World's 200 Hardest Brain Teasers (7 page)

2.     one word

Okay, that may be a cheap one! The fact that “one word” in the question was italicized could indicate that the word was in fact “one word.”

3.     (a) 30

Average rate
is not the
average of the rates,
and the answer is not 40. Also, the distance does not need to be known. Where
a
and
b
are the two rates, the average rate can be shown to be 2
ab
/(
a
+
b
), so 2(20)(60)/(20 + 60) = 30.

Detailed explanation: Average rate = Total distance/Total time. Let’s say the distance is
D
one way. Then the total distance is 2
D
. Let’s say the time the car travels 20 mph is
t
and the time the car travels 60 mph is
T
. Then from the formula Rate x Time = Distance, 20 x
t
=
D
and 60 x
T
=
D
. This gives you
t
=
D
/20 and
T
=
D
/60. So the total time is
t
+
T
=
D
/20 +
D
/60. This is equal to
t
+
T
= 80
D
/1,200 =
D
/15. So the average rate = 2
D
/(
t
+
T
) = 2
D
/(
D
/15) = 30.

4.     (b) succeeding

PRE means before; CURS means to run. So, PRECURSORY means to run (or go) before. The opposite is running or going after, or “succeeding.”

5.     The label BC only could have come into usage after 0 BC.

6.     Thirteen nickels, one dime, and one quarter

The cleverest way to solve this problem is to try to reduce the number of possibilities to a minimum and then figure out all of those possibilities. The highest number of quarters I can have is three, since if I have at least one of every coin, I can’t have four quarters (and I can’t have more than four quarters because the total would be more than $1). So, if I have three quarters, I am left with fourteen dimes/nickels, which must add up to 25 cents. That’s impossible, so suppose I have two quarters. That leaves 50 cents for the dimes/nickels. I can’t get fourteen dimes/nickels that add up to 50 cents. So, try one quarter. I have 75 cents left. I can get thirteen nickels and one dime to total 75 cents.

There is also an algebraic way of solving this problem:

Let’s say I have
n
nickels,
d
dimes, and
q
quarters. The total number of coins can be represented as:

(Equation 1)
n
+
d
+
q
= 15.

The value of all the coins is:

(Equation 2) 5
n
+ 10
d
+ 25
q
= 100, since a nickel is worth 5 cents, a dime is worth 10 cents, and a quarter is worth 25 cents.

Let’s divide the second equation by 5. We get:

(Equation 3)
n
+ 2
d
+ 5
q
= 20

Multiply Equation 1 by two:

(Equation 4) 2
n
+ 2
d
+ 2
q
= 30

Subtract Equation 3 from Equation 4. We get:

(Equation 5)
n
- 3q = 10

Now, because of Equation 2,
q
must be either 1, 2, 3, or 4 and not more than 4, since
n
and
d
must be both positive numbers.

We know from Equation 1 that
n
must be less than 15, since
d
+
q
must be positive numbers.

If
q
= 4, Equation 5 tells us
n
= 22, which is impossible.

If
q
= 3,
n
= 19, which is impossible.

If
q
= 2,
n
= 16, which is impossible.

Therefore,
q
= 1, which makes
n
= 13 and
d
= 1.

Therefore, I have thirteen nickels, one dime, and one quarter.

7.     He could type “The file will be deleted.”

Think of a statement that will be in conflict with what is mentioned. If the user types “The file will be deleted” and the statement is true, the file’s name will change but not be deleted. Thus the statement “The file is deleted” cannot be true. So it is false. But if the statement “The file will be deleted” is false, according to what is mentioned in the question, the file will be deleted, making the user’s statement true, which would be contradictory. So if the user types “The file will be deleted,” the computer will not be able to perform a function with the file and probably shut down.

8.     Terry is 5 years old.

Translate words to math. “Alice was five years older than Terry is now” translates to
a
= 5 +
T,
where
a
is the age that Alice was.

Now translate again. Terry is half as old as Alice was:
T
= (1/2)
a.
Substitute for
a:

T
= (1/2)(5 +
T
).

2
T
= 5 +
T,

T
= 5.

So, Terry is 5 years old.

9.     Choices (d) negative : positive and (e) disordered : ordered are correct.

An imaginary number is a number such that when multiplied by itself it becomes a negative number. However, there is no way a real number multiplied by itself will give you a negative number. Thus, the term
imaginary.
For example, two times an imaginary number cannot be thought of as greater or less than three times the number. Therefore they are called “not ordered.” The real numbers are ordered. For example, three times the number 25 is greater than two times the number 25.

10.   355 x 356 is greater than 354 x 357.

There are more than seven ways to answer this question depending on how your mind works. One strategy is to find a way you can divide to make the problem simpler. The simple way is to divide both quantities by 356 x 354. You then get to compare 357/356 with 355/354. 357/356 = 1 1/356 and 355/354 = 1 1/354. So, the original second quantity is greater than the original first quantity.

11.   A single 50 percent discount is better.

It is better to get a single discount of 50 percent. Do not get lured into a process that sounds superficial. In fact, it is always better to get a single discount of the sums of the successive discounts than to get the successive discounts. For example, suppose the item was originally $100. A single discount of 50 percent would give you the item at $50. Now, if I had successive discounts of 20 percent and 30 percent, the first 20 percent discount would give me $80. The second 30 percent discount on $80 would give me $56.

12.   If the client died in his sleep, there would be no way of knowing what he was dreaming.

13.   Look for something that does not link smoking to cancer directly, but indirectly. That is, something that causes one to smoke and the same thing that causes cancer. So research could find that there is a certain condition that causes one to smoke and the same condition causes one to have cancer. Thus, smoking does not cause cancer; it is the condition that causes it. Unfortunately, that is not the case.

14.   (b) 3

Do this problem in steps by starting with two socks. If you get only two socks, they could be different colors, but getting three guarantees that you will have a pair. The strategy is to realize that in order to be sure of what you get, you have to consider the worst-case scenario. The worst case is that if you reach in the drawer, you’ll get two different color socks the first two tries—let’s say a blue sock and a brown sock the first two tries. But the third try you’ll have to get either a blue or a brown sock, which will make a pair with one of the first two socks.

15.   Thursday

The key is to realize that “now” must be Friday. Look for the phrase in the problem that tells you something you can work with and use that with another part of the problem to gradually and stepwise lead to a solution. In the phrase “Two days from now will be Sunday,” you can see that
now
must be Friday, since two days from Friday is Sunday. Now look at the phrase “the day before yesterday.”
Yesterday
is Thursday since
now
(today) is Friday. “The day before yesterday” is Wednesday, and the “day that follows the day before yesterday” is
Thursday.

16.   (d) furniture : carpentry tools

Put MUSIC and VIOLIN in a sentence relating the two words. Music is played on a violin by someone who knows how to play a violin, just as furniture is created by carpentry tools by a person who knows how to use carpentry tools. A crayon is not done with a drawing (drawing is done with a crayon). Note: a symphony is not played on a piano—it is played by an orchestra.

17.   (c) 10

There are two alternating sequences: 0, 1, 2, 3, 4, 5 and 0, 2, 4, 6, 8.

18.   (e) John Hancock : signature

Look at what is superficial and what is not. George Washington was superficially identified with the cherry tree as John Hancock was superficially identified with his flamboyant signature. All the other people were not superficially identified in the phrase with their name.

19.   (b) C minus B is always less than A

Subtract the same thing from both sides. Since the sum of two sides of a triangle must be greater than the third side, A + B > C, so subtracting B from both sides, A > C - B.

20.   (c) 19

Use a Venn diagram or write down all the possibilities.

Total number of people:

(a) Blonds without blue eyes (14 - 5 = 9).

(b) Blue-eyed people who are not blond (8 - 5 =
3).

(c) Blue-eyed blonds (5).

(d) People with neither blue eyes or blond hair (2) Adding a, b, c, and d, we get 9 + 3 + 5 + 2 = 19.

21.   (d)

It is very tempting to just subtract the times 9:09 from 10:10, etc., and get 61 minutes, or if you’re careless get 101 minutes. However, think of the times closest to one another, 12:12 and 1:01, and you will find the difference is 49 minutes.

22.   (c) 5

Draw lines to see that BD is a radius of the circle. The two diagonals of a square will have the same length.

23.   (a) 25 x 25 x 25 x…(where there are fifty 25s)

Try to find a connection between the numbers. You are comparing 50 x 50 x 50 x 50…(100 times) to 100 x 100 x 100 x 100… (50 times). Write 100 as 50 x 2, so now you are comparing 50 x 50 x 50 x 50…(100 times) to 50 x 2 x 50 x 2 x 50 x 2 x 50 x 2.(50 times).You can now cancel 50 x 50 x 50 x 50.50 times from both sides of the comparison. You would then get 50 x 50 x 50 x 50.(50 times) compared with 2 x 2 x 2 x 2.(50 times). You can see the left side of the comparison is 25 x 25 x 25 x 25…(50 times) times the right side.

24.   Say IN means NOT, then associate EXTRIC with another word, EXTRACT. So INEXTRICABLE means not extractable—incapable of being extracted—or INSEPARABLE. Association is a powerful strategy for getting the meaning of words.

25.   The doctor is the son’s mother.

26.   If many people paid attention to the ad, it would be very crowded in the early hours. Of course the reason why the ad was put in was because the store did not think that so many people would read the ad.

27.   (b) second

Many people who get this problem wrong think of just the numbers, not the wording, assuming that if you overtake the second runner, you are first. But when you overtook the second runner, you took his or her place. Therefore you are now in second place, not first place.

28.   (e) none of the above

If the four daughters are those mentioned, think of who the fifth daughter could be—the fifth daughter is Bonnie herself.

29.   (e) thimble : finger

Create a sentence expressing a specific relationship between the capitalized words. HELMET is worn on the HEAD to protect the head, as THIMBLE is worn on the FINGER to protect the finger.

30.   If a number is an exact multiple of 9, the sum of the digits of that number is also a multiple of 9. So 1 + 2 + 3 +
x
= 9 and
x
= 3.

31.   The knight could tear up the paper he picks and offer the other one to the king. He could then tell the king that since the untorn paper reads “Death,” the one torn must have read, “Marriage.”

32.   From first to last: John, Mary, Sarah, Barry

The easy way to find the answer is to draw the situation with labels for the people’s names.

(1) Sarah is between Barry and Mary: B S M or M S B.
(2) John is directly in front of Mary: J M
(3) Mary is in front of two other people: M S B

So we get from (2) and (3): J M S B

33.   One-half the surface area of a ball is greater. Blow up the circle like a balloon to get the ball. One half the surface area of the ball is greater than the area of the circle because the circle is being expanded by being blown up.

34.   Write a three-digit number with
h
hundreds digit,
t
tens digit, and
u
units digit as 100
h
+ 10
t
+
u
. You will find that A = 1, B = 0 and C = 9.

We have 100A + 10B + A - 10C - A = 10A + B. This gives us 90A + 9B = 10C or 10A + B = (10/9)C.

The only way A and B can be integers is if C = 9. That makes 10A + B = 10. The only way this is possible with A and B as integers (from 0 to 9) is if A = 1 and B = 0.

35.   (b) m

Letters are arranged in pairs, backward skipping every third letter: m n (o) p q (r) s t (u) v w (x) y z.

36.   5

Draw a perpendicular line to make a rectangle in the figure and you will also have a 3-4-5 triangle.