World's 200 Hardest Brain Teasers (10 page)

86.   (f) 36

The final result must be divisible by 9. It is very interesting that when you add the digits of a number and subtract that from the original number you get a number that is a perfect multiple of 9. Here’s the proof: Represent the two-digit number as 10
t
+
u
where
t
is the tens digit and
u
is the units digit. Adding the digits, we get
t
+
u.
Subtracting from the original number, we get 10
t
+
u
-
t
-
u
= 9
t
. Since
t
is an integer, the only choice that fits is (f) 36. What’s more interesting is that any number that is a multiple of 9 has digits that add up to a multiple of 9.

Here’s a great parlor trick: Have someone choose a number. Then have that person add the digits. Then have the person subtract that result from the original number to get a final result. Have the person now cross out one of the digits in the final answer. You will be able to tell the person what digit he crossed out if he tells you the remaining digit. For example, he starts with 23. 2 + 3 = 5. 23 - 5 = 18. He crosses off the 8. He is left with 1. You will be able to tell the digit crossed out. Why?

Any number that is a multiple of 9 has digits that add up to a multiple of 9. So whatever number you crossed out, the crossed-out number must be 9 minus the number left!

87.   The mind may give you the pronunciation of DOUS as “doos.” Don’t assume that is the correct pronunciation. Realizing that, you may come up with the words
stupendous, tremendous, or horrendous.

88.   (e) a country

MEANYRG spells GERMANY.

89.   (d) Spaceship

Look for similarities in the messages:
Avion
occurs in (1) and (2) and so does
Serious.
So
Avion
must mean
Serious. Balcon
appears in (1) and (3) and so does
Fumes.
So
Balcon
must mean
Fumes.
So looking at (1),
Sondor
must mean
Spaceship.

90.   (d) 240

Do this in steps: If eight people can wash 50 cars in 60 hours, then four people can wash 50 cars in 120 hours. It would take twice as much time to wash, since there are half as many people to wash. Thus, it would take four people 240 hours, twice as long, to wash 100 cars, since there are twice as many cars now.

91.   (c) cannot be determined as true or false

Translate to something you know. For example, let Blips be Students and Plips be Teachers. And let Jips be Actors. So “Some students are actors” is neither false nor true.

92.   (c) 99

This is tricky. If Matt is the fiftieth fastest runner, he would be number 50 in the sequence 1, 2, 3…50. To be the fiftieth slowest, he’d have to be number 50 in the sequence 50, 51, 52…99, since there are fifty numbers from 50 to 99 inclusive.

93.   (d) None of the above can be proved true.

Write P > N and D < P. This is the same as P > N and P > D. You cannot determine the relationship of D and N. For example, if P is be 6', N can be 5', and D can be 5.5' or N can be 5' and D can be 5' or N can be 5.5' and D can be 5.5'.

94.   (d) 24

Write the number of fish Harry caught as
H
and the number of fish Sam caught as
S
. Then translate to math: (1)
H
= 3
S
. So, (2)
H
+
S
= 32. Substitute
H
= 3
S
in (2) and we get 3
S
+
S
= 32. 4
S
= 32,
S
= 8. So,
H
= 3
S
= 24.

95.   (c) 10

Draw a diagram to illustrate the situation.

The distance between the two runners is 10.

96.   MAINE is the shortest name of a state that shares a letter in common with each of the other fifty states

97.   24

Start with the first person,
a,
at the left side in a corner position. Then figure out the combinations you can have
(ab-cd
or
ac-bd,
etc.) Since
a
is in the left corner, you can play around with combinations of
bcd
for the remaining positions. There are 3 x 2 = 6 of them. Now
b, c,
or
d
can be in the left corner also, so there are 6 + 6 + 6 more combinations. That gives us a total of 24.

98.   No

Watch the wording. A widow has lost her husband. His widow would be his present wife, but he is dead, so that’s impossible. If the wording said “a widow’s sister,” then it would be possible, since he would not be her dead husband.

99.   9

You may have thought of subtracting 9 from 17, giving you 8. But the question says “all but 9 die.” That means you have
9
left!

100. (d) 201

Place 11 cartons with the 40” side along the back of the room, and repeat in front of this row so you have 15 rows deep of 11 cartons wide (165 cartons). In the remaining space, place two cartons with their 48” side against the back and make 18 rows of these (36 cartons). This gives 165 + 36 = 201 refrigerators stored. You can also get 201 fridges in by changing the numbers so you have 15 rows of 5 cartons and 18 rows of 7 cartons.

101. Quantity B

Understand the difference between “average rate” and the “average of the rates.” Then
cross-multiply,
then
subtract
4
ab
from both quantities.

Detailed explanation: The average rate of a car going uphill at
a
miles per hour and downhill at
b
miles per hour the same distance is just 2
ab
/(
a
+
b
). Proof: Call the distance
d
. Call the time it takes for the car to go uphill
t
. Call the time it takes for the car to go downhill the same distance,
d, T
. Because Rate x Time = Distance,

(1)
a
x
t
=
d

(2)
b
x
T
=
d

The average rate is the total distance divided by the total time. That is 2
d
/(
t
+
T
).

Using (1), we get
t
=
d/a
and (2),
T
=
d/b.

So 2
d/(t +T)
= 2
d/( d/a
+
d/b),
which can be seen to be just 2
ab/( a
+
b).

The average of the rates
a
and
b
is just (
a
+
b
)/2.

So Quantity A is just 2
ab
/(
a
+
b
) and

Quantity B is just (
a
+
b
)/2.

Multiply both quantities by 2. You get

Quantity A: 4
ab
/(
a
+
b
)

Quantity B:
a
+
b

Now multiply both quantities by (
a
+
b
).

You get

Quantity A: 4
ab

Quantity B: (
a
+
b)
x
(a
+
b)
=
a
²
+
b
²
+ 2 x
b
x
a

Now subtract 4
ab
from both quantities. You get Quantity A: 0

Quantity B:
a
²
- 2 x
b
x
a
+
b
²
= (
a
-
b
) x (
a
-
b
)

Since
a
is not equal to
b
, (
a
-
b
) x (
a
-
b
) is always greater than 0.

Thus Quantity A is less than Quantity B and so the original Quantity A [2
ab
/(
a
+
b
)] is less than the original Quantity B [(
a
+
b
)/2]. Thus, the average rate of the car going uphill at
a
miles per hour and downhill at
b
miles per hour is less than the average of the rates
a
and
b.

102. (b) Mike is a child.

103. Small

Adding
er
gives you
smaller.
You can also do this with
meter.
Adding
milli
makes the word
millimeter,
which is smaller.

104. Yes

Don’t get lured by the fact that the fourth of July is a holiday celebrated only in the United States. It doesn’t say
celebrated
or
holiday
in the question. So of course they have a fourth of July (July 4) in England, since that’s also a day in their calendar.

105. One

Analyze what a birthday is. Don’t get lured into the word
average.
It’s a single day that someone was born. So the average man (or any man) has only
one
birthday, his date of birth.

106. 6

You may have thought the answer was “three outs.” But there are
two
teams that play in an inning. So there are
six outs.

107. See what you have been given to work with in answering the question. Since the problem doesn’t give any indication of the butcher’s weight, the word
weigh
must refer to something else. The butcher weighs
meat!

108. (e)

The ? must have only one set of parallel lines.

109. 12 stamps

You may have multiplied 2 x 12 to get 24. But a dozen stamps means 12 stamps no matter how much each stamp is worth!

110. 60 minutes

Many of you probably think that I should multiply 3 pills by 30 minutes to give me 90 minutes. But think of how you take the pills. I take the first pill, and in a half-hour I take the second pill, and then in the next half-hour I take the third pill. So the number of minutes that pass from the first to the third pill is 60 minutes.

111. Ten numbers

Start with the lowest number: 4,567. The next number is 4,568, then 4,569; 4,578; 4,579; 4,589; 4,678; 4,679; 4,689; 4,789. So there are ten numbers.

112. 1

Note that the numbers in the sequence are integers multiplied by themselves three times, that is 125 = 5 x 5 x 5; 64 = 4 x 4 x 4; 27 = 3 x 3 x 3; 8 = 2 x 2 x 2. So the next number would be 1.

113. (e) 45

If John = 10, then his mother is 40. When John is 15, he is 5 years older. So, his mother must be 5 years older, and then is 45.

114. (a) 6

You need to use the formula Rate x Time = Distance, that is
r
x
t
=
d
. For the uphill trip,

r
(uphill) x
t
(uphill) = 1 mile

For the downhill trip,

r
(downhill) x
t
(downhill) = 1 mile

The average rate of the car is the total distance traveled (2 miles) divided by the total time traveled,
t
(uphill) +
t
(downhill).

Since the average rate was given as 20 mph, 20 = 2 divided by [
t
(uphill) +
t
(downhill)]. Thus, we get 10 =
t
(uphill) +
t
(downhill).

115. (d) You can’t do anything.

Since you’re going from a very high speed to 0 (when the elevator hits the ground) the force is tremendous (from physics, force is proportional to the acceleration). You can’t jump up because you’d be going from a very high speed to a speed of less than 0 and that would also require a tremendous force. The force is what gets you, so there’s nothing you can do!

116. 46 x 767 x 72 is less than 767 x 46 x 74.

Cancel 46 and 767 (common numbers) from both products.

117. The house
that
is painted yellow has just been sold. The house,
which
is painted yellow, has just been sold.

In (1), “The house” refers to one of a number of houses. In (2), “The house” does not refer to one of a number of houses.

118. Seven

Draw a line in the circle and place nine people on the line. Choose two people on the line and draw another circle inside the first so that those two people are on the circumference of that circle. Thus you would have to move the rest of the people (7 people) to place them also on the circumference of that circle.

119. 1 is greater.

Multiply 1 by 99/77 and compare that with 77/99.

120. (b) replace…important

Use key words:
while, is not able, it is still able.

121. It confuses people with playing styles.

122. (e) freezing : spoilage

A VACCINATION is used to prevent a DISEASE as freezing is used to prevent spoilage. Note that aspirin is not used to prevent a headache; it can be used to reduce the symptoms of a headache and also as a regiment to prevent against heart attacks.

123. 7:04 AM

The clock gains 3 minutes every day, or 1 minute every 8 hours. Between 11 PM Sunday night and Tuesday morning 7 AM is 24 + 8 hours. So the clock gains 4 minutes.

124. Average speed is total distance divided by total time. So for the first half, 25 = 50/time of first half. Thus the time for first half is 2 hours. For Phil to average 50 miles per hour for the whole trip, we would get 50 = 100/time for the whole trip. Time for the whole trip then is 2 hours. That would mean that Phil must go an infinite speed the second half of the trip to go 50 miles in 0 hours.