Write A if the quantity in Column A is greater. Write B if the quantity in column B is greater.

1. Write A if the quantity in Column A is greater. Write B if the quantity in column B is greater. Write C if the quantities are equal. Write D if there is not enough information to determine the relationship. Column A Column B • z z2 • (r+t)2 r<0,t<0 (r-t) 2 • 3. • 4. (x + 2 )2(x - 1)2

2. Determine if the UPC code is valid. • 1-34987-65432-8 2. 2-93847-65674-8 Find the value of the check digit that will make the UPC code valid. 3. 3-02468-13579-d 4. 4-13579-02468-d 5. Come up with 2 valid UPC codes of your own. 6. Check out 2 real UPC codes and see if they are valid under our formula.

3. Determine if the UPC code is valid. • 1-34987-65432-8 Valid 2. 2-93847-65674-8 Not valid Find the value of the check digit that will make the UPC code valid. 3. 3-02468-13579-d d = 0 4. 4-13579-02468-d d = 9 5. Come up with 2 valid UPC codes of your own. 6. Check out 2 real UPC codes and see if they are valid under our formula.

4. Credit cards have 16-digit numbers, of which the first 15 digits identify the credit card and the sixteenth digit is the check digit. Visa card begin with a 4 and MaterCard cards begin with a 5. 1. MasterCard numbers begin with 51,52,53,54,or 55. What is the maximum number of credit cards that MasterCard can issue? 5[(first two digits] 1013 1[check digit is determined by the previous digits]= 5(1013)

5. A check digit is used to help validate credit card numbers. The credit card companies use the CODABAR method to determine the check digit. This method consists of the following: • Add the digits in the odd-numbered positions and double the total • add how many odd-position digits that are more that 4 to the total • add the even-position digits • choose a check digit that makes this calculation total a number whose final digit is 0.

6. 2(4+6+0+1+3+5+7+9)+ 4 +(1+2+0+2+4+6+8+d) • Visa card 4162 0012 3456 789d (d=3?) 2(35)+ 4 +(23+d) 2(35)+ 4 +(23+d) 97 + d 97 + d needs to equal a number that ends in 0 so d = 3

7. 2(5+2+9+1+2+2+0+8)+ 3 +(4+4+8+3+7+0+0+d) • What is the check digit (d) for the MasterCard number 5424 9813 2720 008d? 2(29)+ 3 +(26+d) 87+d so d = 3 4. Show that 4128 0012 4389 0110 is an invalid Visa Credit card number. 2(4+2+0+1+4+8+0+1)+ 1 +(1+8+0+2+3+9+1+0) 2(20)+ 1 +(24) 65, so not valid because it does not end in 0.

8. Suppose you entered 8 instead of 9 when recording the credit card number 4001 2560 0196 4310 explain why it will detect this error… 2(9) – 2(8) = 2, so the sum of the weighted sum of the digits will be off by 2 and will not end in 0. Do you think the Codabar method will detect all such single-digit errors? YES

9. 7. The codabar method detects 98% of all transposition errors. There is one pair of numbers, however, that when transposed will not be detected by the Codabar method. When will it not matter? 4001 2560 0196 4310 4001 2560 0196 4310 if you transpose any of the red numbers with each other or any of the black numbers with each other it will not effect the Codabar method,

10. HW --Determine if the following credit card numbers are valid. 1. 5234 0012 9876 2425 2. 5365 3437 2298 0655 3. 4145 3232 6578 9630 4. 4325 6509 2275 3341 Determine the value of d so that the credit card number is valid. 5. 4265 8876 4543 221d 6. 5568 2245 3387 001d 7. 4141 6789 0054 235d 8. 5243 5990 2245 302d