SAT Challenge #1
How much greater than r-2 is r + 5?
(a)
2
(b)
3
(c)
5
(d) 6
(e) 7
SAT Challenge #2
If 3/7 of n is 42, what is 5/7 of n?
(a)
70
(b)
45
(c)
30
(d) 18
(e) 10
SAT Challenge #3
If m is the greatest prime factor of 38 and n is the greatest prime factor of 100, what is the value
of m + n ?
(a)
7
(b)
12
(c)
24
(d)
29
(e)
44
SAT Challenge #4
The eggs in a certain basket are either white or brown. If the ratio
of the number of white eggs to the number of brown eggs is 2/3,
each of the following could be the number of eggs in the basket EXCEPT:
(a)
10
(b)
12
(c)
15
(d)
30
(e) 60
SAT Challenge #5
There is the same number of boys and girls on a school bus when it departs from school. At the first stop, 4 boys get off the bus and nobody gets on. After
the first stop, there are twice as many girls as boys on the bus. How many girls
are on the bus?
(a)
4
(b)
6
(c)
8
(d)
12
(e)
16
SAT Challenge #6
<see example in class>
In the figure above, three lines segments meet at a point to form three angles.
What is the value of x?
(a) 20
(b) 36
(c) 40
(d) 45
(e) 60
SAT Challenge #7
<see example
in class>
In the figure above, a small square is inside a larger square. What is
the area, in terms of x, of the shaded region?
SAT Challenge #8
If rstv = 1 and stuv = 0, which of the following must be true?
(a)
r < 1
(b)
s < 1
(c)
t > ½
(d)
u = 0
(e)
v = 0
SAT Challenge #9
If a + 2b is equal to 100% of 4b, what is the value of a
?
b
SAT Challenge #10
A measuring cup contains 1/5 of a cup of orange juice.
It is then filled to the 1-cup mark with a mixture that contains equal amounts of orange, grapefruit, and pineapple
juices. What fraction of the final mixture is orange juice?
SAT Challenge #11
The numerator of a
certain fraction is 5 less than the denominator. If the fraction is equal to
¾, what is the denominator of this fraction?
(a)
8
(b)
12
(c)
16
(d)
20
(e)
24
SAT Challenge #12
If x and y are integers and xy
is an even integer, which of the following must be an odd integer?
(a) xy + 5
(b) x + y
(c) x/y
(d) 4x
(e) 7xy
SAT Challenge #13
If E is the set of even integers, P is the set of positive integers, and
F is the set of integers less than 5, which of the following integers will be in
all three sets?
(a)
6
(b)
4
(c)
1
(d)
0
(e)
-2
SAT Challenge #14
There are 8 sections
of seats in an auditorium. Each section contains at least 150 seats but not more
than 200 seats. Which of the following could be the number of seats in this auditorium?
(a)
800
(b)
1,000
(c)
1,100
(d)
1,300
(e)
1,700
SAT Challenge #15
If x + 1 is an even integer, which of the following must be an odd integers?
(a)
x - 1
(b)
x2 + 1
(c)
x + 1
2
(d)
x + 3
(e)
x + 4
SAT Challenge #16
Set X contains all even integers between -5 and 20, including -5 and 20. If
S and T are distinct members of Set
X, which of the following is the largest possible value of T - S?
a)
13
b)
15
c)
20
d)
24
e)
25
SAT Challenge #17
If 4 less than 3 times
a certain number is 2 more than the number, what is the number?
(a)
–1
(b)
-3
(c)
1
(d)
2
(e)
3
SAT Challenge #18
A family of 5 is planning
a 4-day camping trip. Each person will need to bring 1 bottle of water for each
day of the trip. If water is sold in only 3-bottle packages, how many packages
must the family buy for the trip?
SAT Challenge #19
7, 15, 31, 63,…
The first term in the
sequence above is 7, and each term after the first is determined by multiplying the preceding term by m and then adding p. What
is the value of m?
a)
1
b) 2
c)
3
d)
4
e)
9
SAT Challenge #20
In a neighborhood with
60 households, 32 households have VCRs and 18 have cable. If 12 have both a VCR
and cable, how many of the households have neither?
a) 20
b) 22
c)
30
d)
44
e)
50
HARD
CORE BRAINTEASER #1
Miranda is now
half as old as her brother Prospero. In two years, she will be as old as he is
now. In 10 years, she will be three times as old as he is now. How old are they both now?
(Hint: Neither one is a teenager yet.)
HARD CORE BRAINTEASER #2
In a footrace,
Ben was neither first nor last. Ken beat Adam, Charlie beat Ben, Ben beat Ed
but was beaten by Ken, and Adam beat Charlie.
Who was last?!
HARD
CORE BRAINTEASER #3
Four explorers lost deep in the
Amazon jungle have to cross a rope bridge in the middle of a moonless night. Unfortunately,
the bridge is only strong enough to support two people at a time. Also, it is
so dark that the explorers must have a torch to guide them across the bridge ( otherwise they would surely loose their footing
and plunge to their death below). The problem is that there is only one torch
between them.
The first explorer, John, can cross
the ravine in 4 minutes. His sister, Maria, can cross in 6 minutes. Their cousin, Albert, can cross in 12 minutes. Finally, there
is old man Witherspoon, who takes a whopping 25 minutes to cross the bridge.
How quickly can all four explorers safely reach the other side of the bridge?
Keep in mind that an explorer
from the safe side must return with the torch so that the remaining stranded explorers can use the torch to
cross. Also, the two explorers crossing the bridge must remain together because
there is only one torch between them (meaning that the two explorers cross only as fast as the slowest person).
HARD
CORE BRAINTEASER #4
A car full of teenagers drove
past a display of totem poles. Joseph thought that there were 20, Jane thought
that there were 25, Tamika thought that there were 22, and Summer thought that there were 24.
One count was off by 4, one by 1 and one by 2. One was correct.
How many totem poles were there?
HARD
CORE BRAINTEASER #5
The entire population of a small
village turns out for a concert one summer evening. There are 120 people attending
and they pay a total of $120 altogether.
Tickets are priced: $5 adults
$2 over-65 years old
10 cents children
How many adults, over 65s and children are there?
HARD
CORE BRAINTEASER #6
Insert the missing numbers so
that the calculations are correct, both across and down.
-
All numbers to be inserted are less than 10.
-
Zero is not used
|
1.
5 |
+ |
2. |
- |
3.
3 |
= |
4.
8
|
|
+ |
|
x |
|
x |
|
- |
|
5. |
- |
|
+ |
2 |
= |
|
|
÷ |
|
- |
|
- |
|
+ |
|
6.
3 |
+ |
9 |
÷ |
|
= |
|
|
= |
|
= |
|
= |
|
= |
|
7.
|
x |
9 |
÷ |
3 |
= |
9 |
HARD
CORE BRAINTEASER #7
In eight years,
Janice will be twice as old as she was four years ago. How old is she now?
(Hint: She is not yet 20)
HARD
CORE BRAINTEASER #8
Supply the missing
number.
|
X |
X |
Y |
Y |
|
Z |
X |
Y |
Y |
|
W |
X |
Y |
Z |
|
X |
Y |
Z |
Z |
HARD
CORE BRAINTEASER #9
Columbia High School’s
football team was planning to march in the annual 4th of July parade. With
3 across, 1 was left over. With 4 across, 1 was left over; the same for 5 and
6 across. With 7 across, 2 were left over; with 8 across, 1 was left over; with
9 across, 4 were left over; with 10, 1 was left over. With 11, it worked out
evenly. What is the smallest number to meet these conditions?
Be sure to show
all of your work.
HARD
CORE BRAINTEASER #10
<see example in class>
HARD
CORE BRAINTEASER #11
Five people want
to share a square pizza. The first person (who is really hungry) removes one
quarter of the pie. When the others find out, they are annoyed and try to divide
the remaining three-fourths into four equal and identically shaped slices. The
cuts must be straight. How must they cut the remaining pizza in order to produce
four identical slices?
The picture below
is of the remaining pizza.
<see example in class>
HARD
CORE BRAINTEASER #12
In a spelling bee,
Carol was neither first nor last. Alice beat Dennis but was beaten by Elise,
who was beaten by Carol. Betty beat Carol.
Who won?
HARD
CORE BRAINTEASER #13
There once was
a contest to guess the number of pumpkins in a Halloween display. Alice guessed
34, Bob guessed 33, Charlie guessed 35, Dan guessed 27, and Edith guessed 36. One
person was off by 1, one by 4, one by 3, one by 2, and one by 5. No one was right.
How many pumpkins were there?
HARD
CORE BRAINTEASER #14
Jane has two more
brothers than she has sisters. Her brother Charles has the same number of sisters
as he has brothers. How many girls and boys are there? (Hint: There are fewer than 10.)
HARD
CORE BRAINTEASER #15
Charlie was buying
things for his Fourth of July party. He spent one-third of what he had plus $3
on patriotic plates and tablecloths, then one-third of what was left plus $2 on food, then half of what was left plus $10
on soda. He then had $10 left for potato chips and other snacks.
How much did he start with?
HARD
CORE BRAINTEASER #16
What is the smallest
number that is divided by 3, 4, and 5 with a remainder of 1, 2, and 3, respectively?
HARD
CORE BRAINTEASER #17
If five hungry
pizza eaters can eat two and a half pizzas in half an hour, how many pizzas will 12 hungry pizza eaters eat in one hour?
HARD
CORE BRAINTEASER #18
Supply the missing
number.
|
A |
A |
A |
D |
17 |
|
C |
B |
B |
A |
16 |
|
B |
B |
B |
C |
15 |
|
D |
B |
D |
C |
11 |
|
14 |
17 |
? |
13 |
|
HARD
CORE BRAINTEASER #19
The figure below
is made using 12 line segments. Remove three line segments from the figure to
form three equilateral triangles. You
may not move or rearrange any of the remaining line segments.
<see example in class>
HARD
CORE BRAINTEASER #20
Imagine that you
have 2 hourglasses. One hour glass will measure 5 minutes and the other hourglass
will measure 3 minutes. Can you use these two measuring devices to time an egg
that must be boiled for exactly 2 minutes? If so, how…
(You can not estimate and your timing must be precise!!!)
