Jim Bolen Challange 1
Jan makes a 10% down payment on a used car and pays off the balance in quarterly payments of $540 for one year. Find the cost of the car.
A. $2400 B. $2500 C. $2700 D. $2750 E. $3000
A. $2400
A store sells 10 apples for $6 or 20 apples for $10. How much would you save by buying 25 apples at the 20 apple rate instead of the 10 apple rate?
A. $2 B. $2.50 C. $3.00 D. $3.25 E. $4
B. $2.50
Alice takes her favorite number, adds 5 to it, multiplies the answer by 10, subtracts 20 from the result, and then drops the final 0. If Alice’s (correct) answer is 9, what is her favorite number?
A. 5 B. 6 C. 7 D. 8 E. 9
B. 6
It takes Kim twice as long to run 2,255 decimeters as it takes Cara to run 1/10 of a mile. They start 1 kilometer apart and begin running toward each other. How far, to the nearest meter, will Kim have run when they meet? Assume that 1 mile = 1.61 kilometers.
A. 357 m B. 412 m C. 467 m D. 489 m E. 588 m
B. 412 m
When each is given in Fahrenheit, the sum of the high and low temperatures for Memphis, TN on a particular day is 68. What is the sum of the high and low temperatures in Memphis on the same day if each is given in Celsius? Hint: F = (9/5)C + 32
A. 20/9 B. 36/5 C. 20 D. 772/9 E. 772/5
A. 20/9
Define the binary operation $ by a$b = ab + 2a – 3b. Find x$(2$x).
A. x^2 – 9x + 12 B. x^2 + 12x + 9
C. - x^2 + 12x – 9 D. x^2 – 12x – 9
E. - x^2 + 9x – 12
3. The
E. - x^2 + 9x – 12
For real numbers x and y, define the binary operation # by: x # y = (xy^2 + yx^2) / (5 + x^2 y^2)
Find 2 # (5 # 2).
A. 17/105 B. 17/61 C. 32/61 D. 2/3 E. 61/17
C. 32/61
Let A and B be single nonzero digits, so that AA is a 2-digit number with identical digits. Which of the following is a value of A which satisfies AA + A = B * AB?
A. 1 B. 2 C. 3 D. 4 E. 5
B. 2
For real numbers a and b, define an operation Δ as aΔb = ab^2 – |a|. Find [(-2) Δ 5] Δ (-1).
A. -104 B. -96 C. -53 D. 0 E. 96
A. -104
A town has 3.75 people per family and 2.5 TV’s per family. Find the number of TV’s per person.
A. 3/5 B. 2/3 C. 3/4 D. 4/5 E. 5/6
B. 2/3
A triangle with integer-length sides has no two sides equal. What is its least possible perimeter?
A. 6 B. 7 C. 8 D. 9 E. 10
D. 9
Points A and B lie on a circle with radius 6 units centered at C. The measure of ∠ACB is 120°. Point X is outside the circle such that segments XB and XA are both tangent to the circle. Find the area of quadrilateral XACB.
A. 18√3 B. 48 C. 36√3 D. 64 E. 48√3
C. 36√3
An open box is made by cutting an N-inch by N-inch square from each corner of a 10-inch by 12-inch rectangular piece of material and then folding up the flaps. There are two different values of N that will result in a volume of 80 cubic inches. Find the sum of these two values of N, rounded to the nearest hundredth.
A. 2.76 B. 3.76 C. 7.24 D. 8.24 E. 10
B. 3.76
An isosceles triangle has two sides of length 40 and a base of length 48. A circle circumscribes the triangle. What is the radius of the circle?
A. 20√2 B. 28 C. 18√3 D. 12√5 E. 25
E. 25
There are exactly 2 noncongruent rectangular boxes with integer-length edges whose space diagonals have length 17. Find the ratio of the larger to the smaller volume.
A. 2 B. 3 C. 4 D. 5 E. 6
E. 6
The sum of the slopes of the perpendicular lines with equations y = mx and y = Mx equals 9/20. Find |M−m|.
A. 29/20 B. 23/20 C. 37/20 D. 41/20 E. 43/20
D. 41/20
The two lines with equations ax + 12y = 6 and ax - 3y = 12 (a ≥ 0) are perpendicular. Find a.
A. 2 B. 3 C. 4 D. 6 E. 8
D. 6
Let p and q be two constants for which the equation 2x + p = q has the solution x = 12. Find the solution to the equation 3x + q = p.
A. -18 B. -8 C. -4 D. 8 E. 18
B. -8
The line Ax + By = 1 passes through the point (-9, 10), has negative slope, and has intercepts (p, 0) and (0, q). If p + q = 14, find A + B.
A. -1/28 B. -14/45 C. 1/28 D. 5/ 17 E. 14/45
E. 14/45
The area of the four-sided region in the first quadrant bounded by the x-axis, y-axis, and the lines 3x + 4y =12 and 2y - x = 2 is cut in half by the line y = kx. Find k.
A. 33/76 B. 2/5 C. 11/19 D. 1/2 E. 21/38
A. 33/76
Let P(x) = Ax^5 + Bx^4 + Cx^3 + Cx^2 + Bx + A be a fifth-degree polynomial with integer coefficients where A > 0 and the greatest common factor of A, B, and C is 1. If √7 is a zero of P(x), find A + B + C.
A. -50 B. -36 C. 0 D. 36 E. 50
B. -36
For a third-degree polynomial P(x), P(-1) = P(1) = P(2) = 2 and P(3) = 10. Find P(4).
A. 20 B. 24 C. 28 D. 30 E. 32
E. 32
Suppose a, b, and c are integers. What is the sum of the reciprocals of the five complex solutions of the equation x^5 + ax^4 + bx^3 + cx^2 – 12x + 8 = 0?
A. -√3/2 B. -1 C. 2/√3 D. 4/7 E. 3/2
E. 3/2
The roots of 𝑎𝑥^2+bx+c, where a, b, and c are real numbers with a nonzero, are r and s. If r/(1+r) and s/(1+s) are the roots of 𝑥^2+dx+e=0 0 (d, e are real), find d + e.
A. (b-c)/(a-b+c) B. (b-c)/(b-a+2c)
C. (3c-b)/(a-b+c) D. (3c-b)/(b-a+2c)
E. (b+c)/(b-a+2c)
A. (b-c)/(a-b+c)
The polynomial 2x^3 + x^2 + cx + d is divisible by x + 1. If d and c are integers with d + c = 29, find the sum of the two non-real roots of this polynomial.
A. -1 B. -1/2 C. 0 D. 1/2 E. 1
D. 1/2