2017 State Competition Sprint Round Problems 1 30-Books Download

2017 State Competition Sprint Round Problems 1 30
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inches If the total area enclosed by the seven congruent squares shown is 112 in2 what. is the perimeter of the outer polygon, 2 Sasha added all but one of the first ten positive integers together Her sum is a. square number Which integer did Sasha not include,3 If 2 what is the value of. For every 50 worth of supplies Bill buys at a local hardware store he receives. a 5 discount If Bill bought 846 worth of supplies from this store what was. the cost after the discounts were applied, 5 Ayasha Beshkno and Chenoa were all born after 2000 Each of them was born. in a year after 2000 that is divisible by exactly one of the prime numbers 2 3 or. 5 Each of these primes is a divisor of one of the birth years What is the least. possible sum of their birth years, Copyright MATHCOUNTS Inc 2016 All rights reserved 2017 State Sprint Round. degrees The grade of a ski slope is the ratio of the vertical drop to. the horizontal distance What is the measure of the angle. between the ski slope and the vertical as shown of a. ski slope whose grade is 100, percent Jeff has been collecting string and has wound it into a sphere with a diameter of.
1 2 meters He has collected enough additional string to increase the diameter. of the sphere by 0 2 meters What is the percent increase in the radius of the. sphere Express your answer as a decimal to the nearest tenth. baskets Allie plays basketball with her friends and makes 10 baskets If each basket. is worth either 2 or 3 points and Allie scores a total of 26 points how many. baskets worth 3 points did she make, cm3 A small cube is built inside a large cube as shown The edge. length of the large cube is four times the edge length of the. small cube If the small cube has volume 5 cm3 what is the. volume of the space inside the large cube surrounding the. small cube, 10 Andre can complete of a job in of the time that it takes Michael to do. the whole job What is the ratio of the rate at which Andre works to the rate at. which Michael works Express your answer as a common fraction. Copyright MATHCOUNTS Inc 2016 All rights reserved 2017 State Sprint Round. 11 Eleven boastful bees are all lined up in a row Each bee after the first one brags. that it collected one more than twice as many grains of pollen as the bee in front. of it If the first bee has 100 grains of pollen how many grains did the last bee. 12 The mean of a list of nine numbers is 17 and the modes are a b and c If a 4. 1 b and c 8 are distinct numbers in the list and none of them are modes of. the list then what is the value of 3 a b c, in2 The perimeter of a rectangle is 40 inches and each diagonal of the rectangle is. 18 inches long What is the area of this rectangle, ways The figure shows five rows each containing five bricks In how many ways can. Mario choose five bricks one in each row so that any two bricks chosen in. adjacent rows are adjacent, 15 What is the least positive base 10 integer that can be written as a 4 digit number.
in base 3 and as a 3 digit number in base 4, Copyright MATHCOUNTS Inc 2016 All rights reserved 2017 State Sprint Round. 16 If x and y are integers such that x 3 2 y 4 2 25 what is the greatest. possible value of x 2 y 2, 17 A positive integer q is the product of a prime number and a perfect square. Additionally q is the product of a different prime number and a perfect cube. What is the least possible value of q,18 If 1 and 2 what is the value of x. 2 x y 3 2 x y 3, 19 A pole of radius 1 inch and height h inches is perpendicular to the ground A. snake is coiled around the pole in a spiral pattern making a 60 degree angle. with the ground If the snake is 9 inches long and reaches from the ground to. the top of the pole then h can be written in the form a b where a is a rational. number and b is a positive integer that is not divisible by the square of any. prime What is the value of a b Express your answer as a common fraction. 34 43 24 33 23, 20 The median of the five numbers 2 2 3 4 and 4 is equal to.
p k for some prime number p and some positive integer k What is the value of. Copyright MATHCOUNTS Inc 2016 All rights reserved 2017 State Sprint Round. numbers The number 40 231 is a five digit positive integer that uses five consecutive. digits although not necessarily in order How many such five digit numbers are. inches Chloe finds a coin as shown wedged tightly into the corner of. her drawer behind a rectangular box with a 2 5 inch edge One. corner of the box is 1 5 inches from the corner of the drawer and. the other corner of the box is 2 inches from the corner of the. drawer What is the diameter of the coin, 23 What four digit number has tens digit 2 and units digit 8 is a multiple of 16 and. when its digits are reversed the result is also a multiple of 16. units What is the radius of the inscribed circle of a triangle with side lengths 9 13 and. 14 Express your answer in simplest radical form, 25 On an infinitely large grid of squares a two by two. 13 14 15 16 17, region is shaded Starting in the square above the upper. left shaded square the squares in the grid are numbered 12 1 2 3 18. with consecutive positive integers moving in a clockwise 11 4. direction to the next open square The figure shows the. grid with the first 18 squares numbered What integer. will appear in the 6th square to the right of the square 9 8 7 6. numbered 5, Copyright MATHCOUNTS Inc 2016 All rights reserved 2017 State Sprint Round. 26 A triangle in the coordinate plane has vertices at 4 0 6 0 and 0 5. The line y x c where c is a positive number divides the triangle into a. trapezoid and a smaller triangle whose areas respectively are in the ratio 5 4. What is the value of c Express your answer as a common fraction. 27 In how many ways can 20 identical coins be given to 4 distinct people so that. each person gets at least 2 coins, 28 What is the sum of all values of x that satisfy the equation 4.
29 Lines AB and DC are parallel and transversals AC and BD intersect at a point X. between the two lines so that Points P and Q lie on segments AB and. DC respectively The segment PQ intersects transversals BD and AC at points. M and N respectively so that PM MN NQ What is the ratio Express. your answer as a common fraction, 30 Suppose that a is a number such that the system of equations. has an odd number of distinct solutions What is the product of all possible. values of a, Copyright MATHCOUNTS Inc 2016 All rights reserved 2017 State Sprint Round. Forms of Answers, The following list explains acceptable forms for answers Coaches should ensure that Mathletes are familiar. with these rules prior to participating at any level of competition Judges will score competition answers in. compliance with these rules for forms of answers, Units of measurement are not required in answers but they must be correct if given When a problem. asks for an answer expressed in a specific unit of measure or when a unit of measure is provided in the answer. blank equivalent answers expressed in other units are not acceptable For example if a problem asks for the. number of ounces and 36 oz is the correct answer 2 lbs 4 oz will not be accepted If a problem asks for the. number of cents and 25 cents is the correct answer 0 25 will not be accepted. All answers, must be expressed in simplest form A common fraction is to be considered a fraction in the.
form b where a and b are natural numbers and GCF a b 1 In some cases the term common fraction. is to be considered a fraction in the form BA where A and B are algebraic expressions and A and B do not. share a common factor A asimplified mixed number mixed numeral mixed fraction is to be considered. a fraction in the form N b where N a and b are natural numbers a b and GCF a b 1 Examples. Problem What is 8 12 expressed as a common fraction Answer 3 Unacceptable 6. Problem What is 12 8 expressed as a common fraction Answer 2 Unacceptable 8 1 2. Problem What is the sum of the lengths of the radius and the circumference of a circle with diameter 4 unit. expressed as a common fraction in terms of Answer 8. Problem What is 20 12 expressed as a mixed number Answer 1 2. Unacceptable 1 12 5, Ratios should be expressed as simplified common fractions unless otherwise specified Examples. Simplified Acceptable Forms 2 6,Unacceptable 3 12 34 3 5 2 1. Radicals must be simplified A simplified radical must satisfy 1 no radicands have a factor which possesses. the root indicated by the index 2 no radicands contain fractions and 3 no radicals appear in the denominator. of a fraction Numbers with fractional exponents are not in radical form Examples. Problem What is the value of 15 5 Answer 5 3 Unacceptable 75. Answers to problems asking for a response in the form of a dollar amount or an unspecified monetary. unit e g How many dollars How much will it cost What is the amount of interest should. be expressed in the form a bc where a is an integer and b and c are digits The only exceptions to this. rule are when a is zero in which case it may be omitted or when b and c both are zero in which case they. both may be omitted Answers in the form a bc should be rounded to the nearest cent unless otherwise. specified Examples, Acceptable 2 35 0 38 38 5 00 5 Unacceptable 4 9 8 0. Do not make approximations for numbers e g 3,5 3 in the data given or in solutions unless the. problem says to do so, Do not perform any intermediate rounding other than the rounding a calculator does when calculating.
solutions All rounding should be done at the end of the computation process. Scientific notation should be expressed in the form a 10n where a is a decimal 1 a 10 and n is an. integer Examples, Problem What is 6895 expressed in scientific notation Answer 6 895 103. Problem What is 40 000 expressed in scientific notation Answer 4 104 or 4 0 104. An answer expressed to a greater or lesser degree of accuracy than called for in the problem will not be. accepted Whole number answers should be expressed in their whole number form. Thus 25 0 will not be accepted for 25 and 25 will not be accepted for 25 0. The plural form of the units will always be provided in the answer blank even if the answer appears to.


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