7/28/2019 Week 6 Lesson

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MATHCOUNTS Practice

Week 6, 2010This week’s mini-lesson: How to multiply to numbers in the 90’s mentally.

There are two steps to multiply 9A x 9B. First calculate x = (10 – A) and y = (10 – B). Thencalculate Z = 100 – (x + y). Z will be a two-digit number that will be in the thousands andhundreds place. To find the tens and units place, find the product of A x B. That is yourfour-digit solution!

Example: 97 x 92 x = (10 – 7) = 3 and y = (10 – 2) = 8. Z = 100 – (3 + 8) = 89. Lastly,3 x 8 = 24 and we can say that 97 x 92 = 8924!

You try: 98 x 94 = 92 x 93 = 96 x 91 = 97 x 97 =97 x 91 = 94 x 92 = 932 = 91 x 95 =

Contest Opportunity: The first mathleague.org middle school competition of the year willbe on Sunday, November 7th at Diablo Valley College. This is NOT a school sponsoredevent (and since this is on Sunday, I will not be attending). However, for students thatwould like to participate, the fee is $10 and all information can be found on themathleague.org website. If you are going to attend, I encourage you to form your own

team of four students – you will be responsible for transportation and fees (this is not aschool sponsored event). For those that attend, registration is open until November 3rd.The check-in begins at 1:30 and the competition starts at two with the countdown round

and awards presented at 5 p.m. All you need to bring is pencil, calculator and yourentrance fee ($10). It is usually a good idea to bring a snack and water as well. Theaddress of Diablo Valley College, school map and room numbers are all available on themathleague.org website.

Challenge Solutions to week 5 questions - 

#1 The arithmetic mean of 12 numbers is 1/12 of the sum, so 81

3%  

#2 Bag A has 10 marbles and Bag B has 8. Probability of red from first bag and red from

second would be5

10•

4

8=

1

2•

1

2=

1

4. The probability of drawing blue marbles from both

bags is3

10•

2

8=

3

5•

1

8=

3

40. There is no other way to get two marbles of the same color

– so1

4+

3

40=10

40+

3

40=13

40chance of getting two marbles of the same color! 

7/28/2019 Week 6 Lesson

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MATHCOUNTS Practice Set Week 6 – Solutions in classrooms on Monday!

Problem #2: The arithmetic mean of the numbers in the set {1, 7, 9, 20, x } is 11 less than x . Whatis the arithmetic mean of the set?

Problem #3: What perfect-square integer is closest to 240?Problem #4: The sequence 12, x , y , z , 15 is an arithmetic sequence. What is the value of y ? Express

 your answer as a decimal to the nearest tenth.

Problem #5: Two complementary angles, A and B, have measures in the ratio 9:21, respectively. Indegrees, what is the measure of angle B minus the measure of angle A?

Problem #6: You are kidnapped by an evil zombie. The zombie says, "I will let you go if you guessthe positive three-digit number I am thinking of. The sum of the three digits is 12. The sum ofthe hundreds and tens digit is 5 times the ones digit. The tens digit is 1." What number is the

zombie thinking of?Problem #7: A palindrome  is a number that reads the same forward and backward, such as 717 or

3003. What is the smallest palindrome greater than 12345?

Problem #8: On Mondays, Tuesdays, Wednesdays, and Thursdays, Johnny spends 9 hours of eachday sleeping. On Fridays, Saturdays, and Sundays, Johnny spends 10 hours of each day sleeping.If you choose a random day of the week and then choose a random time of that day, what is theprobability that Johnny is asleep at that time on that day? Express your answer as a commonfraction.

Problem #9: M and N are positive integers that satisfy the equation M(M-N )=31. What is the valueof N ?

Problem #10: A certain ninja clan first came together on January 1, 2002, with an unknown numberof members. Throughout the rest of 2002, 3 more members joined. During 2003, the number of

members doubled. During 2004, 54 members joined. There were a total of 90 ninjas in the clanat the end of 2004. Assuming that no ninjas left the clan (that's against ninja rules), how manymembers were there to start with on January 1, 2002?

Problem #1: Boxes A, B, C, D, and E representunderground chambers, and the arrows representtunnels between them. You start in Chamber A and crawl

through the tunnels, eventually ending up either inChamber D or Chamber E. If you end up in Chamber D,

 you will be eaten by a cave bear. If you end up in

Chamber E, then you will be attacked by vampire bats. You can only move in the direction inwhich the arrows are pointing. When leaving a chamber, you are equally likely to use any ofthe available exit tunnels. What is the probability that you will end up in Chamber D?