Solve the following (handwriting) 119!' 4. Find at least 2 primitive Pythagorean triples in which the difference between b and c is 2. 5. Find all Pythagorean triples containing the integer 13. 6. A certain number of sixes and nines are added to give a sum of 126. If the number of sixes and nines are interchanged, the new sum is 114. How many of each were there originally? 7. Find two positive fractions whose denominators are 3 and 7 which gives a sum of 14. 8. Find the last two digits of 999. 9. What time does the clock read 220 hours after it reads 11:00 A.M.? 10. Find all integral solutions of the following congruences: a) 17x=21(mod 23) b) 23x=41(mod 53) c) 45x = 20(mod 57) 11. Find the least positive integer which leaves 0, 1, 2, 3 when divided by 2, 3, 5, 7, respectively. 12. Find all integers that leave a remainder of 2 when divided by either 3 or 7, but which are divisible by 8. 13. Find the smallest multiple of 10 which has remainder 2 when divided by 3, and remainder 3 when divided by 7. 14. An old woman goes to market and a horse steps on her basket and crushes the eggs. The rider offers to pay for the damages and asks her how many eggs she had brought. She does not remember the exact number, but when she had taken them out two at a time, there was one egg left. The same happened when she picked them out three, four, five and six at a time, but when she took them seven at a time they came out even. What is the smallest number of eggs she could have had? 15. Determine the remainder of the following: = a) 138,388,606 (mod 8,388,607) = b) 2,0488,191 (mod 8,191) = c) 5108 (mod 18) = 16. Calculate the (2).
Solve the following (handwriting) 119!' 4. Find at least 2 primitive Pythagorean triples in which the difference between b and c is 2. 5. Find all Pythagorean triples containing the integer 13. 6. A certain number of sixes and nines are added to give a sum of 126. If the number of sixes and nines are interchanged, the new sum is 114. How many of each were there originally? 7. Find two positive fractions whose denominators are 3 and 7 which gives a sum of 14. 8. Find the last two digits of 999. 9. What time does the clock read 220 hours after it reads 11:00 A.M.? 10. Find all integral solutions of the following congruences: a) 17x=21(mod 23) b) 23x=41(mod 53) c) 45x = 20(mod 57) 11. Find the least positive integer which leaves 0, 1, 2, 3 when divided by 2, 3, 5, 7, respectively. 12. Find all integers that leave a remainder of 2 when divided by either 3 or 7, but which are divisible by 8. 13. Find the smallest multiple of 10 which has remainder 2 when divided by 3, and remainder 3 when divided by 7. 14. An old woman goes to market and a horse steps on her basket and crushes the eggs. The rider offers to pay for the damages and asks her how many eggs she had brought. She does not remember the exact number, but when she had taken them out two at a time, there was one egg left. The same happened when she picked them out three, four, five and six at a time, but when she took them seven at a time they came out even. What is the smallest number of eggs she could have had? 15. Determine the remainder of the following: = a) 138,388,606 (mod 8,388,607) = b) 2,0488,191 (mod 8,191) = c) 5108 (mod 18) = 16. Calculate the (2).
Chapter1: Taking Risks And Making Profits Within The Dynamic Business Environment
Section: Chapter Questions
Problem 1CE
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Transcribed Image Text:Solve the following (handwriting)
119!'
4. Find at least 2 primitive Pythagorean triples in which the difference between b and c is 2.
5. Find all Pythagorean triples containing the integer 13.
6. A certain number of sixes and nines are added to give a sum of 126. If the number of sixes and
nines are interchanged, the new sum is 114. How many of each were there originally?
7. Find two positive fractions whose denominators are 3 and 7 which gives a sum of 14.
8. Find the last two digits of 999.
9. What time does the clock read 220 hours after it reads 11:00 A.M.?
10. Find all integral solutions of the following congruences:
a) 17x=21(mod 23)
b) 23x=41(mod 53)
c) 45x = 20(mod 57)
11. Find the least positive integer which leaves 0, 1, 2, 3 when divided by 2, 3, 5, 7, respectively.
12. Find all integers that leave a remainder of 2 when divided by either 3 or 7, but which are
divisible by 8.
13. Find the smallest multiple of 10 which has remainder 2 when divided by 3, and remainder 3
when divided by 7.
14. An old woman goes to market and a horse steps on her basket and crushes the eggs. The rider
offers to pay for the damages and asks her how many eggs she had brought. She does not
remember the exact number, but when she had taken them out two at a time, there was one egg
left. The same happened when she picked them out three, four, five and six at a time, but when
she took them seven at a time they came out even. What is the smallest number of eggs she
could have had?
15. Determine the remainder of the following:
=
a) 138,388,606 (mod 8,388,607) =
b) 2,0488,191 (mod 8,191) =
c) 5108 (mod 18) =
16. Calculate the (2).
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