Math Trivia Questions — page 2

Exits on a highway are numbered consecutively from 1 to 50. The distance from exit 41 to exit 50 is 100 km. If each exit is at least 6 km from the next exit, what is the longest possible distance, in kilometers, between exit 47 and exit 48?

• A52
• B49
• C51
• D50

Jean threw a softball a distance of 9 feet. Lee threw a softball 3 times as far as Jean. Which equation can be used to determine thedistance, d, that Lee threw the ball?

• Adx3=9
• B3+9=d
• C3x9=d
• Dd+3=9

Ramanujan and Hardy played a game where they both picked a complex number. If the product of their numbers was $32-8i$, and Hardy picked $5+3i$, what number did Ramanujan pick?

• A5+3i
• B4-4i
• C4-i
• D32-8i

Which ratios are equal to 4 : 32?

• A12 : 96; 12 : 16
• B2 : 96; 2 : 16
• C12 : 96; 2 : 16
• D2 : 96; 12 : 16

Eleven pencils cost as much as three pens. If seven pens cost $\$ 9.24$, what is the cost, in cents, of one pencil?

• A11
• B52
• C33
• D36

Let V be the real vector space of all real 2 x 3 matrices, and let W be the real vector space of all real 4 x 1 column vectors. If T is a linear transformation from V onto W, what is the dimension of the subspace kernel of T?

• A5
• B2
• C4
• D3

The domain of the function $h(x) = \sqrt{25-x^2}+\sqrt{-(x-2)}$ is an interval of what width?

• A2
• B5
• C7
• D25

A company makes 5 blue cars for every 3 white cars it makes. If the company makes 15 white cars in one day, how many blue cars will it make?

• A17
• B25
• C9
• D13

At Academic Academy, to pass an algebra test you must score at least $80\%$. If there are 35 problems on the test, what is the greatest number you can miss and still pass?

• A28
• B8
• C7
• D35

Four packages are delivered to four houses, one to each house. If these packages are randomly delivered, what is the probability that exactly two of them are delivered to the correct houses? Express your answer as a common fraction.

• A\frac{1}{2}
• B\frac{27}{128}
• C\frac{1}{4}
• D\frac{1}{9}

Find all positive values of $c$ so that the inequality $x^2-6x+c<0$ has real solutions for $x$. Express your answer in interval notation.

• A(0, 9)
• B(1, 1)
• C(6, 0)
• D(6, 6)

Which pair of expressions below are equivalent?

• A4(2x — 6) and 8x — 24
• Bx+x+x+x and x^4
• C3x + 5x and 15x
• D7(2x) and 9x

A tank is in the shape of a triangular prism. If the triangular base has an area of 116 square feet, and the tank is 30 feet tall, how much water would the tank contain when it is full?

• A1725 ft^3
• B3480 ft^3
• C6960 ft^3
• D1740 ft^3

Find the product of 0.07 • 5.8.

• A4.06
• B0.0406
• C40.6
• D0.406

Compute $\dbinom{85}{82}$.

• A252
• B98770
• C4680
• D101170

Use the equation below to answer the question. 0.75 × 6.5 = m Which expression shows one way to solve the equation?

• A75 × 65 ÷ 1,000
• B0.7 × 6 + 0.7 × 5 + 0.5 × 6 + 0.5 × 5
• C0.7 × 6 + 0.7 × 0.5 + 0.5 × 6 + 0.5 × 0.5
• D75 × 650 ÷ 1,000

An investment of $4000 grows at the rate of 320*e^(0.08t) dollars per year after t years. Its value after 10 years is approximately

• A$4,902
• B$8,902
• C$7,122
• D$12,902

What is the second number in the row of Pascal's triangle that has 43 numbers?

• A43
• B42
• C44
• D16

If the finite group G contains a subgroup of order seven but no element (other than the identity) is its own inverse, then the order of G could be

• A35
• B37
• C27
• D28

A group of hikers climbed from Salt Flats (elevation −55 feet)to Talon Bluff (elevation 620 feet). What is the difference in elevation between Talon Bluff and Salt Flats?

• A675 feet
• B575 feet
• C565 feet
• D665 feet

Lily is going to give away all the pieces of candy in a bag. She can give an equal number of pieces of candy to 5, 3, or 2 people. Which number of pieces of candy could be in Lily's bag?

• A45
• B30
• C20
• D12

Each time Rami turned the dial on a machine, the dial moved 1 degree. Rami turned the dial 10 times. What is the total number of degrees the dial moved?

• A360
• B10
• C110
• D90

What is the area, in square units, of a square whose sides are the same length as the radius of a circle with a circumference of $12\pi$ units?

• A10
• B12
• C11
• D36

Simon used 3 pears and 9 apples to make a fruit salad. What was the ratio of the number of pears to the number of apples in the fruit salad?

• A1:09
• B1:03
• C1:04
• D1:06

A group of friends go out to lunch. d people buy salad and p people buy soup. Each salad costs $3.99 and each soup costs $2.99. Write an expression for the total costs of the soup and salads.

• A2.99p + 3.99d
• B(2.99 + 3.99)(p + d)
• C3.99p + 2.99d
• D(3.99p + 2.99)d

What is the shortest distance from the origin to the circle defined by $x^2-24x +y^2+10y +160=0$?

• A12
• B16
• C10
• D24

Find the number that makes the statement 2 over 9 = 14 over ? true.

• A63
• B15
• C14
• D16

Find the GCD of 25 and 55.

• A275
• B5
• C11
• D50

Consider a segment of length 10. Points A and B are chosen randomly such that A and B divide the segment into three smaller segments. What is the probability that the three smaller segments could form the sides of a triangle?

• A50%
• B25%
• C0
• D10%

A post office delivered eighteen thousand ninety-six pieces of mail in a week. What is this number of pieces of mail written in expanded form?

• A10,000 + 8,000 + 900 + 60
• B18 + 1,000 + 90 + 6
• C10,000 + 8,000 + 90 + 6
• D18 + 1,000 + 900 + 60

Roslyn has twenty boxes. Thirteen of the boxes contain pencils, nine of the boxes contain pens, and three of the boxes contain neither pens nor pencils. How many boxes contain both pens and pencils?

• A5
• B139
• C2
• D13

Marguerite earned a score between 75 and 89 on all of her previous spelling tests. She earned a score of 100 on her next test. Which of the following statements is true?

• AThe mean will increase.
• BThe mean will decrease.
• CThe median will decrease.
• DThe mode will increase.

For which of the following rings is it possible for the product of two nonzero elements to be zero?

• AThe ring of continuous real-valued functions on [0, 1]
• BThe ring of complex numbers
• CThe ring of integers modulo 11
• DThe ring {a + b * sqrt(2) : a and b are rational numbers}

When a certain number is divided by 4, the answer is 160 with a remainder of 2. What is the number?

• A638
• B42
• C642
• D38

Use mental math to find the sum of 11.7 + 3.4 + 6.3.

• A20.4
• B21.4
• C22.4
• D20.3

Simplify −4 + 7 • 3^2. Use a calculator, paper and pencil, or mental math.

• A289
• B437
• C59
• D27

Which pair of ratios can form a proportion?

• A2 over 5 and 6 over 15
• B2 over 5 and 4 over 25
• C2 over 5 and 10 over 15
• D2 over 5 and 8 over 10

Order the numbers 6, −1, 8, −3, −4 from least to greatest.

• A6, −1, 8, −3, −4
• B−3, −4, 6, −1, 8
• C−1, −3, −4, 6, 8
• D−4, −3, −1, 6, 8

Suppose $f(x)$ is an invertible function, and suppose that $f(2)=f^{-1}(2)=4$. What is the value of $f(f(2))$?

• A2
• B4
• C1
• D0

Consider the system of linear equations w + 3x + 2y + 2z = 0 w + 4x + y = 0 3w + 5x + 10 y + 14z = 0 2w + 5x + 5y + 6z = 0 with solutions of the form (w, x, y, z), where w x, y, and z are real. Which of the following statements is FALSE?

• AThe system has infinitely many solutions.
• BThe sum of any two solutions is a solution.
• CEvery solution is a scalar multiple of (-5, 1, 1, 0).
• DThe system is consistent.

A grocerystore sells a bag of 5 lemons for $2.00. What is the unit cost of each lemon in the bag?

• A$0.10
• B$0.60
• C$2.50
• D$0.40

Simplify the fraction by rationalizing the denominator: $$\frac{4}{\sqrt{108}+2\sqrt{12}+2\sqrt{27}}.$$

• A2\sqrt{27}
• B\frac{\sqrt{3}}{12}
• C\frac{4\sqrt{3}}{33}
• D\frac{1}{4\sqrt{3}}

A scientist measured the diameters of four human hairs. The diameters, in millimeters, were 0.091, 0.169, 0.17, and 0.023. Which inequality correctly compares the diameters of two of the human hairs?

• A0.17 > 0.023
• B0.091 < 0.023
• C0.169 > 0.17
• D0.17 < 0.091

A librarian receives two boxes of booksfor the library. The first box has 136 books. The second box has 58 fewer books than the first box. What is the total number of books the librarian receives?

• A214
• B78
• C194
• D58

If 30,000 is divided by 10 and then divided by 10 again, what will be the resulting number?

• A3,000
• B30
• C300
• D3

What is the smallest whole number that has a remainder of 1 when divided by 4, a remainder of 1 when divided by 3, and a remainder of 2 when divided by 5?

• A57
• B67
• C37
• D43

If the ratio of $2x-y$ to $x+y$ is 2 to 3, what is the ratio of $x$ to $y$? Express your answer as a common fraction.

• A\frac{2}{5}
• B\frac{5}{2}
• C\frac{4}{5}
• D\frac{5}{4}

Let A be the set of all ordered pairs of integers (m, n) such that 7m + 12n = 22. What is the greatest negative number in the set B = {m + n : (m, n) \in A}?

• A-3
• B-5
• C-4
• D-2

If x − 3 = 6, what is the value of x?

• A2
• B9
• C3
• D6

The length of a rectangle is twice its width. Given the length of the diagonal is $5\sqrt{5}$, find the area of the rectangle.

• A2
• B50
• C2500
• D25