Welcome to **AMBiPi (Amans Maths Blogs)**. SAT (Scholastic Assessment Test) is a standard test, used for taking admission to undergraduate programs of universities or colleges in the United States. In this article, you will get * SAT 2022 Math Test 45 Grid Ins Questions with Answer Keys | SAT Online Tutor AMBiPi*.

### SAT 2022 Math Test 45 Grid Ins Questions with Answer Keys

**SAT Math Practice Online Test Question No 1:**

If 3x = 12, what is the value of 8/x?

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**Correct Answer: 2 **

First, solve for x. Divide both sides of the equation by 3, and you get x = 4. Then divide 8 by 4, which gives you 2.

**SAT Math Practice Online Test Question No 2:**

If [x^{2} + x – 6]/[x – 8x + 12] = 4, what is the value of x?

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**Correct Answer: 9 **

Factor the numerator and the denominator into [(x – 2)(x + 3)]/[(x – 2)(x – 6)] = 4

The (x – 2) cancels out of the top and bottom to leave (x + 3)/(x – 6) = 4. Multiply both sides by (x – 6) to get x + 3 = 4x – 24. Subtract x from both sides: 3 = 3x – 24. Add 24 to both sides: 27 = 3x. Divide by 3 to get x = 9.

**SAT Math Practice Online Test Question No 3:**

The estimated population of rabbits in a certain forest is given by the function P(t) = at + 120 where t is an integer that represents the number of years after the rabbit population was first counted, 0 ≥ t ≥ 10, and a is a constant. If there were 192 rabbits 3 years after the population was first counted, how many rabbits will there be 7 years after the population was first counted?

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**Correct Answer: 288 **

We can’t figure out how many rabbits there were after 7 years until we know the constant a.

To find it, let’s use one of the data points that we’re given. We know that after 3 years (t = 3) there were 192 rabbits (P(t) = 192).

Plug both of those into the equation and we get 192 = a(3) + 120, which we can solve to find a = 24. Now plug that into our original equation, and we have P(t) = 24t + 120. To find out how many rabbits there were after 7 years, plug in t = 7: P(t) = 24(7) + 120 = 288.

**SAT Math Practice Online Test Question No 4:**

Ellen If 9^{-2} = (1/3)^{x}, then x =

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**Correct Answer: 4 **

Negative exponents mean to take the reciprocal and raise it to the power. So 9^{-2} = (1/9)^{2} = 1/81. Now find what power of (1/3) = 1/81.

Because 3^{4} = 81, (1/3)^{4} = 1/81, and x must be 4.

**SAT Math Practice Online Test Question No 5:**

There were 320 students at a school assembly attended only by juniors and seniors. If there were 60 more juniors than seniors and if there were 30 more female juniors than male juniors, how many male juniors were at the assembly?

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**Correct Answer: 80 **

You know that the total number of students is 320. Because you know that there are 60 more juniors than seniors, the easy way to find out how many of each there are is to take half of 320 (which is 160) and then add half of 60 to get the number of juniors and subtract half of 60 to get the number of seniors.

This means that the number of juniors is 190 and the number of seniors is 130. (Their difference is 60 and their sum is 320.) Therefore, there are 190 juniors.

Knowing that there are 30 more female juniors than male juniors, you can find the number of male juniors the same way—take half of 190 (which is 95) and subtract half of 30: 95 – 15 = 80.

**SAT Math Practice Online Test Question No 6:**

If Alexandra pays $56.65 for a table, and this amount includes a tax of 3% on the price of the table, what is the amount, in dollars, that she pays in tax? (Ignore the dollar sign when gridding your answer.)

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**Correct Answer: 1.65 **

The best way to approach this problem is to set up an equation. There is some price such that if you add 3% of the price to the price itself, you get $56.65.

This means that you can set up an equation: x + 3% of x = 56.65, or x + 0.03x = 56.65.

Now you can just solve for x, and you get the original price, which was $55. Subtract this from $56.65 to get the tax of $1.65.

**SAT Math Practice Online Test Question No 7:**

Alan and Ben each run at a constant rate of 7.5 miles per hour. Carla runs at a constant rate of 10 miles per hour. Debby runs at a constant rate of 12 miles per hour. In a relay race with these four runners as a team running one right after the other, Alan runs 0.3 miles, then Ben runs 0.3 miles, then Carla runs 0.5 miles, then Debby runs 0.24 miles. What is the team’s average speed in miles per hour?

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**Correct Answer: 8.93 **

To solve this problem, it is important to remember the formula distance = rate × time.

Here, to get the overall average speed, you need to know the total distance and total time. The total distance is found by adding all of the distances given: 0.3 + 0.3 + 0.5 + 0.24 = 1.34.

To find the time for each, rewrite the rate formula as follows: time = dist/rate, thus time = 0.3/7.5 = 0.04 hours for both Alan and Ben. For Carla, time = 0.5/10 = 0.05 hours, and for Debby, time = 0.24/12 = 0.02 = 0.02 hours.

The total time is 0.04 + 0.04 + 0.05 + 0.02 = 0.15 hours. Thus the average rate is 1.34 miles/0.15 hours = 8.93 miles per hour.

**SAT Math Practice Online Test Question No 8:**

If –1 ≤ a ≤ 2 and –3 ≤ b ≤ 2, what is the greatest possible value of (a + b)(b – a)?

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**Correct Answer: 9 **

This looks suspiciously like a quadratic equation, and if you multiply it out, its equivalent is b^{2} – a^{2}.

You want to make this as large as possible, so you want b^{2} to be large and a^{2} to be small. If b = –3, b^{2} = 9; if a = 0, a^{2} = 0. So b^{2} – a^{2} can be as large as 9.

**SAT Math Practice Online Test Question No 9:**

Twelve tomatoes are checked, and four of them are found to be rotten. What is the probability that one tomato chosen at random will not be rotten?

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**Correct Answer: 0.667 **

Out of the 12 tomatoes, we know 4 are rotten, but the question asks for the probability of choosing a not rotten tomato. If 4 tomatoes are rotten, 8 must not be rotten so the probability is 8/12. You could grid in the fraction as is, reduced to 2/3, or transform it into a decimal.

**SAT Math Practice Online Test Question No 10:**

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**Correct Answer: 15 **

We can’t find the value of y without first finding the value of x. A straight line is 180°, so 5x + x = 180, and 6x = 180.

Divide both sides by 6 to find that x = 30. Vertical angles are equal, so 2y = x, or 2y = 30, so y = 15.