Approximation & Simplification
Q. If 2x - 3 = 5, what is the value of x?
Solution
Adding 3 to both sides gives 2x = 8, so x = 4.
Correct Answer: B — 2
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Q. If 5x - 3 = 12, what is the value of x?
Solution
Add 3 to both sides to get 5x = 15, then divide by 5 to find x = 3.
Correct Answer: B — 3
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Q. If 5x - 3 = 2x + 12, what is the value of x?
Solution
Rearranging gives 5x - 2x = 12 + 3, so 3x = 15, thus x = 5.
Correct Answer: B — 4
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Q. If 5x = 20, what is the value of x?
Solution
Dividing both sides by 5 gives x = 4.
Correct Answer: B — 4
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Q. If a number is divisible by both 2 and 3, what is it also divisible by?
Solution
A number divisible by both 2 and 3 is also divisible by their least common multiple, which is 6.
Correct Answer: C — 6
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Q. If a number is divisible by both 2 and 3, what is the smallest number it could be?
Solution
The least common multiple of 2 and 3 is 6.
Correct Answer: A — 6
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Q. If a number is divisible by both 2 and 3, what is the smallest possible value?
Solution
The least common multiple of 2 and 3 is 6.
Correct Answer: C — 6
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Q. If a number is divisible by both 4 and 6, what is the smallest positive integer that is also divisible by 12?
Solution
The least common multiple of 4 and 6 is 12.
Correct Answer: A — 12
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Q. If a sequence is defined by a_n = 2n + 1, what is a_4?
Solution
a_4 = 2(4) + 1 = 8 + 1 = 9.
Correct Answer: A — 7
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Q. If x + 5 = 12, what is the value of x?
Solution
Subtracting 5 from both sides gives x = 7.
Correct Answer: B — 7
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Q. If x = 3, what is the value of 2x^2 - 5?
Solution
Substituting x = 3 gives 2(3^2) - 5 = 18 - 5 = 13.
Correct Answer: B — 7
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Solution
12 divided by 7 is 1 with a remainder of 5, so 12 mod 7 = 5.
Correct Answer: A — 5
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Q. What is 15 divided by 4?
Solution
15 divided by 4 equals 3.75.
Correct Answer: A — 3.75
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Q. What is the next number in the sequence 2, 4, 8, 16?
Solution
The sequence doubles each time, so the next number is 32.
Correct Answer: C — 32
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Q. What is the next term in the sequence 2, 4, 8, 16?
Solution
The sequence doubles each time, so the next term is 32.
Correct Answer: C — 32
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Q. What is the remainder when 57 is divided by 5?
Solution
57 divided by 5 is 11 with a remainder of 2.
Correct Answer: B — 3
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Q. What is the result of 15 mod 4?
Solution
15 divided by 4 gives a remainder of 3, so 15 mod 4 = 3.
Correct Answer: A — 3
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Q. What is the value of 10 - 3(2 + 1)?
Solution
Calculating gives 10 - 3(3) = 10 - 9 = 1.
Correct Answer: B — 4
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Q. What is the value of 5^2 + 3^2?
Solution
5^2 = 25 and 3^2 = 9, so 25 + 9 = 34.
Correct Answer: B — 34
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Q. What is the value of 7 mod 3?
Solution
7 divided by 3 gives a remainder of 1.
Correct Answer: B — 2
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Q. What is the value of 9 - 3(2 + 1)?
Solution
Calculating gives 9 - 3*3 = 9 - 9 = 0.
Correct Answer: C — 6
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Q. What is the value of 9 mod 5?
Solution
9 divided by 5 gives a remainder of 4.
Correct Answer: A — 4
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Q. What is the value of 9^2?
Solution
9 squared is 81.
Correct Answer: A — 81
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Q. What is the value of x in the equation 3x + 5 = 20?
Solution
Subtract 5 from both sides to get 3x = 15, then divide by 3 to find x = 5.
Correct Answer: A — 5
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Q. Which of the following is a factor of 30?
Solution
5 divides 30 evenly, so it is a factor.
Correct Answer: A — 5
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Q. Which of the following is a prime number?
Solution
11 has no divisors other than 1 and itself.
Correct Answer: D — 11
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Q. Which of the following is a solution to the equation 2x + 3 = 11?
Solution
Solving for x gives 2x = 8, so x = 4.
Correct Answer: C — 4
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Q. Which of the following is a valid proof for the statement: If n is an even integer, then n^2 is even?
-
A.
n = 2k for some integer k
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B.
n = 2k + 1
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C.
n = k^2
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D.
n = 2k - 1
Solution
If n = 2k, then n^2 = (2k)^2 = 4k^2, which is even.
Correct Answer: A — n = 2k for some integer k
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Q. Which of the following is equivalent to 3(2x + 4)?
-
A.
6x + 12
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B.
6x + 4
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C.
6x + 8
-
D.
2x + 12
Solution
Distributing gives 6x + 12.
Correct Answer: A — 6x + 12
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Q. Which of the following numbers is divisible by 6?
Solution
18 is divisible by both 2 and 3, hence by 6.
Correct Answer: B — 18
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