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1.The sum of two natural numbers is 100 and their positive difference is 42. What is the positive difference of the squares of these two natural numbers?A.1600B.2800C.3600D.4200E.84002.The sum of 16 consecutive integers is 2008. What is the largest of these?A.132B.133C.134D.135E.141–1120pqrstuvwxyUse this number line, with ten points labeled with letters, to answer questions #3 and #4, below.3.Which of these points is closest to the sum q + u ?A.rB.sC.tD.vE.w4.Which of these points is closest to r2 ?A.qB.sC.tD.uE.v5.For every 3oC rise in temperature, the volume of a certain gas increases by 4 cubic centimeters. 50 cubic centimeters of this gas at –8oC is heated from –8oC to 19oC. By what percent does the volume increase?A.36%B.42%C.58%D.60%E.72%6.If two standard 6-sided dice are tossed, what is the probability that the product of the two numbers rolled is even?A.1/4B.1/2C.5/8D.19/39E.3/47.For all families with an income over $30,000, a state’s income tax is $900 plus 4% of all income over $30,000. If a family’s income is $56,500, what amount of state income tax do they pay?A.$1960B.$2260C.$2460D.$2860E.$31608.From an 8x8x8 cube, a 2x2x2 cube is removed from each corner. What fraction of the 8x8x8 cube is removed?A.1/4B.1/8C.1/2D.3/32E.3/89.Gabe was born on February 29th, 1916. So his first true ‘birthday’ was February 29th, 1920. By today, how many ‘true’ birthdays has Gabe celebrated?A.21B.22C.23D.24E.2510.In September, 2006, a team led by mathematicians from the University of Central Missouri found the 44th Mersenne Prime. It is: . What is its units’ digit?A.1B.3C.5D.7E.911.A bicycle rider rides at a constant speed. By 10:00 AM, she has completed 2/5 of her ride; by 10:42 AM, she has completed 3/4 of her ride. At what time did she start her ride?A.9:06 AMB.9:12 AMC.9:18 AMD.9:24 AME.9:30 AM 12.For how many natural numbers N doesdiffer from 20 by less than 1?A.78B.79C.80D.81E.8213.The Poorone couple receives their credit card bill on the first of each month. On the 2nd of each month, they immediately make the minimum payment of $50. At the end of each month, the credit card company increases their total due by 1.5%. If their January 1 credit card bill is $3000, and if they don’t put any more purchases on this credit card, which of the following is closest to their credit card bill on April 1? A.$3156B.$3045C.$2982D.$2805E.$274114.US and Mexican citizens who often drive across the border can purchase their gasoline in the US or in Mexico. Lupe intends to purchase 70 liters of gasoline that would cost 7.01 pesos per liter in Mexico. In the US, he could buy the gasoline for $2.85 per gallon. There are 3.785 liters to a gallon. One US dollar is worth 10.73 pesos. Rounded to the nearest US dollar, how much would he lose or save by purchasing the 70 liters in Mexico?A.Save $7B.Save $2C.Lose $2D.Lose $5E.Lose $8ABCD15.Given: AB = BD = DC. If , what is the measure of angle A.22.5oB.25oC.30oD.36oE.45o16.In a lake with 4000 fish, 90% are labeled ‘small’ which means that they are less than 5 cm long. How many of these ‘small’ fish must be removed from the lake to reduce the percent of small fish in the lake from 90% to 75%?A.600B.1000C.1800D.2400E.280017.A semi-circle with diameter 18 cm is inscribed in a rectangle. Rounded to the nearest tenth, what per cent of the rectangular region is shaded?A.21.5%B.22.8%C.23.4%D.24.2%E.25%18.A 3-digit natural number is divisible by 5 but not by 10. The hundreds’ digit is odd and the tens’ digit is twice the hundreds’ digit. What is the sum of all numbers that meet all of these conditions?A.490B.540C.560D.600E.66019.As the value of x increases from –1 to 0, how many of these five numbers also increase?A.1B.2C.3D.4E.520.A square magazine page, 12 cm by 12 cm, is to be filled with any mix of ads that each measure 12x6, 6x12, 6x6, 12x3, or 3x12. If at least one 3x12 or 12x3 ad is used, how many different designs are possible? Note: Being a magazine page, these three sample designs are considered distinct.A.7B.12C.14D.16E.2121.A circle with diameter s sits on top of a square with side s. Pulled tight, an 80 cm piece of tape is wrapped exactly once (without overlap) to hold the square and circle together,as shown. To the nearest tenth of a square centimeter, what is the area of the square?A.116.4B.144.6C.182.5D.206.2E.240.6ECHBGAFD22.Eight identical sheets of paper were placed, one at a time, overlapping as shown in the diagram. Which sheet(s) of paper could have been the fifth one placed?A.Only AB.Only EC.Only GD.Only A or GE.Only D or G23.In the past 15 years at Pythagoras High school, the number of students acting in school plays increased 15%. Among boys, it increased 10%, and among girls, it increased 40%.15 years ago, what percent of the acting students were female?A.16 2/3 %B.20%C.50%D.80%E.83 1/3 %24.For how many natural numbers N is the 8-digit number: 76,__ __ __, __ __ 4 = N2 a perfect square? A.6B.8C.9D.10E.1225.When the decimal point of a certain positive number is moved one placed to the right, the positive difference between the two numbers is 18.072. What is the sum of these two numbers?A.22.088B.22.88C.220.08D.220.88E.222.0826.What is the area of the triangle bounded by the three lines x=4; y=10; and x+y = 8?A.18B.20C.22D.24E.2627.The first and second numbers in a sequence are 512; 1/32. Each new number in the sequence is the product of the previous two numbers. The 17th number in this sequence is 2N. What is N?A.50B.64C.128D.343E.55528.A bag contains only blue marbles, green marbles, and 24 red marbles. If the probability of drawing a blue marble is 1/2 and the probability of drawing a green marble is 1/8, how many green marbles are in the bag?A.3B.4C.5D.6E.829.The operation on two ordered pairs is defined by: If , what does x+y equal?A.–14B.–2C.0C.2E.830.Let x be the length of the diagonal of a rectangle with perimeter 24. The area of the rectangle can be written: A = M + Nx2. What is the product MN?A.–36B.48C.72D.–72E.–14453558335355885ABDCFE31.Two pairs of congruent shapes that form a square are shownto the right.? They are rearranged (without overlap) to form the given rectangle AECF.? Lengths are in centimeters.What is the area in square centimeters of the region ABCD?A.0B.0.25C.0.5D.1E.1.532.Assume that x, y, and z are distinct prime numbers. The largest perfect square factor of can be written in the form . What is the sum a+b+c ?A.15B.17C.20D.22E.2333.In the board game Careers, when Zan is sent to the Park Bench square she rolls two standard 6-sided dice on each turn.? She can leave the Park Bench square only if she rolls a sum of 7, a sum of 11, or rolls the same number on each die.? What is the probability that she can leave Park Bench on either her first roll or her second roll? Round to the nearest per cent.A.63%B.67%C.75%D.78%E.85%34.When expanded, how many 0’s are at the end of: ?A.60B.90C.100D.120E.13035.a, b, c, and d are Real numbers such that a < b < c < d.Of the 6 possible sums of any two of these four numbers, the four least sums are 7; 9; 12; 13.What is the sum a+b+c+d?A.20.5B.22C.22.5D.23.5E.2536.Bo is playing the computer game, “Flip the Coin”. Bo starts with 256 chips. On each turn he guesses “Heads” or “Tails” and there is a 50% probability of each outcome. On each turn he bets 1/2 of his remaining chips; he will either lose or win that number of chips. After 8 turns, what is the probability that Bo has a total of at least 256 chips?Round to the nearest tenth of a per cent. A.14.5%B.27.3%C.36.3%D.50.0%E.63.7%37.a and b are integers such that ab = 64 . What is the sum of all possible values of a?A.68B.70C.72D.76E.7826222838.The six numbers on the faces of this cube are consecutive even numbers. The sums of the two numbers on each pair of opposite faces are equal. What number is on the face opposite 22?A.18B.20C.24D.30E. 3239.Two squares are inscribed in a circle, as shown. What is the ratio of the area of the larger square to the area of the smaller square?A.16B.25C.32D.E.8 cm4 cm4 cm40.This quadrilateral can be divided into 4 congruent quadrilaterals. What is the perimeter of each of these 4 quadrilaterals?A.B.C.D.E. ................
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