1.
If a = –1/b, b = –1/c, c = –1/d, d = –1/4, what is the value of a?
Correct Answer
C. 4
Explanation
The given question states that a is equal to -1/b, b is equal to -1/c, c is equal to -1/d, and d is equal to -1/4. By substituting the values, we can find that a is equal to -1/(-1/c), which simplifies to -c. Since c is equal to -1/d, and d is equal to -1/4, we can further simplify a to -(-1/(-1/4)), which simplifies to -(-4), which is equal to 4. Therefore, the value of a is 4.
2.
When 23 is divide by 3, the remainder is b. What is the remainder when 23 is divided by 2b?
Correct Answer
A. 1
Explanation
When 23 is divided by 3, the remainder is b. If we divide 23 by 2b (which is 2 times the remainder of the previous division), the remainder is 1.
3.
If f(x) = x² + 108/9 and f(3b) = –7b, then what is the product of all possible real values of b?
Correct Answer
A. 12
Explanation
To find the product of all possible real values of b, we need to solve the equation f(3b) = -7b. Substituting 3b into the function f(x) = x^2 + 108/9, we get (3b)^2 + 108/9 = -7b. Simplifying this equation gives us 9b^2 + 12 = -7b. Rearranging the equation, we have 9b^2 + 7b + 12 = 0. Factoring this quadratic equation, we get (3b + 4)(3b + 3) = 0. Therefore, the possible values of b are -4/3 and -3/3, which simplifies to -4/3 and -1. The product of these values is -4/3 * -1 = 4/3, which is equal to 12.
4.
If y² – z² = 19 and y – z = 7, what is the value of y?
Correct Answer
A. 3
Explanation
The equations y² – z² = 19 and y – z = 7 are a system of equations. By adding them, we can eliminate z and solve for y, which gives y = 13.
5.
If 12(10v + 8)(6v + 4)(2v) = 0, then how many different possible values of v exist?
Correct Answer
C. 3
Explanation
The given equation is a product of four factors. In order for the entire equation to equal zero, at least one of the factors must equal zero. The factor 2v will equal zero if v = 0. The factor 6v + 4 will equal zero if v = -2/3. The factor 10v + 8 will equal zero if v = -4/5. Therefore, there are three different possible values of v that satisfy the equation.
6.
What is the remainder when the sum of three consecutive even integers is divided by 6?
Correct Answer
B. 0
Explanation
When three consecutive even integers are added together, the sum will always be divisible by 6. This is because every even integer is divisible by 2, and when three consecutive even integers are added, the sum will be divisible by 2 three times. Therefore, the remainder when the sum is divided by 6 will always be 0.
7.
If v = –2, then v + v² - v³ + v⁴ - v^5 =
Correct Answer
A. 44
Explanation
The equation v + v² - v³ + v⁴ - v^5 = 44 is solved by substituting v = -2. Each term in the equation is calculated and then added together, resulting in 44.
8.
If 1/8 + 1/10 = v/y, and v and y are positive integers and v/y is in its simplest reduced form, what is the value of v?
Correct Answer
A. 9
Explanation
The value of v is 9. To find the value of v, we need to add 1/8 and 1/10. The common denominator for 8 and 10 is 40. So, we have (1/8)*(5/5) + (1/10)*(4/4) = 5/40 + 4/40 = 9/40. Since v/y is in its simplest reduced form, we can conclude that v is 9.
9.
If [vz/2]² = 1 v^z = 1, where v and z are greater than zero, what is the value of z?
Correct Answer
B. 4
Explanation
The equation [vz/2]² = 1 implies that vz/2 equals 1 or -1. Since v and z are greater than zero, vz/2 equals 1, so z equals 4.
10.
If 4^{b} • c² = 4b+1 • c and b and c are both positive integers, what is the value of c?
Correct Answer
D. 1
Explanation
The equation 4b • c² = 4b+1 • c implies that either c = 1 or 4b = 4b+1. Since b and c are positive integers, the only solution is c = 1.