This is our second free set of SAT Math practice questions. Working through practice questions is the best way to prepare for this section of the SAT.
Directions: Solve each problem and select the best of the answer choices given.
3(16) + 2(20) = Total Money Spent for every 5 kites
88 = Total Money Spent for every 5 kites
To find the average per kite cost, we can simply divide 88 by 5. 88/5 = 17.6. If you chose (A), it doesn’t logically make sense that the average price of the kites would be so close to the cheaper price, especially since 2 out of every 5 purchased will be $20. If you chose (B) or (D), these are close, but you probably make a small calculation error. If you chose (E), you simply took the average of the prices: 16 and 20. Remember that we’re given the ratio for a reason. It affects the average!
3, 8, 24
7, 9, 17
6, 9, 12
5, 15, 18
9, 10, 13
The third requirement is that we have at least one even number. Between (B) and (E), only choice (E) contains an even number, 10.
If you chose (A), the phrase “only one” means we cannot have more than one multiple of 3. Both 3 and 24 are multiples of 3.
If you chose (B), one number must be even and all three of these numbers are odd.
If you chose (C), the phrase “only one” tells us there cannot be more than one multiple of 3. All three of these numbers are multiples of 3.
If you chose (D), remember that the phrase “only one” means there cannot be more than one multiple of 3 in an answer choice. Both 15 and 18 are multiples of 3.
The difference between the diameters is 24 – 6 = 18.
If you chose (A), this is the diameter of the smaller circle.
If you chose (B), this is the difference between the radii.
If you chose (C), this is the radius of the larger circle.
If you chose (E), this is the diameter of the larger circle.
If the average speed of the entire journey was 2/3 miles per hour, then every 3 hours 2 miles were travelled. Since the total distance was 2 miles, the total time must have been 3 hours. If the way back took half as much time as the way there, then for every 3 hours, 2 hours was spent on the way there, and 1 hour was spent on the way back.
Average Speed = Distance/Time = 1 mile / 2 hours. The average speed for the way to Lark Rise was ½ mph.
We’re told that the radius of B is three-fourths the radius of A, so we can set up a proportion:
2 + x / 3 + x = 3/4
Now cross-multiply to solve:
8 + 4x = 9 + 3x
4x = 1 + 3x
1x = 1
1 = x
If x = 1, the radius of circle B is 2 + 1 = 3. The area will be πr2 = 9π.
If you chose (A), this is much too small to be the area, since we know the area is the produce of pi and the square of the radius.
If you chose (B), remember that x + 2 is the radius of the smaller circle. Though the radius is 3, we have to square it to find the area.
If you chose (C), this is the circumference of the smaller circle, not the area.
If you chose (E), you found the area of the larger circle, not the smaller one.
The credited response is (B). This is a great question to pick numbers for, especially since the correct answer is a ratio. Let’s say the length of the original square is 4. The midpoint divides the sides into two halves, each with a value of 2. The isosceles triangles formed by the lines connecting the midpoints are 45-45-90 special right triangles. Therefore the hypotenuse of those triangles would be 2√2.
The area of the original square is 4x4 = 16.
The area of the inscribed square is 2√2 x 2√2 = 4x2 = 8. The original square’s area is two times greater than the inscribed square’s area.
If you chose (A), you probably misread the question. The ratio here is the original square’s area to the inscribed square’s area, not vice-versa.
If you chose (C), this is the area of the inscribed square.
If you chose (D), this is the perimeter of the inscribed square. Make sure you carefully re-read what the question is asking.
If you chose (E), this is the area of the original square.
The increase is 324π - 100π = 224π. An increase of 224/100, or approximately 225%.
If you chose (A), be careful not to reuse values that are simply given in the question stem.
If you chose (C), this is close, but a little too large.
If you chose (D), this is the value of the new percent, not the percent increase.
If you chose (E), you may want to practice picking values for these types of questions.
y (x – z)/z – x
100xy / x – z
100x / y (z – x)
100yz / y(x – z)
(A) 10/5 = 2
(B) 10 (5 – 3) / 3 – 5 = 20/-2 = -10
(C) 100(5)(10) / 5 – 3 = 5000 / 2 = 2500
(D) 100(5) / 10(3 – 5) = 500/-20 = -25
(E) 100(10)(3) / 10(5-3) = 3000/20 = 150 Correct!
Likewise, ⏀-84⏀is defined as -83 x -81 x -79 x -77…-5 x -3 x -1. When these numbers are divided, we can see that every value will cancel out. The answer is 1.
I chose variables “x” and “y” to help express the ratios. Right now the ratio of LO to MP is (2x + 3y)/(x + 7y). If we could find the values of x and y we can determine the ratio.
Let’s set up a few equations based on the given information:
x + 3y = 13, or x = 13 – 3y
2x + 7y = 28
Using substitution: 2(13 – 3y) + 7y = 28
26 – 6y + 7y = 28
26 + y = 28
y = 2
Now we can find x: x + 3(2) = 13
x + 6 = 13
x = 7
Therefore the ratio is (2x + 3y)/(x + 7y) = 14 + 6 / 7 + 14 = 20/21.
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