggs, there number of eggs must be a multiple of (2 + 3) = 5. The only answer choice not a multiple of 5 is (B) 12. Select that answer.
- Estimate the answer: It's difficult to come up with an exact estimate; however, To find r, we would multiply 18 by some number (say x) and, to find t, we could divide 18 by x². So, r has to be greater than 18, and t has to be a fair bit less than 18. So, the answer has to be more than 18 and less than 18 × 18 = 324.
- Look at the answer choices: The answer can't be (A) 18 or (E) 324. Eliminate those three choices. There are still three choices to choose from.
- 18√18 can be written as 18√9√2. Since √9 = 3, the expression becomes 54√2, which is what we're looking for. To find rt, multiply 54 and 2: 54 × 2 = 108. Select (C) 108.
- Solution 1: This question is pretty easy if you notice that the three triangles on the left-hand side form a quadrilateral, and you remember that the interior angles of a quadrilateral sum to 360°. The four angles of the quadrilateral are:
The sum of these must be equal to 360°:
+ b° + b°
+ a° + c°
+ b° = 360°
Select (E) 360 − 2a −3b.
2a + 3b + c = 360
c = 360 − 2a −3b
Solution 2: If the above solution didn't occur to you, it's still possible to solve the problem; it just takes a bit longer.
- Don't try to solve for t. Instead, just multiply both sides of the equation by 4:
4t³ = 1404
- Draw a diagram: You may find it helpful to draw a number line to visualize the problem.
- Looking at the number line or thinking about the problem, the difference between 53 and 62 is 9. So, the number we're looking for will be a distance of 4.5 from both. The answer is 53 + 4.5 = 62 − 4.5 = 57.5. Enter 57.5.
- Draw a diagram: It may be helpful to draw a diagram of a triangle with two equal angles and/or sides of 50 and 30.
- If a triangle has two angles that are equal and one angle not equal to the other two, it must have two sides that are equal and one side not equal to the other two. So, the third side must be equal to one of the other two sides—it must be either 30 or 50. The least possible value for the perimeter would occur when the third side is 30. So, the perimeter is 30 + 30 + 50 = 110. Enter 110.
- It's possible to solve this problem in a more intuitive manner, but I've chosen to include a solution with all of the steps.
- Solution 1: Try a special case: Say that Tameka cut the pieces so that the angle is 24°. There would be 360/24 = 15 pieces. So, 15 is a possible answer. Enter 15.
Solution 2: Consider a different problem: Say that we were asked to find the number of pieces if Tameka cut the pizza into slices with a 30° angle. There would then be 360/30 = 12 pieces. However, the actual question specifies that the angle is less than 30°, so there must be more than 12 pieces. Enter the next integer higher than 12, which is 13.
- Solution 1: Guess and check: Say that a = 1. The sum of the terms would be 1 + 3 + 9 + 27 + 81 = 121. This isn't right. More importantly, though, it is 121/605 = 1/5 of the correct answer.
Since it appears that the value should be 5 times larger, try a = 5. 5 + 15 + 45 + 135 + 405 = 605. This answer is correct. Enter 5.
- Solution 1: There are three different places in which the shaded card can go. Having placed the shaded card, there are four different places where the next card can go, three different places for the card after that, two different places for the card after that, and one place for the final card. This makes 3 × 4 × 3 × 2 × 1 = 72 possible arrangements. Enter 72.
Solution 2: To find the number of arrangements, find the total number of arrangements if there were no conditions, and subtract the number of arrangements where the shaded card is at either end. If there were no conditions, there would be 5! = 120 arrangements. However, there are 4! = 24 ways to arrange the cards so that the shaded card is on the left end, and 24 ways to arrange the cards so that the shaded card is on the right end. So, the total number of valid possibilities is 120 − 24 − 24 = 72. Enter 72.