World's 200 Hardest Brain Teasers (15 page)

158. There was no extra dollar.

Watch that your mind doesn’t deceive you. They thought the bill came to $30, but that doesn’t make it the amount that we want to work with.

159. 95,999

You may have thought the number was 96,666. But then you didn’t account for the 9 in the original number. So the least whole number is 95,999.

160. facetious

161. Four states

Hawaii (Honolulu), Oklahoma (Oklahoma City), Indiana (Indianapolis), Delaware (Dover).

162. (d) song : hymn

Put the analogy in a very specific sentence: CHURCH is a religious type of BUILDING as hymn is a religious type of song.

163. (e) cottage : house

Put the analogy in a very specific sentence: HAMLET is a small VILLAGE as cottage is a small house.

164. (e) strength…bored

The key words are
in spite of.
Look for a contrast or opposites.

165. (c) shun

The key word is
moreover.
Not only was Wagner intolerant, but with his “strange behavior,” people would avoid (or shun) the composer.

166. (b) feed on poisonous plants

Try to get clues from the rest of the passage and use inferences. Since the fish and shellfish become toxic, it can be inferred that they must eat the plankton, which could only be small animals or plants. (a) swim in poisonous water is incorrect because “coastal plankton” is distinguished in the sentence from “fishes and shellfish.” (d) give off a strange glow is incorrect because nowhere in the passage does it mention that the fish give off a “strange glow.” Choices (c) change their feeding habits and (e) take strychnine into their system are incorrect because it is unlikely that fish and shellfish would eat sand deposits or glacier or rock formations—they would eat plants or smaller animals.

167. (e) phenomena of the sea

Pay attention to the three parts of a passage: The opening sentence leads into what is going to be discussed, the middle tells us about the passage, and the last sentence or paragraph usually summarizes or wraps up the passage. Look at the opening phrase, which introduces the passage. The fact that glowing water is mentioned indicates that the paragraph preceding the sentence probably talks about the sea.

168. (a) 36

Draw the figure with angle C as a right angle. Now the key strategy is to draw an extra line, BD.

Triangle BCD is then a right triangle and is a 3-4-5 right triangle. Now you have triangle BAD as a 5-12-13 triangle. This is also a right triangle. (In high school you prove these things by using the Pythagorean theorem, but usually students are told to remember certain right triangles like the popular 3-4-5 and 5-12-13 ones.) So if triangle BAD is a right triangle (where angle ABD is a right angle), you can show the area is (5 x 12)/2 = 30. The area of triangle BCD is (3 x 4)/2 = 6, so the total area of the figure is 36.

169. 41

Square (
x
+
y
) = 7. You get
x
²
+
y
²
+ 2
xy
= 49. Now substitute
xy
= 4.

You get
x
²
+
y
²
+ 2(4) = 49. So
x
²
+
y
²
+ 8 = 49 and so
x
²
+
y
²
= 41.

170. equal to

Draw the figure and notice that there are two right angles because the sum of the angles of the four-sided figure is 360°.

Since there are then two right triangles, with the use of the Pythagorean theorem, we get

a
²
+
b
²
=
c
²
+
d
²
. Thus, we find that
a
²
-
c
²
=
d
²
-
b
²
.

171. less than

Compare 2
ab
divided by (
a
+
b
) with (
a
+
b)
divided by 2 by manipulating the inequality or equality: Multiply both sides by 2 and then by (
a
+
b
). Then multiply out
(a
+
b
) x (
a
+
b
) and subtract the 4
ab
on the left side from both sides. You will get 0 as compared with (
a
-
b)
x (
a
-
b).
Since
a
is not equal to
b
(given), 0 is always less than

(
a
-
b)
x (
a
-
b).

172. (a) acclaim…reservations

The key words are
even though.
This signals a contrast.

173. (e) car : garage

A SHIP is put in a HARBOR as a car is put in a garage. Although bird is put in a nest, the analogy presents the ideas in the reverse order, and a nest is not put in a bird.

174. 50

Draw lines to get additional information.

175. (b) tranquil

One strategy is when the word sounds “big” like
effervescent, magnanimous,
and
scintillating,
it probably will mean something big or flashy. Think of
ebullient
as a big-sounding word. The opposite would be
tranquil.

176. 30

From 10 to 100, you have 12, then 15, etc., up to 99. This is 4 x 3, 5 x 3, up to 33 x 3. So there are 33 - 4 + 1 = 30 integers.

177. 36

The edge of the cube is 3 and there are 12 edges.

178. (e) o

179. 3

In 4 hours Jim can do one job, and in 4 hours Tom can do two jobs.

180. (a) 30

Total number of people = Number who can write with both hands + Number who can write with only the left hand + Number who can write with only the right hand. Or, 50 = 10 + 20 +
x
. Thus
x
= 20 can write with only the right hand. But 10 can write with both the left and right hand, so 30 can write with the right hand.

181. cannot be determined

Translate words to math. We have (10 +
x
)/2 divided by (10 +
x)
= 1/2. So we get

Cancel (10 +
x):
we get 1/2 = 1/2.

Thus,
x
cannot be determined.

182. (b) 84

96 - 12 = 84

183. 4,400 feet

In one revolution the wheel would roll one circumference or 2πr feet = 2π feet.

2π x 700 = 1,400π = 4,400 feet (approximately).

184. 33 1/3 percent

185. 150 square inches

186 - 2 x (6 x 3) = 150

186. c, e, a, b, d
or
e, a, b, d, c

187. (e) tournament : joust

LITIGATION is done in a COURT as joust is done in a tournament.

188. (b) 28

Using symbols, let
S
= 3
W. S
+
W
= Number of string and wind musicians. Thus, 3
W
+
W
= 4
W
is the number of string and wind musicians. The only choice where
W
is a whole number is where 4
W
= 28 (
W
= 7).

189. (a) viola : cello

OBOE and BASSOON are in the same family of instruments—woodwinds—as viola and cello are in the same family of instruments—strings.

190. 120

Write a relation:
C
= 4
S
, C = 3
W
,
C
+
S
+
W
< 200.

191. Jane, Ellen, Ann, Joyce

Translate from words to math:

Ja
= 3
A
,

A
- 3 =
Jo
- 1,

E
= 2
A
.

So,
Ja
= 3
A
,
A
=
Jo
+ 2,
E
= 2
A
, so
Ja
>
E
>
A
> Jo

192. Six

3
Sw
+ 2
Sk
= 3
Sk
. So, 3
Sw
=
1
Sk
.

193. (e) I, II, and III

Where
x
is a whole number, the number of beads is 3
x
+ 2 since you are left with only a red and a white and all the rest are red, white, and green. Thus, see if
x
is a whole number where 3
x
+ 2 = 17, 29, and 35. Alternate solution: If the order is red, white, green…, then the number of beads you have ending in white is
r, w
= 2;
r, w, g, r, w
= 5;
r, w, g, r, w, g, r, w
= 8, so the sequence is 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35.

194. d, b, e, a, c

195. (b) barcarole : gondola

LULLABY is sung to a person in a CRADLE, and barcarole is sung to a person in a gondola.

196. (f) I and V only

The statement implies the following possibilities: Susan, but not Freddie will be hired; Freddie, but not Susan will be hired; and neither Freddie nor Susan will be hired. Statement (I) and (V) are equivalent and possible. (II) is true. (III) is false. (IV) is false.

197. (b) less than 30

Draw a line that makes the third side of the triangle with sides 4 and 5.