p: it is a square q: it is a rectangle p q

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1 Test 1 Review Solutions 1 What number is most likely to come next in the following sequence? 2, 3, 5, 7, 11, Since this is a list of the first 5 prime numbers, the next most likely number is the sequence is 13 2 Use the statements p: it is a square q: it is a rectangle how would you represent the sentence " If it is a rectangle or a square, then it is not a square " in symbolic form? The part "it is a rectangle or a square " translates into ( q p ) it is not a square translates into ~ p Now we put the whole thing q ~ together with the symbol for if then to get ( p ) p The part 3 Under what conditions is the statement p q true? p q T T T F F T F F p q T F T T The statement is true when p is true and q is true The statement is true when p is false and q is true The statement is true when p is false and q is false Spring 2012 Test 1 Review Solutions Page 1 of 8

2 4 If n(u) 150, n(a) 37, n(b) 84, and n ( A B) 100, find n( A B) n( A B) n( A B) 121 n( A B) How many cards in a standard deck of 52 cards are aces or spades? n(aces or spades) n(aces) + n(spades) - n(aces and spades) n(aces or spades) A department store surveyed 428 shoppers and obtained the following information 214 shoppers made a purchase 299 shoppers were satisfied with the service 52 of those shoppers who made a purchase were not satisfied with the service they received How many shoppers were satisfied with the service but did not make a purchase? The number of shoppers who were satisfied with the service but did not make a purchase are in the part of the satisfied circle that does not overlap with the purchased circle and is 137 Spring 2012 Test 1 Review Solutions Page 2 of 8

3 7 If U { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A {1, 2, 3, 4, 5}, and B {4, 5, 6, 7, 8}, then find the set n( A B) This is the set of items that occur in both the set A and the set B n( A B) {4, 5} 8 Given 13 morks is 1 gloe, 5 gloes is 1 flit, 7 kits is one lonk, and 10 lonks is 1 gall Convert 90 morks per kit to flits per gall To solve this problem we will need to do some multiplication by a faction equal to 1 We can multiply by more than a single fraction that is equal to 1 at a time, but for this problem we will only multiply by a single fraction equal to 1 at a time The number that we are converting is 90 morks per kit is really the fraction 90 morks 1 kit I am going to start by converting the morks to flits Since the morks are on the top of the fraction, we will need it to be on the bottom of the fraction that is equal to 1 in order for the morks to cancel Since 13 morks equals 1 gloe, the fraction equal to 1 that we will use is 1 gloe This will give us 13 morks 90 morks 1 kit 1 gloe 90 gloes 13 morks 13 kits We now have to get from gloes to flits Since there are 5 gloes in 1 flit, the fraction equal to 1 that we will use is 1 flit Since the 5 gloes gloes are in the denominator of the fraction, they will cancel with the gloes in our current fraction 90 gloes 13 kits 1 flit 90 flits 5 gloes 65 kits Spring 2012 Test 1 Review Solutions Page 3 of 8

4 Now that we have the morks converted to flits, we need to convert the kits to galls Since the kits are in the denominator of our fraction we will need a fraction equal to 1 that has kits in the numerator This fraction will be 7 kits This will give us 1lonk 90 flits 65 kits 7 kits 630 flits 1lonk 65 lonks We are almost done We need to complete the solution by multiplying by the fraction us 1 gall which is equal to 1 This will give 10 lonks 630 flits 65 lonks 10 lonks 1 galls 6300 flits 65 galls This can be simplified to 1260 flits 13 galls or flits per gall 9 Given that one ork is equivalent to 5 umphs, convert 214 square orks to square umphs First we need to realize that square orks are orks orks This means that we will have to convert each ork to umphs in order to get umphs umphs which are square umphs As is normal with conversion, we will need to multiply by a fraction that is equal to 1 The number that we are converting is 2 14 square orks 214 orks orks Since orks are in the 1 1 numerator, we will need our fraction that is equal to 1 to have orks in the denominator so that the orks will cancel This means we will 5umphs need to multiply by This will give us 1 ork Spring 2012 Test 1 Review Solutions Page 4 of 8

5 2 14 orks orks 5 umphs 5 umphs 535 umphs umphs 1 1 ork 1 ork 1 So 214 square orks is equal to 535 square umphs 10 Given a brunk is equivalent to 5 plops, and a plop is equivalent to 4 nerd, convert 20 nerds to brunks Our problem here is to convert 20 nerds which is the same as 20 nerds to brunks This will take multiplying by two fractions that 1 are equal to 1 since we do not have a single equivalency for nerds and brunks We will have to go through plops first Since the nerds are in the numerator, we will need a fraction equal to 1 with nerds in the 1 plops denominator so that the nerds will cancel This fraction is 4 nerds This will give us 20 nerds 1 plops 20 plops 5 plops 1 4 nerds 4 1 Now we have plops and need to finally make it to brunks The 1 brunk fraction equal to 1 that we need to multiply by is This 5 plops fraction will allow us to cancel the plops since they are in the numerator of our problem and in the denominator of this fraction This will give us 5 plops 1 brunk 5 brunks 1 brunk 1 5 plops 5 Spring 2012 Test 1 Review Solutions Page 5 of 8

6 11 Harry earns$ per year Tonks earns $3680 per month Who earns more money in one year? How much more? We need to know how much Tonks makes in one year Since she earns $3680 per month, we can multiply her monthly salary by 12 to find out how much she makes in one year This will give us an annual salary of 3680* Tonks s annual salary of $44160 is less than Harry s salary of $56000 Thus Harry earns more money in one year To find the amount more, we just need to subtract Tonks s annual salary from Harry s annual salary This will give us Thus Harry makes $11840 more in one year than Tonks 12 Cassie stood on the middle rung of a ladder She climbed up 2 rungs, moved down 5 rungs, and then climbed up 6 rungs Then she climbed up the remaining 4 rungs to the top of the ladder How many rungs are there in the whole ladder? I find this problem most easily solved with a picture Cassie starts at the middle rung of a ladder That means that there are an equal number of rungs above her and below her We have enough information to find out how many rungs are above her 3 Cassie climbs up 4 rungs (new rungs used shown in purple) 4 Cassie climbs up 6 rungs (new rungs used shown in orange) 5 Cassie climbs down 5 rungs (new rungs used shown in blue) 2 Cassie climbs up 2 rungs (shown in 1 Cassie starts here Spring 2012 Test 1 Review Solutions Page 6 of 8

7 Now we have a basic picture of the upper half of the ladder If we count all the rungs above where Cassie started, we will know how many rungs are in the upper half of the ladder In our problem there are 7 rungs above Cassie when she starts This means that there are also 7 rungs below Cassie This means that there are 14 rungs that Cassie is not standing on Now if we add the rung that Cassie standing on, we know that there are 15 rungs total on the ladder 13 Amanda decided to ride her bike from her home to visit her friend Sean Three miles away from home, her bike got a flat time and she had to walk the remaining four miles to Sean s home She could not repair the tire and had to walk all the way back home How many more miles did Amanda walk than she rode? There are a couple of different ways to figure this problem out One way is to break the problem down into the two parts of the journey On the way to Sean s house, Amanda rode 3 miles and walked 4 miles On the way back Amanda walked 7 miles Altogether, Amanda walked 11 miles and rode 3 miles Since the question asks how many more miles did Amanda walk than she rode, we can subtract the number of miles Amanda rode from the number of miles Amanda walked This will give us more miles that Amanda walked than she rode Spring 2012 Test 1 Review Solutions Page 7 of 8

8 14 A plastic page designed to hold trading cards will hold up to 9 cards What is the minimum number of pages that will need to be purchased to store 640 cards? I think of the problem as a proportion We know that there are 9 cards in 1 page We have 640 cards in an unknown number of pages 9 cards 640 cards (we will use x) This gives us the proportion To 1 page x pages solve this proportion, we can cross-multiply and solve for x 9 cards 640 cards 1 page x pages 9 cards x pages 640 cards 1 pages x pages 640 cards 1 pages 9 cards x pages pages Since we cannot buy part of a page, we will need to purchase 72 pages Spring 2012 Test 1 Review Solutions Page 8 of 8