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# SAT Math Practice Problems Test 35 Grid Ins Questions | SAT Online Tutor AMBiPi

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 Practice Problems Test 35 Grid Ins Questions with Answer Keys | SAT Online Tutor AMBiPi.

### SAT 2022 Math Practice Problems Test 35 Grid Ins Questions with Answer Keys

SAT Math Practice Online Test Question No 1:

If p > 0, and the distance between the points (4, -1) and (-2, p) is 10, find p.

The distance formula tells you that the distance between two points, (x1y1) and (x2y2), is √[(x₂ – x₁)² + (y₂ – y₁)²].

Substituting the numbers from the question, you get

10 = √[((-2) – (4))² + (p – (-1))²] = √[(-6)² + (p + 1)²] = √[36 + (p + 1)²]

Because this is a radical equation, square both sides, so 100 = 36 + (p + 1)2. Subtract 36 from both sides to get 64 = (p + 1)2. The easiest way to solve this problem is to think about squares. If a quantity (in this case, p + 1) squared is 64, then the quantity must equal 8 or –8. But the question tells you that p is positive, so p + 1 = 8, and p = 7.

SAT Math Practice Online Test Question No 2:

Find the smallest even number that is divisible by 3, 5, and 7.

Every even number must be divisible by 2, so 2 × 3 × 5 × 7 = 210.

SAT Math Practice Online Test Question No 3: In this diagram, lines l and m are parallel. Find a – b, in degrees.

In this problem, you can’t actually figure out a and b. Because the problem asks for – a – b, one good way to start is to look for an angle that would be equal to a – b.

First off, look at the angle marked p in the diagram below, in which p and b are vertical angles. Hence p = b. Now check out the (unnamed) angle where I’ve drawn a curve in the following diagram. Because this drawing contains parallel lines, this unnamed angle is equal to a; these angles are called corresponding angles. The angle marked x is equal to a – b. Again, you can use the properties of parallel lines: x corresponds to the (unmarked) angle right below 115°. Because this angle and 115° make a straight line, it must equal 180° – 115° = 65°. So x = 65, and a – b = 65.

SAT Math Practice Online Test Question No 4:

If x + 100 = 2x, what is the value of x?

Just subtracting x from each side gives you the answer here as 100.

SAT Math Practice Online Test Question No 5:

If the area of an equilateral triangle is 64√3, find the length of one of its sides.

To solve this problem, I recommend creating a simple sketch: An equilateral triangle can be divided into two 30-60-90 triangles, as you can see in my sketch. If you let each side of the base equal x, then the height equals x√3. Because the area is half the base times the height, the area is x²√3, which means that  = 64, and x = 8. But wait! x was half the base, not the whole base, so your answer is 16.

SAT Math Practice Online Test Question No 6:

What is the value of the smallest number that is divisible by 2, 3, 4, 5, and 6?

You can actually ignore the 2 and 3 here because every number that’s divisible by both of them is also divisible by 6. Now, because the number is divisible by 4 and 5, it must also be divisible by 20 (because 4 and 5 have no common factors).

If you try out multiples of 20, you see that 20 and 40 aren’t divisible by 6, but that 60 is divisible by 6, so 60 is your answer.

SAT Math Practice Online Test Question No 7:

At a certain school, each student has an ID number containing three digits. The number may not begin with a zero, and may not end with a 7, 8, or 9. How many possible ID numbers are there?

There are 9 possible first digits, 10 possible second digits, and 7 possible third digits. The counting principle tells you to multiply, and 9 × 10 × 7 = 630.

SAT Math Practice Online Test Question No 8:

Find n if 32n = 22n + 33.

The key here is to recognize that 32 is 2 to the fifth power. Having done so, you can rewrite the equation as (25) = 22n + 33.

For this to work, it must be true that 5n = 2n + 33, which makes n equal 11.

SAT Math Practice Online Test Question No 9: In the drawing above, l || m. Find the value of w in degrees.

Because lines l and m are parallel, w + 75 must be equal to 122.

Straightforward subtraction gives you w = 47.

SAT Math Practice Online Test Question No 10:

If x + 11 = 5y and 3x – 11 = 9y, find the value of x/y.