World's 200 Hardest Brain Teasers (5 page)

And do it without trigonometry!

139. I throw a five-cent coin and a ten-cent coin in the air. If one of them lands as a head, what is the probability that the five-cent coin will land as a head?

(a) 1/3

(b) 1/2

(c) 2/3

(d) 3/4

(e) 7/8

140. Three items in a department store are sold with successive discounts.

The first is sold with successive discounts of 60 percent and 40 percent.

The second is sold with successive discounts of 50 percent and 50 percent.

And the third is sold with successive discounts of 30 percent and 70 percent.

Which of the following is true:

(a) The equivalent single discount of all three items is the same, but not 100 percent.

(b) The equivalent discount of each of the three items is between 70 percent and 80 percent.

(c) The equivalent discount of each of the three items is between 80 percent and 90 percent.

(d) The equivalent discount of each of the three items is 100 percent.

(e) None of the above statements is true.

141. You have an empty three-gallon bottle and an empty five-gallon bottle. How can you measure exactly one gallon of milk without wasting any milk?

142. You have three playing cards lying face up, side by side. A five is just to the right of a two. A five is just to the left of a two. A spade is just to the left of a club, and a spade is just to the right of a spade. What are two possible layouts for the three cards?

143. If the following four statements are presented, which one of them is true?

(a) The number of false statements here is one.

(b) The number of false statements here is two.

(c) The number of false statements here is three.

(d) The number of false statements here is four.

144. Find a four-digit number where the first digit is one-third the second, the third is the sum of the first and second, and the last is three times the second.

145. A boy and a girl are sitting on a bench. “I’m a girl,” says the child with brown hair. “I’m a boy,” says the child with blond hair. If at least one of them is lying, which one is lying, or are they both lying?

146. You have twelve balls that are identical in all ways, except one ball is heavier than the rest. With a balance scale, how could you determine in three weighings which is the heavy ball?

147. If you add the age of a man to the age of his wife, the result is 91. He is now twice as old as she was when he was as old as she is now. How old is the man and how old is his wife?

148. Suppose you have fifty American coins with at least one quarter, totaling exactly $1.00. If you drop a coin at random, what is the probability that it is a penny?

149. Bill bought four times as many apples as Harry, and this amount happened to be three times as many as Martin bought. If Bill, Harry, and Martin purchased a total of less than 190 apples, what is the greatest number of apples that Bill could have purchased?

(a) 168

(b) 120

(c) 119

(d) 117

(e) 108

(f) 90

150. Put the numbers 1 through 9 in the circles below so that the numbers in four circles on each side add up to 17. Note: You can’t use a number more than once.

151. Using six straight lines without retracing, connect all sixteen circles.

152. Suppose there are two buckets, one that contains a gallon of water and the other that contains a gallon of alcohol. A cup of alcohol from the second bucket is poured into the bucket of water. A cup of the resulting mixture is then poured back into the bucket of alcohol. Which is now true?

(a) There is more water in the alcohol than alcohol in the water.

(b) There is more alcohol in the water than water in the alcohol.

(c) There is the same amount of water in the alcohol as alcohol in the water.

153. A figure is divided into two squares by drawing one straight line. The original figure could have been a/an:

(a) nonrectangular trapezoid

(b) triangle

(c) square

(d) circle

(e) octagon

154. What is the next letter in the following series: s t n o j k g h ?

(a) g

(b) c

(c) d

(d) e

(e) f

155. A bus can hold
x
people. It is half full, and
y
people now get off. How many people could now get on the bus?

156. Unscramble the words to make a phrase about the movies:

SGITHL, AEMRAC, CTONIA

157. If I have 3 dimes, 3 nickels and 3 quarters, how many ways can I make change for $1.00?

(a) 1

(b) 2

(c) 3

(d) 4

(e) 5

158. Three friends eat breakfast at a restaurant. They estimate that the bill should come to $30. They split the bill 3 ways and pay $10 each. When the bill comes, it is $25. Since this is not divisible by 3, they each take $1 back, and a $2 tip is left. Since each paid $9 and $9 x 3 = $27, plus $2 for the tip, where did the extra dollar go?

159. What is the least whole number greater than 95,555 where four of the digits of the number are the same?

160. What English word contains all the vowels, in alphabetical order?

161. How many states are there in the United States where the first letter of the capital city is the same as the first letter of the state?

162. BUILDING : CHURCH ::

(a) dance : ballet

(b) poetry : sonnet

(c) museum : relics

(d) song : hymn

(e) morality : ethics

163. HAMLET : VILLAGE ::

(a) street : sidewalk

(b) highway : car

(c) building : skyscraper

(d) photograph : portrait

(e) cottage : house

164. Fill in the blanks:

In spite of the________of her presentation, many people were

________with the speaker’s concepts and ideas.

(a) interest…enthralled

(b) power…taken

(c) intensity…shocked

(d) greatness…gratified

(e) strength…bored

165. Fill in the blank:

Richard Wagner was frequently intolerant; moreover, his strange behavior caused most of his acquaintances to________ the composer whenever possible.

(a) contradict

(b) interrogate

(c) shun

(d) revere

(e) tolerate

Read the following passage and answer the questions that follow:

Sometimes the meaning of glowing water is ominous. Off the Pacific coast of North America, it may mean that the sea is filled with a minute plant that contains a poison of strange and terrible virulence. About four days after this minute plant comes to dominate the coastal plankton, some of the fishes and shellfish in the vicinity become toxic. This is because in their normal feeding, they have strained the poisonous plankton out of the water.

166. Fish and shellfish become toxic when they:

(a) swim in poisonous water

(b) feed on poisonous plants

(c) change their feeding habits

(d) give off a strange glow

(e) take strychnine into their system

167. If there was a paragraph preceding the one in the passage, it most probably discussed:

(a) phenomena of the Pacific coastline

(b) poisons that affect man

(c) toxic plants in the sea

(d) characteristics of plankton

(e) phenomena of the sea

168. A four-sided figure, ABCD, contains interior right angle C. AB = 12, BC = 3, CD = 4, and AD = 13. What is the area of the figure ABCD?

(a) 36

(b) 108

(c) 156

(d) 1,872

(e) cannot be determined

169. If
x
+
y
= 7 and
xy
= 4, then find the value of (
x
x
x
) + (
y
x
y
). Note:
x
and
y
may not be integers.

170. A four-sided figure has sides of lengths
a, b, c,
and
d.
Sides of lengths
c
and
d
meet at a right angle (90°). Sides of lengths
a
and
d
meet at a 140° angle. Sides of lengths
b
and
c
meet at a 40° angle. Is
a
²
-
c
²
greater than, equal to, or less than
d
²
-
b
²
?

171. If
a
does not equal
b
and
a
+
b
is greater than 0, is 2
ab
divided by (
a
+
b
) greater than, equal to, or less than (
a
+
b
) divided by 2?

172. Fill in the blanks:

His choice for the new judge won the immediate________of city officials, even though some of them had ________about him.

(a) acclaim…reservations

(b) disdain…information

(c) apprehension…dilemmas

(d) vituperation…repercussions

(e) enmity…preconceptions

173. SHIP : HARBOR ::

(a) flower : garden

(b) village : people

(c) nest : bird

(d) editor : newspaper

(e) car : garage

174. In the diagram, where a circle is inscribed in a square and another square is inscribed in the circle, if a side of the larger square is 10, what is the area of the smaller square?