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Total 1634 questions
If the volume of a cube is x -
cubic units, what is the number of square units in the surface area of the cube?
- A. x
- B. x
- C. x
- D. 6x
- E. 6x
Answer : D
Explanation:
If the volume of the cube is x -
, then one edge of the cube is x. The surface area of a cube is six times the area of one face, which is x times x. The total surface area is 6x
.
If x גˆ’ 3 is a multiple of two, what is the next larger multiple of two?
- A. 2x
- B. x גˆ’ 2
- C. x גˆ’ 1
- D. x גˆ’ 5
- E. x + 2
Answer : C
Explanation:
The next larger multiple of two would be x גˆ’ 3 + 2, which is x גˆ’ 1. In this case, remember that any even number is a multiple of two and all evens are two numbers apart. If x גˆ’ 3 is a multiple of two, you can assume that it is also an even number. This number plus two would also produce an even number.
If 3x + 1 = 81, then x גˆ’ 1 =
- A. 2
- B. 3
- C. 4
- D. 9
- E. 27
Answer : A
Explanation:
Solve for x first. Since 3x + 1 = 81, and 81 is 34, make an easier equation just based on the exponents. This would be x + 1 = 4. x = 3. Therefore, x גˆ’ 1 = 3 גˆ’ 1 =
2.
For dinner at a restaurant, there are x choices of appetizers, y + 1 main courses, and z choices of dessert. How many total possible choices are there if you choose 1 appetizer, 1 main course, and 1 dessert for your meal?
- A. x + y + z + 1
- B. xyz + xz
- C. xy + z + 1
- D. xyz + 1
- E. xyz + 1/2
Answer : B
Explanation:
Use the counting principle: Take the number of choices you have for each course and multiply them together to get the total possible combinations. x ֳ— (y + 1) ֳ— z.
Use the distributive property to simplify to xyz + xz.
If x ג™¦ y is defined as 2(x + y)
, then what is the value of 2 ג™¦ 3?
- A. 25
- B. 36
- C. 50
- D. 100
- E. 144
Answer : C
Explanation:
For this type of problem, substitute the values you are given for x and y. In this case, x = 2 and y = 3. The expression becomes 2(2 + 3)
. Using the order of
operations, perform the operation within the parentheses first and then the exponent. 2(5)
= 2(25). Multiply to get 50.
If x, y, and z are real numbers, which is always true?
I) x(yz) = (xy)z -
II) x/y = y/z -
III) z(x + y) = zx + zy -
- A. I only
- B. II only
- C. I and II only
- D. I and III only
- E. I, II, and III
Answer : D
Explanation:
Statement I is an example of the associative property of multiplication and statement III is an example of the distributive property. These properties will hold for any real numbers that are substituted into them. Statement II is not a property of real numbers and may be true for certain numbers, but not for every real number.
If y = 6 -
, then 6y equals
x
- A. 6 x
- B. 6 x + 1
- C. 6 x + 6
- D. 6 x גˆ’ 1
Answer : B
Explanation:
Since y = 6 -
, multiplying each side of the equation results in 6y = 6(6
). Recall that since 6 = 6
, 6
ֳ— 6
= 6
by the laws of exponents.
x
x
x
x + 1
What is the smallest of six consecutive odd integers whose average (arithmetic mean) is x + 2?
- A. x גˆ’ 5
- B. x גˆ’ 3
- C. x גˆ’ 1
- D. x
- E. x + 1
Answer : B
Explanation:
Remember that consecutive odd integers are numbers that are two apart in order, like 11, 13, and 15. The average of six consecutive odd integers will be an even number. If x + 2 is the average, then this value will be at the middle of the integers if they are arranged in order. Therefore, the three consecutive odd integers smaller than this are expressed as x + 1, x גˆ’ 1, and x גˆ’ 3 in descending order. The smallest odd integer is x גˆ’ 3.
The product of a and b is equal to 11 more than twice the sum of a and b. If b = 7, what is the value of b גˆ’ a?
- A. 2
- B. 5
- C. 7
- D. 24
- E. 35
Answer : A
Explanation:
Write an equation for the question by translating the first sentence. The product of a and b is ab, and 11 more than twice the sum of a and b translates to 2(a + b)
+ 11. The equation is ab = 2(a + b) + 11. Substitute 7 for b. 7a = 2(a + 7) + 11. This simplifies to 7a = 2a + 14 + 11 by the distributive property and then becomes
7a = 2a + 25. Subtract 2a from both sides of the equation and then divide each side by 5; 7a גˆ’ 2a = 2a גˆ’ 2a + 25.
The instructions state that Cheryl needs
/
square yards of one type of material and
/
square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has
/
square yards left that she did not use. What is the total amount of square yards of material Cheryl used?
A.
/
B.
/
C.
/
D. 1 -
/
E. 2 -
/
Answer : C
Explanation:
To solve the problem, you need to add
/
and
/
then subtract
/
since the amount she has not used is
/
, which reduces to
/
. If you were to add
/
and
/
,
and then subtract
/
, you would end up with
/
.
Which of the following values of x would satisfy the inequality x > 1?
- A. I only
- B. II only
- C. II and III only
- D. I and III only
- E. I, II, and III
Answer : C
Explanation:
Statement I simplifies to -
/
, which is less than 1. Statement II simplifies to
/
, which is greater than 1. In statement III, you need to take the reciprocal of the fraction inside the parentheses (because the exponent is negative) and then evaluate using an exponent of 2. This results in (ג€"3)
= 9, which is also greater than
1. Both statements II and III would satisfy the inequality x > 1.
John is three times as old as Sam. If John will be twice as old as Sam in six years, how old was Sam two years ago?
- A. 2
- B. 4
- C. 6
- D. 8
- E. 16
Answer : B
Explanation:
Let x = Samג€™s current age and 3x = Johnג€™s current age. If John will be twice as old as Sam in six years, this sets up the equation 3x + 6 = 2(x + 6). Solve this equation for x by using the distributive property on the right side of the equation and then subtracting 2x from both sides. 3x + 6 = 2x + 12. 3x גˆ’ 2x + 6 = 2x גˆ’ 2x +
12. Subtract 6 from both sides. x + 6 גˆ’ 6 = 12 גˆ’ 6. x = 6. Since x is Samג€™s current age, Sam was four years old two years ago.
Given a spinner with four sections of equal size labeled A, B, C, and D, what is the probability of NOT getting an A after spinning the spinner two times?
- A. 9/16
- B. 1/8
- C. 1/4
- D. 1/2
- E. 15/16
Answer : A
Explanation:
By spinning the spinner two times, the probability of not getting an A is
/
ֳ—
/
=
/
.
A case of 12 rolls of paper towels sells for $9. The cost of one roll sold individually is $1. What is the percent of savings per roll for the 12-roll package over the cost of 12 rolls purchased individually?
- A. 9%
- B. 11%
- C. 15%
- D. 25%
- E. 90%
Answer : D
Explanation:
If sold by the case, each individual roll cost $.75
To find the percent of savings, compare the savings to the cost of a roll sold individually.
How many different committees can be formed from a group of two women and four men if three people are on the committee and at least one member must be a woman?
- A. 6
- B. 8
- C. 10
- D. 12
- E. 16
Answer : E
Explanation:
If at least one member must be a woman, the committee will have either one woman and two men or two women and one man. Use combinations because the order does not matter.
Choosing one woman and two men:
Choosing two women and one man:
Since both situations would satisfy the requirement that at least one member is a woman, add the combinations.
12 + 4 = 16 total committees.
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