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21 Cards in this Set

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If a = 5/2 then 1/a =

A. 2
B. 5
C. 2/5
D. 5/2

C. Substitute 5/2 for a, giving you 1/a = 1/(5/2) = 1 x 2/5 = 2/5.
12 is 15% of what number?

A. 0.0125
B. 1.8
C. 18
D. 80
D. Let n represent the number. If 12 is 15% of n, then 12 = 0.15n. Divide both sides by 0.15. Therefore, n = 80.
Evaluate 3x + 7 when x = -3.

A. -2
B. 10
C. 16
D. 30
A. Substitute -3 for x. Then 3(-3) + 7 = -9 + 7 = -2.
Find the diagonal of a square whose area is 36.

A. 6
B. 6√2
C. 9
D. 9 √2
B. The area of a square is s2 where s is a side of the square. If s2 = 36, then s = 6. The diagonal of a square forms two right triangles; d is the hypotenuse and the two legs are 6 units long. Using the Pythagorean theorem, d2 = 62 + 62 = 36 + 36 = 72. Therefore, d = √72 = 6√2.
If a + b = 6, what is the value of 3a + 3b?

A. 9
B. 12
C. 18
D. 24
C. 3a + 3b = 3(a + b). Since a + b = 6, 3a + 3b = 3(6) = 18.
(3 - 1)×7 - 12 ÷ 2 =

A. 1
B. -2
C. 4
D. 8
D. Following the correct order of operations produces: (3 - 1) × 7 - 12÷2 = 2 × 7 - (12÷2) = 14 - 6 = 8.
The greatest common factor of 24 and 36 is

A. 6
B. 12
C. 36
D. 72
B. Factors of 24 are 2 × 2 × 2 × 3. Factors of 36 are 2 × 2 × 3 × 3. The greatest common factor is 2 × 2 × 3 = 12.
Solve for m: 3m - 12 = -6

A. -6
B. 0
C. 2
D. 6
C. 3m - 12 + 12 = -6 + 12; 3m = 6; Dividing both sides by 3 results in m = 2.
If 7p + 5q = -3, find q when p = 1.

A. -1
B. -2
C. -1.142857143
D. -0.285714286
B. Substitute 1 for p and solve for q. 7(1) + 5q = -3 and 7 + 5q = -3. 7 + 5q - 7 = -3 - 7 and 5q = -10. Dividing both sides by 5 results in q = -2.
Simplify (9x2y3z-12xy2z2)/3yz

A. 3xy2z2 - 4xyz
B. 3xy2z - 12xyz
C. 3x2y2 - 4xyz
D. 3y2 - 4xy2z2
C. (9x2y3z - 12xy2z2)/3yz = 9x2y3z/3yz - 12xy2z2/3yz = 3x2y2 - 4xyz
In a standard deck of playing cards, a king of hearts is drawn and not replaced. What is the probability of drawing another king from the deck?

A. 1/4
B. 1/13
C. 1/17
D. 3/52
C Probability is 1/17. Since one king was drawn and not replaced, three kings remain in the deck of 51 cards. So the probability of drawing another king is 1/17.
How many minutes are there in 1 week?

A. 10,080
B. 1,440
C. 420
D. 168
A. There are 60 minutes in 1 hour, 24 hours in 1 day, and 7 days in 1 week. So 1 week = ? = 7 × 24 × 60 = 10,080 minutes.
If 2b+3=1/8, b=

A. -6
B. -3
C. 0
D. 2
A. 1/8=1/23=2-3 so 2b+3=2-3 and b + 3 = -3. Therefore, b + 3 - 3 = -3 - 3 = -6.
The angles of a triangle are in the ratio 3:4:5. What is the measure of the smallest angle?

A. 15°
B. 30°
C. 45°
D. 75°
C. Angles in a triangle add to 180°. So 3x + 4x + 5x = 180° and 12x = 180°. Dividing both sides by 12 results in x = 15°. The smallest angle is represented by 3x = 3(15°) = 45°.
Subtract (2x3-3x+1)-(x2-3x-2)

A. 2x3-x2+3
B. 2x3-x2-6x-1
C. x3-6x-1
D. x2+3
A. Subtraction can be changed to addition by changing the signs in the entire term being subtracted. (2x3 -3x +1) - (x2-3x-2)=(2x3-3x+1) + (-x2+3x+2).. Combine like terms: 2x3-x2-3x+3x+1+2=2x3-x2+3.
If the area of a square is 400, what is the length of its side?

A. 20
B. 40
C. 100
D. 200
A. The area of a square is s2 where s is a side of the square. If s2 = 400, then s = √400 = 20.
Seven more than 3 times a number is equal to 70. Find the number.

A. 10
B. 17
C. 21
D. 30
C. Translate to a mathematical expression and solve. 3x + 7 = 70 so 3x + 7 - 7 = 70 - 7 and 3x = 63. Divide both sides by 3. Therefore, x = 21.
Which expression represents the volume of a cylinder whose height is equivalent to the length of the radius?

A. pr2
B. pr3
C. (pr)2
D. (pr)3
B. The volume of a cylinder is given by the formula V = pr2h, where r is the radius of the circular base and h is the height. Since h = r, V = pr2r = pr3.
How many distinct prime factors are there in 120?

A. 2
B. 3
C. 4
D. 5
B. Prime factors of 120 are 2 × 2 × 2 × 3 × 5. Distinct factors are 2, 3, and 5. Therefore, there are three distinct prime factors.
What percent of 3/4 is 1/8?

A. 9.38%
B. 12%
C. 16.67%
D. 25%
C. Let p represent the unknown percent. p×3/4=1/8. Solve for p by multiplying both sides by the reciprocal of 3/4. p×3/4×4/3=1/8×4/3=4/24=1/6. As a percent, 1/6 is 16 2/3%.
If x is a positive integer, solve x2 + 6x = 16.

A. 2
B. 4
C. 8
D. 10
A. Set the equation equal to 0 and factor. x2 + 6x - 16 = 0 and (x + 8)(x - 2) = 0. Then, either x + 8 = 0 or x - 2 = 0, so x = -8 or x = 2. Since x is positive, x = 2 only.