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MATHCOUNTS 2011State CompetitionTarget RoundProblems 1 and 2NameSchoolChapterDO NOT BEGIN UNTIL YOU AREINSTRUCTED TO DO SO.This section of the competition consists of eight problems,which will be presented in pairs. Work on one pair ofproblems will be completed and answers will be collectedbefore the next pair is distributed. The time limit for eachpair of problems is six minutes. The first pair of problemsis on the other side of this sheet. When told to do so, turnthe page over and begin working. This round assumes theuse of calculators, and calculations also may be done onscratch paper, but no other aids are allowed. All answersmust be complete, legible and simplified to lowest terms.Record only final answers in the blanks in the righthand column of the problem sheets. If you complete theproblems before time is called, use the time remaining tocheck your answers.Total CorrectScorer’s InitialsNational SponsorsRaytheon Company * National Defense Education Program *Northrop Grumman Foundation *National Society of Professional Engineers * CNA Foundation *ThinkFun * Texas Instruments Incorporated * 3M Foundation2011 MATHCOUNTSNational Competition SponsorFounding Sponsors: National Society of Professional Engineers, National Council of Teachers of Mathematics and CNA FoundationCopyright MATHCOUNTS, Inc. 2011. All rights reserved.

1. Blossom is thinking of a positive three-digit integer. She gavesome clues to finding it. None of the digits is a zero. The integer is divisible by 3. Exactly one of the digits is a perfect square.What is the smallest possible integer Blossom could bethinking of?1.2. An employee of a delivery company drives 480 miles at60 miles per hour in a vehicle that averages 20 miles per gallonof gas. The employee is paid 12 per hour, gasoline costs 3per gallon, and maintenance on the vehicle is 0.15 per mile.According to these rates, what is the total cost of this trip forthe company? 2.Copyright MATHCOUNTS, Inc. 2010. All rights reserved. 2011 State Target Round

MATHCOUNTS 2011State CompetitionTarget RoundProblems 3 and 4NameSchoolChapterDO NOT BEGIN UNTIL YOU AREINSTRUCTED TO DO SO.Total CorrectScorer’s InitialsNational SponsorsRaytheon Company * National Defense Education Program *Northrop Grumman Foundation *National Society of Professional Engineers * CNA Foundation *ThinkFun * Texas Instruments Incorporated * 3M Foundation2011 MATHCOUNTSNational Competition SponsorFounding Sponsors: National Society of Professional Engineers, National Council of Teachers of Mathematics and CNA FoundationCopyright MATHCOUNTS, Inc. 2011. All rights reserved.

3. The Math Club ordered the Super Monster pizza from PizzaShack for their meeting. Jose took 1/5 of the pizza. Marti took1/4 of what was left. Then Bobbi took 1/3 of the remainingpizza. Finally, Ms. Gauss, the advisor, took 1/2 of theremaining pizza. What percent of the entire pizza was left afterMs. Gauss took her share?%3.4. In the 21st century, Marco will celebrate his Nth birthday in theyear N2. In what year did he celebrate his 13th birthday?4.Copyright MATHCOUNTS, Inc. 2010. All rights reserved. 2011 State Target Round

MATHCOUNTS 2011State CompetitionTarget RoundProblems 5 and 6NameSchoolChapterDO NOT BEGIN UNTIL YOU AREINSTRUCTED TO DO SO.Total CorrectScorer’s InitialsNational SponsorsRaytheon Company * National Defense Education Program *Northrop Grumman Foundation *National Society of Professional Engineers * CNA Foundation *ThinkFun * Texas Instruments Incorporated * 3M Foundation2011 MATHCOUNTSNational Competition SponsorFounding Sponsors: National Society of Professional Engineers, National Council of Teachers of Mathematics and CNA FoundationCopyright MATHCOUNTS, Inc. 2011. All rights reserved.

5. How many distinct sums can be obtained by adding threedifferent numbers from the set {3, 6, 9. , 27, 30}?sums5.6. Suppose x and y are real numbers such that xy 9 andx2y xy2 x y 100. What is the integer value ofx2 y2?6.Copyright MATHCOUNTS, Inc. 2010. All rights reserved. 2011 State Target Round

MATHCOUNTS 2011State CompetitionTarget RoundProblems 7 and 8NameSchoolChapterDO NOT BEGIN UNTIL YOU AREINSTRUCTED TO DO SO.Total CorrectScorer’s InitialsNational SponsorsRaytheon Company * National Defense Education Program *Northrop Grumman Foundation *National Society of Professional Engineers * CNA Foundation *ThinkFun * Texas Instruments Incorporated * 3M Foundation2011 MATHCOUNTSNational Competition SponsorFounding Sponsors: National Society of Professional Engineers, National Council of Teachers of Mathematics and CNA FoundationCopyright MATHCOUNTS, Inc. 2011. All rights reserved.

7. Hans and Franz are in a shooting competition. The object of thematch is to be the first to hit the bull’s-eye of a target 100 feetaway. The two opponents alternate turns shooting, and eachopponent has a 40% chance of hitting the bull’s-eye on a givenshot. If Hans graciously allows Franz to shoot first, what isthe probability that Hans will win the competition and take nomore than three shots? Express your answer as a decimal to thenearest hundredth.7.8. The solid figure shown has six faces that are squares and eightfaces that are equilateral triangles. Each of the 24 edges haslength 2 cm. The volume of the solid can be expressed in cubicac where c has no perfect squarecentimeters in the formbfactor except 1 and where a and b are relatively prime. Whatis the value of a b c?8.Copyright MATHCOUNTS, Inc. 2010. All rights reserved. 2011 State Target Round

2011 State Competition Target Round Problems 1 and 2 Name School Chapter DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO. This section of the competition consists of eight problems,

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