THE SOLUTIONS
01
Peter wins again. Peter is the faster runner and he can run the extra five meters faster than Bill.
02
Billy sold the card twice, for 10.00 and 8.00. He paid 15.00 for the card so he came out ahead by 3.00.
03
Twenty-five lollipops cost 0.25 each. 6.25 equals 625 cents. And 625 divided by 25 = 25.
04
Twelve months. When one person is host, three other people could be the snack provider. Each person gets a chance to be host for three months, each month with a different snack provider. In total, there are twelve different host/snack combinations.
05
It would be more cost effective to get the rust-proofing done. Without the rust-proofing the cost is 17.50 per wheel per year and with the rust-proofing the cost is 16.66 per wheel per year.
06
Adam got there first using his bicycle.
07
They are both making the same amount. Let’s say that on their first year they both earn 10,000 In year two, Alison gets a raise to 11,000 and Eric’s pay drops to 9,000. In year three, Alison’s pay drops by ten percent and goes to 9,900 while Eric’s pay rises ten percent and goes from 9,000 to 9,900. They are both now earning 9,900 a year.
08
The first shooter has a two-thirds chance of hitting his opponent first.
09
Beth.
10
Dropping it in the rowboat. Since the marble is denser than water, dropping it into the rowboat will raise the water level higher. Try substituting a marble for a fully-inflated balloon. If you managed to push the balloon underwater it would raise the water level considerably higher than if you dropped the balloon into the rowboat.
11
They played eleven games. John lost three games. He had to win three additional games to break even. Then he had to win five more games to win 50.00. 3 + 3 + 5 = 11
12
Nine times. 1:23, 2:34, 3:45, 4:56, 9:10, 10:11, 11:12, 12:13, 12:34.
13
None. 4 + 8 + 12 + 16 + 20 = 60. Because this total is the exact number of pies sold, there could not have been any pies sold on the first day.
14
Forty jellybeans in the jar.
15
One gold bar weighs five kilograms. By removing one gold bar from each side of the scale, two gold bars weigh ten kilograms total.
16
Steve must give Lisa five marbles. He would then have five less, she would have five more for a difference of ten.
17
Six.
18
The only matching colors available for Louisa’s present is red paper and a red bow. The only contrasting paper color remaining for Samantha’s present is silver. Maria’s present is left with green paper and a gold bow.
19
Cut four of the apples into three pieces each, and then cut the three remaining apples into four pieces each.
20
Twenty-nine days. The doubling still occurs each day; we can just rule out the first day since it was doubled initially.
21
Three sons and four daughters.
22
One hour and five minutes.
23
Seven. Jess has none and Courtney has one.
24
She started with 100.00.
25
One. Consider jar #1. Overall possible permutations (N=9!), there is a one-in-nine chance that this jar gets its correct label. Same result concerning each of the eight jars #2, 3, 4,…9. In total, there are 9 × N/9 = N jars correctly labeled; that means (N-correctly-labeled-jars/(N-possible-configurations) = 1 jar is labeled correctly on average.
26
Ninety-nine. With only one winner, there must be ninety-nine losers, requiring ninety-nine matches.
27
Twenty cents.
28
The weight will rise.
29
Seven. To average two hours a day over six days, Olivia must practice 2 × 6, or twelve hours. From Monday through Friday, she practices five hours—one hour each day. To total twelve hours, she must practice 12–5, or seven hours, on Saturday.
30
160.00 dollars. The easy way to solve this is to divide 320 in half, since the half of the seventy-nine percent that tipped two dollars is the same as the full seventeen percent tipping one dollar.
31
Amelia has three handbags, one gold, one brown, and one white.
32
Twelve jellybeans. Ava ate half the remaining jellybeans plus three more to leave none, so she must have eaten six jellybeans. George ate half the jellybeans and left six, meaning there were twelve to start.
33
Five cars. 1,500 × 5 = 7,500 profit.
34
Ten games. Craig won the first three, and Dan had to win the next seven in order to win $4.
35
John is the tallest, then Bill, then Mick.
36
Mia is eight years older than Emily.
37
She lost 100.00.
38
Enriqué is sleeping between Ricardo and Juan.
39
116.00.
40
Tobias made each person ride another person’s horse. This would ensure that everyone would want to come in first so they wouldn’t lose.
41
It only passes ten times.
42
Yes. She has seven daughters.
43
Muhammad started with 62.00.
44
Eleven. Trains pass by every half hour for nine total, plus two pulling into the cities.
45
Thirty-one runners total. Since the track is a closed circuit, we simply add 1/5 + 5/6 = 31/30. 30 runners plus Oscar.
46
Ten kids.
47
France.
48
Eleven tires total. 4,000 kilometers × 4 tires = 16,000 total kilometers. 1,500 × 11 = 16,500 total kilometers.
49
Six pairs. Five pairs will only get her fifty miles and both marathons are fifty-two miles.
50
Total cost of meal is 60.00. 3 people × 20.00 = 60.00. Eight dishes have been eaten, therefore each dish costs 7.50. Blake brought 5 dishes × 7.50 = 37.50 minus his 20.00 share or 17.50. Brian brought 3 dishes × 7.50 minus his share = 2.50.
51
Eight chickens and fourteen goats.
52
Twenty-seven rungs.
53
She should take the first job. In two years, it will have paid 56,000, while the second job will have paid only 55,000.
54
They must charge 4.00 per serving to make a 100 percent profit.
55
Erik can reach the summit using only two Sherpas. The three of them leave base camp, each with four days’ worth of food. At the end of the first day, they all have three days’ worth of food left. The first Sherpa leaves two days’ worth of food with Erik and the other Sherpa, and heads back to base camp with one days’ worth of food in his pack. On the second day, the last Sherpa heads back to base camp after leaving one days’ worth of food with Erik. Erik now has four days’ worth of food and only four days left to get to the summit. He will die of starvation on the way down, however.
56
Fifty-nine cents. Ten seven-cent coins minus the eleven-cent coin.
57
Ten 1.00 bills, one hundred 50.00 bills, nine 10.00 bills, and eighteen 50.00 bills.
58
Her average speed is 6.7 miles per hour. It takes Elena two hours to run the first ten miles and one hour to run the last ten miles, meaning she needs three hours to run the total of twenty miles.
59
Label the sacks from 1 to 5. Take one coin out of sack 1, and label it 1. Take two coins out of sack 2, and label them both with a 2. Take three coins out of sack 3, and label each with a 3. Continue this pattern with sacks 4 and 5. Put these fifteen coins on the tray of the scale. If all fifteen weighed one pound, the scale would register fifteen pounds, but since one or more of the coins weighs only nine-tenths of a pound, the scale will register less than fifteen. Subtract the number on the scale from fifteen. Your answer will tell you the number of the sack with the lighter coins. (If the scale registers 14.8 pounds, it’s sack 2. If the scale registers 14.5 pounds, it’s sack 5.)
60
Bernie had the best average. Derek batted 73.3 percent, and Bernie batted 75 percent.
61
Ten blocks.
62
They both drank the same amount of caffeine.
63
Alison has one cat and one goldfish.
64
The time is 8:30.
65
You still only need seventeen bakers.
66
There are four possibilities:
One spoon and one fork.
Two spoons.
One fork and one spoon.
Two forks.
In three of the four possibilities, you’ll wind up with at least one spoon. So the chances of picking at least one spoon are three in four or, in another phrasing, three to one.
67
If you add up all the losses, you find that 100 students lost a total of 310 items. That total means that, at a minimum, 100 students lost three items, and ten (the remainder when dividing 310 by 100) must have lost all four items.
68
Coco, Rocky, Winston, Fluffy, and Lulu.
69
Ten cookies.
70
Amelia had 6.00 before she found the 4.00.
71
Eight days. The snail makes one foot of progress every twenty-four hours. So after seven days, she will have climbed seven feet. Then on day eight, she will climb the three feet she manages per day and gets out of the well.
72
420 students: This is the only number under 500 that can be divided evenly by 3, 4, 5, and 7.
73
Beth is twenty-two years old.
74
Four flies (twenty-four legs) and three spiders (twenty-four legs). No other combination will work.
75
Andy has gone through eight times, Bill four times, Chris eleven times, Drake six times, Eric three times.
76
From youngest to oldest, the six brothers are ten, fourteen, eighteen, twenty-two, twenty-six, and thirty.
77
Four people can make twelve hats in six hours.
78
Five pieces of candy at 0.10, one piece of candy at 0.03, ninety-four pieces of candy at 2 pieces for 0.01 equals 1.00.
79
Bill took eleven lessons.
80
Six shoes. If he takes out five shoes, he could have one of each color, with no two matching colors.
81
John spent 2,500 and 4,500 for a total of 7,000. John sold the painting for 3,500 and 5,500 for a total of 9,000. John came out ahead by 2,000.
82
260. Sophia makes 280. If Liam makes 50.00 more than this, then Liam must make 280 + 50.00 or 330. Dan makes 70.00 less than this amount, or 260.
83
Juanita solved eighteen puzzles correctly, earning thirty-six points. She failed to solve twelve correctly, losing thirty-six points.
84
The rain gauge was half-filled on Saturday. It doubled on Sunday, to become completely filled.
85
33.3 percent. If the car originally cost 30,000, with the twenty-five percent deduction, it would cost 22,500. To bring the price back to the original 30,000, you’d have to add 7,500, which is one-third of 22,500, or 33.3 percent.
86
He should buy the ring from the first jewelry store. Hypothetically, if Brian proposed twice, Andrea should say yes once and no once. This would mean that if he bought the ring from the first store twice he would have spent 6,600 and if he bought the ring from the second store twice he would have spent 7,000. On average, the ring would cost him 3,300 from the first store and 3,500 from the second one.
87
The Spanish diplomat would get assassinated 5 times (50% × 10) and the French diplomat would get assassinated 1.5 times (25% × 6). Therefore, the Spanish diplomat is in greater danger.
88
Seven rows. eight oranges in the bottom row, two in the top.
89
Sixty feet.
90
There are four players on each team.
91
Four hours.
92
The five football players will win. If there were only four football players on one side and two soccer players on the other side, it would be a tie.
93
Eighty miles.
94
Ralph. Tommy is selling the shoes for 63.75 and Ralph is selling them for 63.00.
95
Charlotte picked fifteen.
96
Container E holds the apple juice. The second customer can buy twice as much as the first customer if the first customer buys Containers A and C (for a total of sixty-six quarts) and the second customer buys Containers B, D, and F (for a total of 132 quarts). The remaining container, E, must hold the apple juice.
97
Ninety-nine seconds. Each cut, including the 99th, produces two pieces of wire.
98
Trent makes 24.00, Mary makes 48.00, Shawn makes 72.00.
99
Forty-five eggs.
100
Fill the three-liter jug and pour it into the five-liter jug. Fill the three-liter jug again and add the water to the same five-liter jug, filling it to the top. What’s left in the three-liter jug is one liter of water.
101
Twenty-two years old.
102
36.00.
103
Georgia slept through half the trip.
104
She drives 200 miles on the last day. If n = miles traveled in one day, let each subsequent day be n + 20 (the daily increase in miles). With this you’ll find that she would have to have traveled forty miles the first day, sixty the second day, 100 on the fourth day, and 200 on the ninth and final day. This is the only way it would add up to 1080.
105
They’ve been playing for 720 weeks or 13.8 years. The number of possible seating arrangements is 6 × 5 × 4 × 3 × 2, which is 720.
106
1,000 divided by 175.00 is 5.7, so they worked on the roof for six days.
107
Twenty-four additional gold rings.
108
Twenty-seven gumballs.
109
The grouper weighs 102 pounds. The weight of the halibut is given indirectly by saying two halibut weigh the same as one swordfish. One grouper and two halibut are equal to the weight of one sturgeon and one halibut. One grouper and one halibut must have the same weight as one sturgeon. So, the grouper is 120 pounds minus eighteen pounds, or 102 pounds.
110
Charlie has twenty-one minutes and forty-nine seconds.
111
Use two cuts to make an X so that you have four pieces, then make a horizontal cut through the cake to make eight pieces.
112
Yes.
XXO
XOX
OXX
113
Twenty-five cows would eat all the grass in five days.
114
One jumbo stapler, twenty-nine regular staplers, and seventy tiny staplers.
115
75.00.
116
Forty-three nails.
117
Two-thirds.
118
Flip both hourglasses over. When the four-minute hourglass runs out, flip it back over immediately. When the seven-minute hourglass runs out, flip that back over immediately, too. One minute later, the four-minute hourglass will run out again. At this point, flip the seven-minute hourglass back over. The seven-minute hourglass has only been running for a minute, so when it is flipped over again it will only run for a minute more before running out. When it does, exactly nine minutes will have passed.
119
Bill had forty-nine watches and Mick had thirty-five.
120
62.5 peanuts.
121
Dragonlady won, Atomic Angie came in second, and Quick Ted came in third.
122
Two half-full barrels are dumped into one of the empty barrels. Two more half-full barrels are dumped into another one of the empty barrels. This results in nine full barrels, three half-full barrels, and nine empty barrels. Each son gets three full barrels, one half-full barrel, and three empty barrels.
123
Take a piece of fruit from the box marked “cherries and strawberries.” If the fruit you take is a cherry, then that box must be the box containing just cherries. Therefore, the box marked “strawberries” can’t be the box containing just cherries, and it can’t be the box containing just strawberries either, so it must be the box containing cherries and strawberries. The remaining box is therefore the box containing just strawberries.
124
Ask one of the men what the other man would answer to the question, “Is the door on the left the correct door?” Then assume the answer you are given is false and act on that knowledge. If the man you ask is the liar, he’ll incorrectly give you the truthful man’s answer. If the man you ask is the truthful man, he’ll correctly give you the liar’s wrong answer.
125
Say It Fast came in first. Lion Heart and Sir Oscar tied for second place. Silver Wagon came in fourth. Master David came in fifth.
126
Five yellow birds were seen.
127
Darren had his own coat, Tom’s hat, Rob’s gloves, and Matt’s cane. Tom had his own coat, Matt’s hat, Darren’s gloves, and Rob’s cane. Rob had Matt’s coat, his own hat, Tom’s gloves, and Darren’s cane. Matt had Rob’s coat, Darren’s hat, his own gloves, and Tom’s cane.
128
Light one fuse at both ends and, at the same time, light the second fuse at one end. When the first fuse has completely burned, a half hour has elapsed and the second fuse has a half hour left to go. At this time, light the second fuse from the other end. This will cause it to burn out in fifteen more minutes. At that point, exactly forty-five minutes will have elapsed.
129
Three-quarters.
130
Seventeen. You just need to find two numbers, seven apart, that add up to 27. With trial and error you should be able to find them soon—ten and seventeen; there must be seventeen women working at the office.
131
Ingrid spent 22.00.
The headphones cost 14.00.
The protective case costs 5.00.
And the screen protector costs 3.00.
132
20.00.
133
Camera: 52.25.
Ruler: 0.50.
Ice cream bar: 0.25.
134
Sixteen. Find the total number of gumballs in the bag, then divide by the new number of children who will be sharing them.
135
Eighteen stations. The subway will pass 60/10 or six times as many stations in one hour as it passes in ten minutes. In ten minutes, it passes three stations; in sixty minutes, it must pass 6 × 3, or eighteen stations.
136
You can learn the contents of all three boxes by drawing just one marble. The key to the solution is your knowledge that the labels on all three of the boxes are incorrect. You must draw a marble from the box labeled “black-white.” Assume that the marble drawn is black. You know then that the other marble in this box must be black also, otherwise the label would be correct. Since you have now identified the box containing two black marbles, you can at once tell the contents of the box marked “white-white.” you know it cannot contain two white marbles, because its label has to be wrong; it cannot contain two black marbles, because you have identified that box; therefore, it must contain one black and one white marble. The third box, of course, must then be the one holding two white marbles. You can solve the puzzle by the same reasoning if the marble you draw from the “black-white” box happens to be white instead of black.
137
You buy one cow, nine pigs, and ninety chickens.
138
IBM is at 70 and Microsoft is at 105 3/8.
139
Fifty percent.
140
27.00.
141
During his five turns at the billiards table he sank eight, fourteen, twenty, twenty-six, and thirty-two balls.
142
There were twenty-six men and twenty women, or forty-six altogether at the club.
143
The balloon is 200 meters above the lake.
144
It will take the train eighteen minutes. The front of the train has to initially travel ten kilometers to leave the tunnel, and then a further one-half kilometer until the rear of the train has left the tunnel—a total of ten and one-half kilometers. Which takes 60 × (10.5 / 35) = 18 minutes.
145
Seven members and seven committees.
146
The price of the TV is less than it was before the twenty-five percent increase and the twenty-five percent decrease. If the TV cost 1,000.00, you know that twenty-five percent of 1,000 is 250. So, after the twenty-five percent increase, the cost was 1,250. Now find twenty-five percent of 1,250. Subtract this amount (312.50) from 1,250.to find the reduced price. It’s 937.50—that’s 62.50 less than the original price of 1,000.
147
FedEx should charge 4,000 for a large truckload. Since each dimension of the large truck (height, width, and length) is twice that of the small truck, the volume of the large truck is eight times that of the small truck. So, for a large truckload, FedEx should charge eight times the price of a small truckload. That’s 8 × 500.00, or 4,000.
148
Anne has 8/35 and Ken has 6/35.
149
Twenty-one percent. 64 + 22 – 7 = 79. 100 – 79 is 21.
150
None.
151
There can only be one brown-haired contestant; therefore, the other ninety-nine have blonde hair..
152
It weighs half a pound. 1/5 × 5/2 = 5/10 half a pound.
153
One and seven-eighths hours.
154
Forty-five.
155
195.
156
325.00 per delivery.
157
One minute. Remember, they double every minute, so when the dish is half full, it will only take one more doubling to fill it.
158
Twenty-four.
159
Fifty.
160
Eight throws.
161
Six. Danielle made five cigarettes from the twenty-five butts, smoked them, and then made an additional cigarette from the five butts that were left from the five that she made.
162
Seventeen percent. Divide the number of juniors (1,903) by the total number of students (11,276).
163
There were twenty-eight total trips made, with Albert making twelve
of them, Bob making five, and Carl making eleven.
164
Mia can run one mile on a flat surface in twenty-four minutes. She can run three miles an hour downhill and two miles an hour uphill. If you take the average of the two rates, you find that Mia runs 2.5 miles per hour on a flat surface.
165
Thirty-five percent are playing both for a total of seventy students.
166
The smallest number of children the Smith family might have is nine.
167
Four minutes. The first wall has twenty- five bricks. The second wall has four times as many, so it will take four times as long, or four minutes.
168
Dennis has thirty-nine cars.
169
Together they cover the distance at eleven miles per hour so they will cover the distance of eighty-eight miles in eight hours. In eight hours they will meet and Erica will have traveled eighty miles.
170
Sophia is eighty years old.
171
There are four tricycles in the park.
172
It would still take five minutes for four dolphins to eat four fish.
173
108 tacks. The four corners of the square have one tack each, so each side of the square now requires twenty- six tacks. The total number of tacks used = 4 + (4 × 26) = 108.
174
Sixteen feet. (64 / 16) × 4 = 16 feet.
175
Twenty-one days. Errol has sixteen pieces in the original box. The small pieces make four new pieces and the small pieces of the four new pieces make one more for twenty-one.
176
Seven days will finish the house.
177
Eighty-four was the average.
Total marks in 4 exams = 4 × 81 = 324.
Total marks for Physics and Math = 2 × 78 = 156.
Total marks in English and History = 324 – 156 = 168.
Average marks in English and History= 168/2 = 84.
178
There are fifteen players in the tournament. 14 + 13 + … + 2 + 1 = 105.
179
Buster weighs 100 pounds.
180
Annika was at camp for nineteen days.
181
300. Twenty percent of the workers are part-time, so eighty percent of the workers are full-time. Thirty percent received bonuses and this amounted to seventy-two workers. Thirty percent of eighty percent of total workers (n) equals seventy-two. 3/10 × 8/10 × n = 72, or 24/100 × n = 72. Therefore, n = 72 × 100/24 or 300.
182
Six. Find out how far the University of Minnesota has moved thus far. They pulled the University of Wisconsin forward three meters, so Minnesota moved backward three meters. Then they were pulled forward five meters and then a further two meters. In total then they have moved forward (–3) + 5 + 2 = 4 meters. They must be pulled a further six meters to be pulled ten meters forward.
183
Six. For every pair of pants, Nate can wear five different jackets, giving five different combinations for each pair of pants, or 3 × 15 = 15 different combinations of pants and jackets. With each of these combinations he can wear any of his different shirts. The different combinations of shirts, jackets, and pants is (number of shirts) / 15. We are told this equals ninety, so ninety divided by fifteen equals six.
184
Josh has a two-thirds chance of successfully hitting the bull’s-eye before Brianna does.
185
Sixty. If you convert everything to seconds, the first fog horn blows every twelve seconds and the second fog horn blows every fifteen seconds. Then find the lowest common denominator, which is sixty, and you arrive at the answer.
186
The jeweler cut four of the pieces into three pieces each and then cut the three remaining pieces into four pieces each, and divided them accordingly.
187
Ten feet. The ship will rise with the tide and so will the ladder, so it won’t affect the amount that is above water.
188
Wednesday.
189
Take the goat across and leave it on the other side. Then go back, get the wolf. Bring the wolf to the other side and take the goat back with you. Take the grain to the other side and leave it there, then go back and get the goat.
190
1.00. Christine is owed 3.00 by Robert, and she owes 5.00 to Alison. She needs a cash loss of 2.00 to settle all debts. Alison, on the other hand, is owed 5.00 by Christine and owes 4.00 to Robert. She must have a gain of 1.00. Since Christine settles all debts, this 1.00 must come from Christine, and this is the answer.