World's 200 Hardest Brain Teasers (9 page)

Since
AED = 90, (1)
x
+
y
+
z
= 90.

Since
BED = 40, (2)
x
+
z
= 40.

Since
AEC = 75, (3)
y
+
x
= 75. Subtracting Equation (2) from Equation (1) we get
y
= 50. Substituting
y
= 50 in Equation (3) we get
x
= 25.

51.   999 x 1,001 is just 1 less than 1,000 x 1,000.

One of the key strategies in mathematics is to write what is presented in a different form: Write 999 x 1,001 as (1,000 - 1) x (1000 + 1) and you’ll find that’s equal to 1,000 x 1,000 - 1, since (
a
-1) x (
a
+1) =
a
x
a
- 1.

52.   276

Each person can shake hands with 23 other people, so we have 24 x 23 possible combinations. But because it takes two people to make a handshake, we must divide this product by 2, so we get (24 x 23)/2, or 276.

53.   DRAW is the only verb on the list with a past tense that does not rhyme with OUGHT.

The strategy is to try to see something curious in the words. Notice something that many of the words have in common. Most of them have a past tense that has a different structure or sound from the word. BRING—not “BRINGED” but BROUGHT, BUY—not “BUYED” but BOUGHT, CATCH—not “CATCHED” but CAUGHT, etc. And all of these past tense words rhyme with OUGHT,
except
“DREW,” which is the past tense of DRAW. So DREW is the odd man out!

54.   (b)

There is one right angle in the first set for each figure and two right angles in each figure in the second set. So the missing figure must have two right angles.

55.   There are actually several correct answers to this problem. Here are some of them:

A-E-T makes EAT, TEA, and ATE;

A-T-R makes ART, RAT, and TAR;

O-T-P makes OPT, TOP, and POT;

A-P-T makes APT, PAT, and TAP;

R-E-A makes EAR, ARE, and ERA.

The thing to do is to figure out how to start a problem like this. What do you do first? First, just try to make a three-letter word—any three-letter word, like TIN. Using those letters, T-I-N, can you make another word? Start with T: TNI does not make a word. Now methodically use I as the first letter: INT and ITN do not make a word. Now start with N: NIT and NTI do not make a word—so T-I-N does not work.

Don’t get discouraged. Try another three-letter word: E-A-T.

EAT is a word. Start with A now: ATE is a word. Now start with T: TEA is a word. Other correct answers are OPT, TOP, POT, and ART, RAT, and TAR.

56.   The only number that meets these requirements is 735.

57.   The only English word that can be formed by two consecutive three-letter abbreviations for months is DECOCT, which means to extract the flavor by boiling or to steep in hot water.

58.   AD x CD is greater than
h
x AB.

To solve,
label
the sides of the parallelogram with letters like
a
and
b,
then
cancel
the like quantities.

h
x AB =
h
x
a
and AD x CD =
b
x
a

We are then comparing
h
x
a
with
b
x
a.
Since the
a
is the same in each expression, we are really comparing
h
with
b,
and
h
is less than
b
because
b
is the largest side (the hypotenuse) of a right triangle. Thus the original
h
x AB is less than AD x CD.

59.   The long hand passes the short hand only eleven times. The long hand passes the short hand at noon, and between the times 1 PM and 2 PM, 2 PM and 3 PM, 3 PM and 4 PM, 4 PM and 5 PM, 5 PM and 6 PM, 6 PM and 7 PM, 7 PM and 8 PM, 8 PM and 9 PM, 9 PM and 10 PM, 10 PM and 11 PM a total of eleven times. Note that the long hand does not pass the short hand between 11 PM and 12 AM, it just meets the short hand at 12 AM.

60.   One word is PASSIVE. When the prefix IM is placed before that word, creating the word IMPASSIVE, that word has the same meaning. Other pairs are RAVEL-UNRAVEL, FLAMMABLE-INFLAMMABLE, and VALUABLE-INVALUABLE.

61.   I know that you probably were trying to figure out the sides and the relationship of all the lengths AC, AB, BD, and CE. But what you probably didn’t think of is that the
area
of triangle ABC is represented as CE x AB/2
but also
as BD x AC/2. So (1) CE x AB = BD x AC. Now if AC is greater than AB (given), in order for (1) to be true, CE must be greater than BD!

62.   24

(3 x 4 x 2)

63.   (c) 4,100

1,000 + 40 + 1,000 + 30 + 1,000 + 20 + 1,000 + 10 = 4,100.

64.   (d) p

Look for a relationship between the letters. Between a and b there are no letters. Between b and d there is one letter (c), Between d and g there are two letters (e, f). Between g and k there are three letters (h, i, j). To continue the pattern, skip four letters (l, m, n, o). The next letter in the sequence is p.

65.   666

The integers between 0 and 1000 that are exactly divisible by 3 are 3, 6, 9, 12, 15, 18… You can see that there are 999/3 = 333 integers between 0 and 1000 that are exactly divisible by 3. The integers between 0 and 1000 are 1, 2, 3… 999. This is a total of 999 - 1 + 1 = 999 integers. Thus 999 - 333 = 666.

66.   100

Don’t be careless. Watch what you are dividing. You’re not dividing by 2, you are dividing by 1/2. So you have to know your basic skills. Diving by 1/2 is like multiplying by two. So the answer is (40 x 2) + 20 = 80 + 20 = 100.

67.   (c) trout : fish

You may have thought the answer was (a), but a TURTLE is a
creature,
which is a type of REPTILE, as trout is a
creature,
which is a type of fish.

68.   1.
please

2.
ground

3.
around

4.
knight

5.
fright

6.
danger

Here are some more:

7.
trivet

8.
strove

9.
shovel

10.
slight

11.
mother

12.
craven

69.   c, e, a, d, b

70.   (c) U

In set I, all three symbols are represented by straight lines. In set II, the two symbols are represented by straight and curved lines.

71.   (b) 2

One of them is not 2, it is 1. But the other is 2.

72.   The triangle shown has a base of 6 and sides 2 and 4. Since 2 + 4 = 6, the triangle has collapsed into a straight line. On this line, the line segment labeled
x
must be 1.

73.   28

Lowest average score = [21 x 80 + (60 - 21) x 0]/60 = 28

74.   640

(9 x 6 x 3)
x
= 6 x 12 x 4 x 12 x 2.5 x 12;
x
= 640

75.   7/16 is greater.

Multiply 16 x 3 and 7 x 7 in the fractions. 48 < 49 so 3/7 < 7/16.

76.   You can simplify the problem by multiplying the numerator and the denominator by the same number. This process will not change the value of the original fraction. So, multiply both numerator and denominator by 4 and you get 4,444 divided by 100, which is 4,444 percent.

77.   Roots are a powerful tool in figuring out the meaning of words. The root MAN means “hand.” The root MIT means “to send.” So MANUMIT means to send by hand or set free.

78.   (a) n

There are actually two sequences here: a (b) c (d) e (f) g (h) i…and z (y) (x) w (v) (u) t (s) (r) q (p) (o) n…

79.   (e) 7

If people are denoted by a, b, c, you have committees a, b, c, ab, ac, bc, and abc.

80.   (a) 11/20

81.   21

Represent
b
=
a
+ 2,
c
=
a
+ 4, so
a
+
b
+
c
= 3
a
+ 6 = 57.

If 3
a
= 51,
a
= 17, so
c
=
a
+ 4 = 21.

82.   400

Let
n
be the number of original shelves. Then 80
n
= 50(
n
+ 3). 30
n
= 150;
n
= 5. 80 x 5 = 400.

83.   An hourglass

84.   No water—it would be all strained out.

85.   35 x 65 is greater. Divide both products by 65 x 34. You then only have to compare 35/34 with 66/65. Since 35/34 = 1 1/34 and 66/65 = 1 1/65, the first product in the question is greater.