1) A certain number is twelve times as large as three times its multiplicative inverse. What is the smallest possible value of this number?

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Warren Morgan
5 years ago
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1 For this test let R be the set of all real numbers, Z be the set of all integers, and Q be the set of all rational numbers. It may be useful to know that 2019 has only two factors outside of 1 and itself. E) NOTA means None Of These Answers. 1) A certain number is twelve times as large as three times its multiplicative inverse. What is the smallest possible value of this number? A) 36 B) 6 C) 6 D) 36 E) NOTA 2) How many elements of Z are solutions to the inequality 2x-3 <5 A) 6 B) 4 C) 2 D) 0 E) NOTA 3) Simplify the following expression down to a mixed number: (9 2 3) A) B) 45 3 C) D) E) NOTA 4) Lillian wants to figure out the y-intercept of a line in the plane, but she only has the following information. What should her answer be? x y A) 3365 B) 1346 C) 1346 D) 3365 E) NOTA 5) What is the y value of the midpoint of the two points (19, 93) and (18, 41)? A) 64 B) 65 C) 66 D) 67 E) NOTA 6) It is known to JonJon that five times a number plus twelve times a different number is equal to the square of thirteen. Through some hard work he also determines that the sum of the two numbers is seventeen. What is the larger of the two numbers? A) 12 B) 13 C) 16 D) 24 E) NOTA 1

2 7) The equation x 3 + ax + 1 = 0 has no real solutions when A) a 2 B) a < 2 C) a > 2 D) a 2 E) NOTA 8) A right triangle has legs of length 12 and 35. What is the length of its hypotenuse? A) 12 B) 23 C) 35 D) 47 E) NOTA 9) Simplify 1 ( 2) A) -3 B) -1 C) 3 D) 4 E) NOTA 10) What is the midpoint of the x-intercept and y-intercept of the line 3x-7y=11? A) 3, 7 B) 422, 22 5? C) 22, 422? 5 D)?, E) NOTA 11) What is the mean of the set {13, 23, 0, 17, 11, 7, 6}? A) 7 B) 11 C) 55 B D) 77 E) NOTA For numbers 12-14, refer to the following system of equations: ax + by = w cy dx = v 12) Describe the system when a = b = c = d = 1, w = 3, v = 4. A) consistent and dependent B) consistent and independent C) inconsistent and dependent D) inconsistent and independent E) NOTA 13) What is the sum of the slopes of the two lines when a = 1, b = 2, c + 1 = d 3 = 5, w = π, and v = 0.5π A) 2 3 B) 1 C)? 3 D) 2 E) NOTA 14) If a + b + c d = w + v, no coefficients are equal to 0, and the system of equations is consistent, find the solution. (Hint: Try adding the two equations together.) A) x, y = 1, 1 B) x, y = 0, 0 C) x, y = 3, 4 D) x, y = 6, 9 E) NOTA 2

3 15) It is known that y varies directly with x and inversely with the square of z. When x is 4 and z is 11, y is 23O. What is y when both x and z are 15? 232 A) 1 B) 2 C) 15 D) 30 E) NOTA 16) Find the greatest common factor of 288x 5 y Q z? and 216x 23 y 3 z 3 A) 72x 5 y? z? B) 144x 5 y 3 z 3 C) 72x 5 y 3 z 3 D) 144x 5 y? z? E) NOTA 17) Compute 111,111 3 A) 12,345,654,321 B) 111,111,111,111 C) 111,111,111,121 D) 121,121,121,121 E) NOTA For numbers 18-20, consider the Tatum family. Parents Jim and Kay have 5 children Jason, Laura, Daniel, Stephen, and Sarah and 4 grandchildren Esther, Verity, and Ryder are Sarah s children and Adeline is Daniel s child. All ages in these problems are integer numbers of years, all less than ) Jim s current age is divisible by 9 and he is 4 years older than Kay. In 5 years, Kay s age will be an even power of 2. How old is Jim right now? A) 59 B) 60 C) 62 D) 63 E) NOTA 19) The sum of Esther s and Adeline s age equals Verity s age. The sum of Esther s and Ryder s age is one plus Verity s age. Adeline s and Ryder s age sum to 5. Find the product of Adeline s and Ryder s ages. A) 4 B) 6 C) 8 D) 9 E) NOTA 20) Jason is two years short of three times Verity s age. He is three years short of four times Esther s age. If Jason s current age is the square of an odd number, what is the positive difference between Verity s maximum and minimum age? A) 17 B) 14 C) 9 D) 8 E) NOTA 3

4 21) Answer the number that has the following properties: I. The number is an odd integer II. The number is both a perfect square and a perfect cube III. The number is strictly between 1 and 1000 A) 1 B) 64 C) 125 D) 729 E) NOTA 22) What is the sum of the exponents in the prime factorization of 78,624? A) 13 B) 12 C) 11 D) 10 E) NOTA 23) Compute the largest exponent appearing in the complete factorization of x? + x 3 y x 3 z xz yz + z 3 A) 1 B) 2 C) 3 D) 4 E) NOTA 24) What is the distance from the point ( 2, 20) to the point whose x-coordinate is the product of the first two prime numbers and the y-coordinate is the product of the next two prime numbers? A) 17 B) 15 C) 13 D) 8 E) NOTA 25) Using the standard FAMAT Regional scoring scale (4 points for a correct, 0 for a blank, -1 for a miss), which of the following scores for this test is IMPOSSIBLE? A) 115 B) 112 C) 111 D) 109 E) NOTA 26) Solve for x: x 1 + x + 20 = 7 A) 7 B) 5 C) 4 D) 3 E) NOTA 27) What is the numerator when the expression 3S + 4? + 2TS is written as one fraction in S42 ST2 S U 42 simplest form? A) x 3 1 B) 2x C) 1 + x + x 3 D) 1 x E) NOTA 4

5 28) Here s a bit of an easier one: How many prime numbers are even? A) 0 B) 1 C) 2 D) 3 E) NOTA 29) Evaluate T3 2 A) -30 B) -2 C) 2 D) 30 E) NOTA 30) Alec is eating a rare kind of shrimp that has the ability to change his skin color temporarily. The color that he changes to is assigned a number, for instance RED = R+E+D=18+5+4=27, because R is the 18 th letter in the alphabet, E is the 5 th and D is the 4 th. To turn a color, Alec would have to eat that color s number of shrimp. How many shrimp does Alec have to eat before he makes his skin turn PINK? A) 25 B) 36 C) 49 D) 81 E) NOTA 5

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