Practice Test. to base ten 5) to base ten 2) 3. Convert 2434 six. to base ten 3) 4. Convert three. to base ten 4)

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1 Abe Mirza Practice Test 1. Convert 2341 five to base ten 1) 2. Convert 3132 four to base ten 2) 3. Convert 2434 six to base ten 3) 4. Convert three to base ten 4) 5 Convert DEED to base ten 5) Convert each of the following from base ten to the indicated base. 6 Convert 916 to base six. 6)? six 7 Convert 2,145 to base seven. 7)? seven 8 Convert 2,103 to base eight. 8)? eight 9. Convert 324 five to base six 9) 324 six 10. Convert 2006 eight to base seven 10) 2666 seven 11. Convert two to base ten 11) Convert five to base ten 12) 2, Convert nine to base ten 13) 58, Convert ABCD to base ten 14) 43, Convert to base nine 15) nine 16 Convert 27 eight to base five. 16) 43 five 17 Convert C 02 to base seven. 17) seven 18 Convert 2406 eight to binary form. 18) two 19. Convert two to octal form. 19) 3275 eight 20. Identify which one is the largest number two, 407 five, 6F to base seven? 20) 6F 1. In how many ways a teacher can select 5 of his 23 students for a fieldtrip? 1)33, In how many ways a teacher can give different prizes to 5 of his 18 students? 2)1,020, If a password should consist of non-repeating of 2 letters first and 3) 468,000 non-repeating 3 digits after, then how many different passwords are possible? L L D D D 4. If a password should consist of 2 letters first and 3 digits after, then how many 4)676,000 different passwords are possible? 1

2 L L D D D 5. How many different 3-letter words can be written ending with vowels (a,e,i,o,u)? 5) 3, How many different 3-letter words can be written not ending with vowels (a,e,i,o,u)? 6) 14, How many different non repeating 3-letter words can be written ending with vowels (a,e,i,o,u)? 7) 3, How many different non repeating 3-letter words can be written not ending with vowels (a,e,i,o,u)? 8) 12, Find P(81,2) 9) 6, Find C(88,3) 10) 109, In how many ways Joe can dress up, if he has 6 shirts, 7, pants, and 5 pair of shoes? 11) How many ways can a president and a treasurer be selected in a club with 11 members? 12) If a password should consist of non-repeating of 3 letters first and 13) 1,404,000 non-repeating 2 digits after, then how many different passwords are possible? 14. If a password should consist of 2 letters first and 2 digits after, then how many 14) 67,600 different passwords are possible? 15. How many different 3-letter words can be written ending with letters (a,c,e,t,o,p)? 15) 4, How many different 3-letter words can be written not ending with vowels (a,c,e,t,o,p)? 16) 13, How many different non repeating 3-letter words can be written ending with letters (h,e,l,p)? 17) 2, How many different non repeating 4-letter words can be written not ending with letters (h,e,l,p)? 18) 30,3600, 19. A computer printer allows for optional settings with a panel of two switches 19) 4 on-off in a row. How many different settings are possible? Hint you need to list them first. 20. A computer printer allows for optional settings with a panel of three switches 20) 5 on-off in a row. How many different settings are possible if no adjacent switches can be both off? Hint you need to list them first. 21. John has 20 ounces of a 20% of salt solution. How much salt should he add to make it a 25% solution? 2

3 . Ans: add 4/3 ounces of salt. 22. John has 20 ounces of a 20% of salt solution. How much water should he evaporate to make it a 25% solution? Ans: He should evaporate 6.67 ounces of water. 23. A tank has a capacity of 10 gallons. When it is full, it contains 15% alcohol. How many gallons must be replaced by an 80% alcohol solution to give 10 gallons of 70% solution? Answer: 8.46 gallons of alcohol. 24. How many pounds of chocolate worth $1.20 a pound must be mixed with 10 pounds of chocolate worth 90 cents a pound to produce a mixture worth $1.00 a pound? Solutions for mixture problems Answer: 5 pounds of the 90 cents chocolate needs to be added. John has 20 ounces of a 20% of salt solution, How much salt should he add to make it a 25% solution? 21. Step 1: Set up a table for salt. John has 20 ounces of a 20% of salt solution. How much salt should he add to make it a 25% solution? The salt added is 100% salt, which is 1 in decimal. Change all the percent to decimals Let x = of salt added. The result would be 20 + x x 20 + x x 20 + x multiply x 0.25(20 + x) Step 4: original + added = result x = 0.25(20 + x) 4 + x = x Isolate variable x x 0.25x = x = 1 x = 1/.75 = 4/ Answer: He should add 1.33 ounces of salt. 3

4 Removing From The Solution 22. John has 20 ounces of a 20% of salt solution. How much water should he evaporate to make it a 25% solution? Step 1: Set up a table for water. The water is removed from the original. John has 20 ounces of a 20% of salt solution. How much water should he evaporate to make it a 30% solution? The original of water is 100% 20% = 80% The resulted of water is 100% 30% = 70% The water evaporated is 100% water, which is 1 in decimal. Change all the percent to decimals. Let x = of water evaporated. The result would be 20 x x 20 x x 20 x multiply x 0.70(20 x) Step 4: Since the water is removed, we need to subtract original removed = result x = 0.70(20 x) 16 x = x Isolate variable x x 0.7x = x = 2 x=2/0.3 = 6.67 Answer: He should evaporate 6.67 ounces of water. Replacing The Solution 23. A tank has a capacity of 10 gallons. When it is full, it contains 15% alcohol. How many gallons must be replaced by an 80% alcohol solution to give 10 gallons of 70% solution? Step 1: Set up a table for alcohol. The alcohol is replaced i.e. removed and added. 4

5 Change all the percent to decimals. Let x = of alcohol solution replaced x x x x 10 multiply x 0.8 x Step 4: Since the alcohol solution is replaced, we need to subtract and add x x = x + 0.8x = 7 original removed + added = result Isolate variable x 0.8x 0.15x = x = 5.5 x = 5.5 /.65 = 8.46 Answer: 8.46 gallons of alcohol solution needs to be replaced. Mixing Quantities Of Different Costs 24. How many pounds of chocolate worth $1.20 a pound must be mixed with 10 pounds of chocolate worth 90 cents a pound to produce a mixture worth $1.00 a pound? Step 1: Set up a table for different types of chocolate. cost How many pounds of chocolate worth $1.20 a pound must be mixed with 10 pounds of chocolate worth 90 cents a pound to produce a mixture worth $1.00 a pound? Let x = of chocolate added. cost x x + 10 cost x x + 10 multiply x 1 (x + 10) Step 4: original + added = result x = 1 (x + 10) x = x + 10 Isolate variable x 1.2x x = x = 1 x = 1/.2 = 5 Answer: 5 pounds of the 90 cents chocolate needs to be added. 5