SAT Practice Test 26 Math Grid Ins Questions | SAT Online Classes AMBiPi

Correct Answer: 29

There are 250 subscribers, 68% of whom are male. That makes 250 × 0.68 = 170 male subscribers. After some females unsubscribe, the total subscriber count is 1.3 times the number of male subscribers, for a total of 170 × 1.3 = 221 subscribers. Here you have to pause and make sure you solve for the right thing: The question asks for the number of females who unsubscribed, which is 250 – 221 = 29 females.

Correct Answer: .29

When data values are arranged from least to greatest, the median is the value in the middle. Add the bar heights to find that there are 52 students represented in the bar graph, which is an even number, so take the average of the two middle values to get the median. Half of 52 is 26, so the values in the middle are the 26th and 27th values. Both of these values are 6, so the median is 6. To find the mean, add all the quiz scores together and divide by the number of students, 52. To speed up the calculations, multiply each bar height by the corresponding score (mentally if possible): [(1 x 1) + (3 x 3) + (5 x 4) + (8 x 5) + (10 x 6) + (11 x 7) + (8 x 8) + (4 x 9) + (2 x 10)] ÷ 52 = 327/52 ≈ 6.2885.

Rounded to the nearest hundredth, the difference between the median and the mean is 6.29 – 6 = 0.29. Grid this in as .29.

Correct Answer: 576 

First, substitute 8√3 for x into the equation and simplify. Next, write √3y as √3√y so you can divide both sides by so you can divide both sides √3. Finally, square both sides to eliminate the radical:

3x = √3y

3(8√3) = √3y

24√3 = √3y

24√3 = √3√y

24 = √y

24² = y

Squaring 24, the final answer is 576.

Correct Answer: 2/3 or 1

Multiplying both sides of the equation by the common denominator (x)(x – 2) yields the following:

[x(x – 2)/1] ⦁ [1/x – 2/(x – 22) = 3]

1(x – 2) – 2(x) = 3(x) (x – 2)

x – 2 – 2x = 3(x² – 2x)

-x – 2 = 3x² – 6x

0 = 3x² – 5x + 2

Now, factor the equation (or use the quadratic formula), set each factor equal to 0, solve for x, and check that the solutions don’t result in a zero denominator.

0 = 3x² – 5x + 2

0 = (3x – 2)(x – 1) 

The solutions are x = 2/3 and x = 1, both of which are valid solutions, so grid in either value.

Correct Answer: 1/81

The notation g(-4) means that you are looking for the y-value when x is -4. Because you cannot tell what the exact value is from the graph, you need to find the equation of the function. To find the base, b, which is being raised to a power, make a list of several points on the graph and look for a pattern: (0, 1), (1, 3), and (2, 9). The y-values are all powers of 3, so try b = 3. Notice that 3⁰ = 1, 3¹ = 3, and 3² = 9. The equation of the function is g(x) = 3^x, so substitute -4 for x and simplify:

g(-4) = 3^-4 = 1/3 = 1/(3 x 3 x 3 x 3) = 1/81 

Correct Answer: 4

The equation is a special product of binomials (the square of a sum), so when factored, it becomes (x + r)² = 0 (you could also factor normally if you didn’t recognize this). Substitute -4 for x, and then solve for r by taking the square root of both sides:

(-4 + r)² = 0

r – 4 = 0

r = 4

Correct Answer: 12

You know that AB – 15 = 60. Solve this for AB by adding 15 to both sides of the equation: AB = 75. Next, substitute the expressions given for A and B, multiply them together, and see where that takes you:

AB = 75

(3 – 4i)(9 + ki) = 75

27 + 3ki – 36i – 4ki² = 75

27 – 36i + 3ki – 4k(-1) = 75

27 – 36i + 3ki + 4k = 75

You now have two options: The only way the expression on the left can equal plain 75 is if the imaginary terms add up to 0, so you could set the two imaginary terms equal to 0 and solve for k:

-36i + 3ki = 0

3ki = 36i

3k = 36

k = 12

The other option is to ignore the imaginary terms (because they add up to 0) and set the real terms equal to 75 and solve for k. The result should be the same:

27 + 4k = 75

4k = 48

k = 12

Either route leads to the correct answer, which is 12.

Correct Answer: 16

The given ratio involves sides of the two small right triangles, and the question asks about a side of one of those triangles, so focus on this. The base angles of ΔJKL are congruent (because it is an isosceles triangle), so ∠J and ∠L are congruent. Additionally, ∠JNM and ∠LPM are both right angles and therefore are congruent. When two pairs of corresponding angles in two triangles are congruent, the third pair must also be congruent, so ΔJNM and ΔLPM are similar by AAA. This means the corresponding sides of these triangles are proportional. Thus, JM/ML = MN/MP. Because MN/MP = 8/5, it follows that JM/ML = 8/5. If we let JM = 8x, then ML = 5x. We also know that JL (which is the sum of the lengths of segments JM and ML) equals 26, so 8x + 5x = 26. Solving this equation yields 13x = 26, or x = 2. Finally, JM = 8(2) = 16.

Correct Answer: 8

The volume of the rectangular solid is 4 × 8 × 16 = 512 cubic units. The cube has the same volume, and its edges are all equal in length, so express this as s³ = 512 and take the cube root of 512 to solve for s. The result is 8, which gives the length of one edge of the cube.

Correct Answer: 146

To calculate the volume of the paperweight, start by finding the radius. The question states that the diameter of the paperweight’s base is 20% larger than (120% of) its height, which is 1.2 × 5 = 6 centimeters, so the radius is half that or 3 centimeters. The volume of a cone (remember to check the formula page) is given by Vcone = (1/3)πr²h, or here (1/3)π x 3² x 5 = 15π cubic centimeters. Now, multiply this volume by the given density (3.1 g/cm³) to find that the mass of the paperweight is 15πcm³ x 3.1g/1cm³ = 46.5πg. Rounded to the nearest gram, the correct answer is 46.5 × 3.14 ≈ 146.