sat 6 full tests phần 8 doc

Solve the equation: 0.66X = 4 – 0.34X  X = 4.
X3 = 3 x 2 = 6.

8. If X + 2Y = 24 and Y – 3X = 10, what is the value of X?

From the second equation, Y = 3X + 10, replace this with Y in the first
equation: X + 2(3X + 10) = 24  X + 6X + 20 = 24  7X = 4 
X=4/7.

9. If X + Y = 15 and X – Y = -5, what is the value of X/Y?

Add the equations to get: 2X = 10  X = 5.
Y = 15 – X = 10.
X/Y = 5/10 = ½.

10.






The triangle in the figure above is not drawn to scale.
If the measurement of angle 4 is 115.5
o
, what is the measurement of
angles 1 and 2 (in degrees) ?

Notice that angles 3 and 4 are vertical angles and thus equal.
The sum of the angles in the triangle is 180
o

and therefore we can write
the following connection: angle 1 + angle 2 + 115.5
o
= 180
o
 the sum
of angle 1 and 2 is equal to (180 – 115.5 = 64.5
o
).

11. ABC is an isosceles triangle, AB = BC. If the measurement of angle
ABC is between 102 and 105, what is the value of the measurement of
angle BCA minus CAB?

Draw a sketch of the triangle.
Since the triangle is an isosceles, angles BCA = CAB and therefore the
answer to the question is always zero no matter what the third angle is.

12. If the sum of two numbers is 6 and their difference is 2, what is the
square of their product?
Let X and Y be the two numbers.
X + Y = 6 and Y – X = 2 are the two equations.
 Y = 4 and X = 2.
Their product is 8 and the square of their product is 8
2
= 64.

Chapter 2:

1. If the product of two numbers is 9 and their difference is 0, what is
their sum?

Let X and Y be the numbers.
We can write the following equations: XY = 9 and Y – X = 0.
Y = X  X
2
= 9  X = Y = 3.
The sum of the numbers is 3 + 3 = 6.

2. If 64
5
= 2
2X
, what is the value of X?

Rewrite the expression: 64
5
= 2
2X
 (2
6
)
5
= 2
2X

 2
30
= 2
2X

Compare the powers: 2X = 30  X = 15.

3. If 125
3
= 5
Y
, what is the value of
2
3Y
?

Rewrite the expression: 125
3
= 5
Y
 (5
3
)
3
= 5
Y
 5
9
= 5
Y

Compare the powers: Y = 9.
The value of 3Y/2 = 27/2 = 13.5.

4. If the perimeter of a rectangle is four times the length of the rectangle,
then the width of the rectangle is what percent of the length?

Let W be the width and L the length of the rectangle.
The perimeter of the rectangle is 2W + 2L.
We can write the following connection: 2W + 2L = 4L  W = L
(square).
Therefore the width is 100% of the length and so the answer is 100.

5. In a certain rectangle, the length is three times the width and the
perimeter is equal to 64. What is the value of the length of the rectangle?

We can write the following connections: L = 3W and 2L + 2W = 64.
Replace L with 3W and write: 2(3W) + 2W = 64  8W = 64  W=8.
L = 3 x 8 = 24.

6. There are 50 blue balls and 120 red balls in a jar containing 170 balls
only. If only blue balls are to be added to the jar so that the probability of
randomly picking a blue ball from the jar becomes 1/2, how many blue
balls must be added to the jar?

Let X be the number of blue balls that must be added.
We want the portion of the blue balls to be half of the entire amount of
balls in the jar and therefore 50 + X (the new number of blue balls)
divided be 170 + X (the entire number of balls) should be ½.
701702100

2
1
170
50



XXX
X
X
. And so if 70 balls are added
there’ll be 120 blue balls and 240 balls in general.

7. A bag contains 15 red marbles, 12 red marbles and 18 blue ones.
What is the probability of drawing two red balls one after the other?

The probability of drawing a red marble is the number of red marbles
divided by the entire number of marbles in the bag.
The probability of drawing the first red marble is (15)/(45) = 1/3.
The probability of drawing the second red marble is (14)/(44) = 7/22.
The joint probability is the multiplication of the probabilities, and
therefore the answer is
66
7
22
7
3
1

.

8. What is the probability of getting a number larger than 3 tossing a fair
dice?

While throwing a dice there are 6 results: 1, 2, 3, 4, 5 and 6.
Only three results are over 3: 4, 5 and 6 and therefore the probability is 3
out of 6 or ½.

9. The average (arithmetic mean) of 6 positive integers is 110. The value
of two of the integers is 24 and 28 and the other integers are greater than
30.
If all the numbers are different from one another, what is the greatest
possible value for any of the 6 integers?

We know the value of 2 integers. If we want one of the integers to be as
large as possible, take all the others as small as possible. In other words,
take the two integers that are given (24 and 28), take three more integers
greater than 30: 31, 32 and 33 and the fourth one would be the greatest.
Write the average formula:
110
6
3332312824






X


24+28+31+32+33+X = 660  X = 512, which is the largest possible
value since we took the rest as small as possible.

10.
If the sum of 4 consecutive numbers is 220, what is the average
(arithmetic mean) of the first and the last among those numbers?

Let x, x+1, x+2 and x+3 be the four numbers.
We can write the equation: x + x + 1 + x + 2 + x + 3 = 220.
 4x + 6 = 220  x = 52.
The average arithmetic mean of the first and the last numbers is
(52 + 55)/2 = 53.5.

11. What is the time elapsed from 12:12 to 23:43, in minutes?

Start from 12:12, add 11 hours to reach 23:12.
Add 31 more minutes to reach 23:43.
Altogether, its 11 hours and 31 minutes.
In minutes its: 11 x 60 + 31 = 691 minutes.

12. What is the angle between the large and the small hand of the clock at
12:30, in degrees?

At 12:30, the angle is not 180
o
since the hour hand (the small hand)
rotated a bit clockwise. Every hour the small hand of the clock moves 30
o

and so in 30 minutes, it moved 15

o
.
The angle between the hands of the clock is (180 – 15 = 165) degrees.
It might go easier if you draw a sketch of a clock.


















Chapter 3:

1. If X > 6 and X
3
X
2.5
X
Y

= X
8
, what is the value of X?

These questions are only solved by comparing the powers of both sides,
in our case of X.
X
3
X
2.5
X
Y
= X
5.5 + Y
= X
8
 5.5 + Y = 8  Y = 2.5.

2. If 2
X+2
= 4
X-1
, what is the value of X?

These questions are only solved by comparing the powers of both sides.
2
X+2
= 4
X-1
 2

X+2
= 2
2(X-1)
 X+2=2(X-1)  X+2=2X – 2  X = 4.

3. If X = (0.5)
2
and Y = X
2
, what is the value of (X + 4Y)?

X = (0.5)
2
= 0.25.
Y = X
2
= (0.25)
2
= 0.0625.
X + 4Y = 0.25 + 4(0.0625) = 0.25 + 0.25 = 0.5.

4. If A=1/X and B=X/Y and if X=1/4 and Y=1/5, what is the value of
(A+B)?

A = 1/X = 1/(1/4) = 4.
B = X/Y = (1/4) / (1/5) = 5/4.
A + B = 4 + 5/4 = 21/4.

5. Nikki and Mike bought a new house for $120,000.
Their families paid 42% of the price and the rest was divided equally and

annually across six years. How many thousand of dollars did Nikki and
Mike pay each year?

Their families paid 42% of $120,000 and so all they had to pay
themselves is
(100% - 42% = 58%) of $120,000.
0.58 x 120,000 = $69,600.
Each year they would pay a sixth of that amount, thus (69,600/6 =
11,600) and so the answer is 11.6 thousands of dollars.

6. A new computer costs a thousand dollars including tax. If Travis paid
for three quarters of his new computer every month for a year, how much
did he spent each month assuming that the payments were equal?

Travis paid for only 75% of his computer, thus $750.
He paid that price in 12 equal payments, each ($750 / 12 = $62.5) and so
the final answer is 62.5.

7.



The following figure is of a parallelogram.
What is the value of X + Y + Z ?

Look at the upper left triangle, the sum of the angles there should equal
180
o
and so X + Y + 115 = 180  X + Y = 65
o

.
Since the shape is a parallelogram, Z = 115
o
and so X + Y + Z = 180.

8.






An isosceles triangle was attached to a rectangle.
If X = 3.5 and Y = 1.5, what is the perimeter of the figure above?

The perimeter of the figure above is made from two sides of the triangle
and three more sides of the rectangle, thus X + X + X + Y + Y = 3X +
2Y, which is also equal to 3(3.5) + 2(1.5) = 13.5.

9. If
100


YX
and
752442
Y
X
Z
Y

X
Z





, what is one possible value
for Y
2
?

Simplify the expression:
752442
Y
X
Z
Y
X
Z






31
1
Y
X




1 = (XY)Y
2
 Y
2
= 1/(XY) = 1/100  Y
2
= 0.01.

10. If
AA 

2
55125 , what is one possible value for A?

Compare the powers of 5 in each side.
AA 

4
55125  5
3
5
A
< 5
4-A
 5
3+A
< 5

4-A
 3+A < 4-A  2A < 1 
A < 0.5 and so one possible value would be anything smaller than 0.5, for
example 0.25 or 1/6.
11. The volume of a cylinder is 3 cubic feet.
The radius was increased by three times and the height was increased by
2 times, what is the new volume of the cylinder in cubic feet?
o
115
o
X
o
Y
o
Z
X
Y

When the radius is increased by 3, the area of the base of the cylinder
increases by 9 times. The new volume of the cylinder is 9 x 2 = 18 times
greater than before and so the new volume is 3 x 18 = 54 cubic feet.

12.



What is the volume of water needed in order to fill a third of the box in
the figure above?

Calculate the volume of the box: V = 12 x 4 x 7 = 336.

A third of that volume is equal to 336/2 = 112.

























12
4
7
Chapter 4:

1. A, B and C are digits between 0 to 9.

CA and AB are double digit numbers and ABA is a three digit
number.
What is the value of ABA?

In the tens digit, we can see that A + B = A and thus B=0.
The sum of two double digit numbers is a three digit number and so its
hundreds digit must be one, thus A=1.
The number is therefore 101.

2. A and B are digits between 0 to 9.
A
2
= 4B (4B is a double digit number)
?


BA


The only number squared with a tens digit of 4 is 7 (7
2
= 49).
And so A=7 and B=9.
A x B = 7 x 9 = 63.

3. X and Y are two digits between 0 and 9. When 36 is multiplied by
another double digit number, the result is 3XY.

What is one possible value for Y?

Start with an easy number, 36 times 10 = 360 add 36 to get 396.
And therefore one answer is 0 and the other can be 6.

4. If A and B are positive integers, A < 34 – B and A > 17, what is the
greatest possible value of (2A – B)?

Since A + B < 34, take A as 32 and B as 1 and this way A will be the
largest and B the smallest. (2A + B) would be equal to (2 x 32 - 1) = 63.

5. If
Y
3065 
, what is the value of Y?

Compare the powers from both sides of the equation.
Y
3065 

Y
3030  
Y
3030
5.0
  Y = 0.5.



6.

CA
AB
ABA


A
B



In the figure above, B is the center of the circle and A is the center of the
square. If the radius of the circle is
2
, what is the area of the square?

The radius of the circle is actually half the diagonal of the square and so
the diagonal is equal to
22
.
The ratio between the sides of a square to its diagonal is 1: 2 and so
each of the sides of the square are equal to 2.
The area of the square is simply 2 x 2 = 4.

7. A chocolate box contains only white, sweet and bitter chocolate in the
following ratio: 2:3:4 respectively. The sweet chocolate is either with or
with out walnuts, and 4 times as many sweet chocolate are with walnuts
than with out. If a chocolate is chosen at random, what is the probability
that it would be a sweet chocolate with walnuts?

In this question it is smart to plug in numbers.

Say that there are 90 chocolates in the box.
According to the ratio, there are (3/9) x (90) = 30 sweet chocolates.
Since there are four times as many chocolates with walnuts as there are
with out there are (4/5 x 30 = 24) walnut chocolate and (1/4 x 30 = 6)
with out.
The probability of pulling a sweet chocolate with walnuts is 24/90 = 4/15
or 0.266 or 0.267.

8. The area of a certain rectangle (which is not a square) is 25 inches
squared, what is one possible length of its smaller side?

If the rectangle was a square each side would be 5 and so 5 x 5 = 25.
Since the rectangle is not a square, the larger side is bigger than 5 and the
smaller side is smaller than 5.
The acceptable answers are 4, 3, 2 and 1.







9. What is the area of a square if the sum of the diagonals is 24

We know (using the Pythagoras principle) that the ratio between the sides
of a square to its diagonal is 1:1: 2 and therefore in this specific square,
each side is (12/
2
) and the area is
72

2
144
2
12
2







.

10. The ratio of 8.25 to 66 is the same as the ratio of X to Y. What is the
value of (X/Y)
2
?

Since we want to know what is the value of X/Y replace X with 8.25 and
Y with 66  X/Y = 8.25/66 = 1/8.
(X/Y)
2
= 1/64 or 0.016.

11. If 2 < X < 7 and -2 < Y < 8, what is the greatest possible value of
(Y – X)?

We want the greatest possible value of (Y – X) and therefore we will take
the largest Y and the smallest of X  Y = 7 and X = 3.

The value would be (7 – 3) = 4.

12. If 6 < A < 20 and -12 < B < -5, what is the greatest possible value of
AB in absolute value?

Since B is negative and A is positive, AB will also be negative.
If we take the most negative B and the largest A, the result would be the
greatest in absolute value. And so A = 20 and B = -12  AB = -240 and
so the answer is 240.















Chapter 5:

1. If (X
4
+ 2X
2

+ X)(X
2
+ X) = aX
6
+bX
5
+cX
4
+dX
3
+eX
2
, what is the value
of
(c – a)?

Open the parenthesis to get: X
6
+X
5
+2X
4
+3X
3
+X
2
, and therefore
a=1 and c=2 and so (c – a) = 1.

2. If (X

2
+ X)(X
2
+ X) = aX
4
+2X
3
+cX
2
+dX, what is the value of
a + b + c + d ?

Open the parenthesis to get: X
4
+2X
3
+X
2
and so a=1, b=2, c=1 and d=0.
a + b + c + d = 1 + 2 + 1 = 4.

3.





In the figure above, (x,y) is the coordinate of a point found in the middle
of the side of the square. 2y-x =

Since the figure is of a square y=5.
The coordinate is of a point in the middle of the side and therefore x=2.5.
2y-x = 10 – 2.5 = 7.5.

4.






In the figure above, (x,y) is the intersection point of the two lines.
What is the value of y/x?

In order to find the intersection point compare the functions of the line:
3x + 4 = -x +8  4x = 4  x=1 and y = 7.
y/x = 7/1 = 7.


y
x
),(
y
x
)0,5(
43


xy
8




xy
y
x
5. A coin is marked with the number 8 on one side and the number 9 on
the other. What is the probability of receiving an odd number on the
second toss?

The probability every single toss is ½ for 8 and ½ for 9.
Therefore the probability of receiving an odd number on the second toss
is 0.5 or ½.

6. A jar contains 4 red balls, 3 green balls and 7 blue balls.
What is the probability of not drawing out a white ball?

Since all the balls are not white, there is not chance of pulling a white ball
and the probability is therefore 1.
This question checks if you know that 1 is the highest probability.

7.



If the area of the square is 30.25, what is the perimeter of the rectangle
ABCD?

The area of the square is its side squared and therefore the side of the
square is 5.525.30  . The diameter of the circle is equal to the side of the

circle since they are both blocked under the same rectangle.
One side of the rectangle is 5.5 and the larger side is 5.5 x 2 = 11.
The perimeter is 2(5.5 + 11) = 2 x 16.5 = 33.

8. There are 52 questions in a certain exam. If the ratio between the easy
questions to the hard questions is 6:7, how many hard questions are
there?

If the number of easy questions is 6Q and the number of hard questions is
7Q, we can write: 6Q + 7Q = 52  13Q=52  Q=4 and so 4 x 7 = 28 is
the number of hard questions in the exam.

9. Every month Paul works 60 hours for 30 pounds per hour. Due to
cutbacks his wage was decreased to 20 pounds per hour. How many
additional hours would Paul have to work in order to make the same
amount of money each month?

Every month Paul made 60 x 30 = 1,800 pounds.
If he still wants to make the same amount of money he should work
D
C
B
A
1,800 / 20 = 90 hours.
90 are 30 hours more than 60 and therefore the answer to the question is
30.

10. The denominator of a certain fraction is bigger by 5 then the
numerator.
If 3 is added to the numerator and to the denominator, the denominator

would be two times bigger than the numerator. What is the original
fraction?

Solve this one from the end.
Take a fraction where the numerator is half the denominator, for example
1/2. This fraction is not good; they both need to be over 4 and so this time
take 5/10. If you subtract 3 from the denominator and the numerator, the
fraction would be 2/7, which does fulfill the requirements.
Therefore the original fraction is 2/7.

11. Every hour Ana sneezes 5 sneezes more than Reese, and each one of
them sneezes an equal number of times every hour. If during a whole day
both girls sneezed 360 times, how many times did Reese sneeze each
hour?

Reese sneezed X times per hour and so Ana sneezed X+5 sneezes.
In one hour, they sneezed X + X + 5= 2X + 5.
In a whole day (24 hours), they sneezed 24(2X + 5) = 48X + 120.
48X + 120 = 360  48X = 240  X=5 and this is the answer.

12. When Tim was 8 he was two times older than Rick during that time.
If today Tim is 14 years of age, how old is Rick today?

During the time that Tim was 8, Rick was half his age, thus 4.
If today Tim is 14 years old (6 years later), Rick is also 6 years older, thus
10 and so the right answer is 10.

Chapter 6:

1. If the average of three different positive integers is 120, what is the
smallest possible value of the median among the three numbers?

All the numbers are integers greater than 0.
The smallest possible value of the numbers is 1 and the smallest possible
value of the median is therefore 2, and that is the answer.
The three numbers is 1, 2 and 357 the median is 2.

2 If X
2
= 2XY – Y
2
+ 14.5, what is the value of (X-Y)
2
?

The expression X
2
= 2XY – Y
2
+ 14.5 can be written as
X
2

– 2XY + Y
2
= 14.5  (X-Y)
2
= 14.5 and so the answer is simply 14.5.

3. If 17XY = 34X + 51X, what is the value of (3.5)Y?

Simplify the expression: 17XY = 34X + 51X  17XY = 85X 
Divide by 17X  Y = 5 and therefore 3.5Y = 3.5 x 5 = 17.5.

4.



Note: Figure not drawn to scale

In the figure above, what is the value of A in degrees?

A, 17
o
and 97
o
are all vertical angles to the inner angles of the triangle
and therefore equal. The sum of the angles in the triangle is 180
o
and so
we can write the following equation: 180 = 97 + 17 + A  A = 180 – 97
– 17 = 66 degrees.

5. The bank gave Elaine a loan with an interest of 8% on the original
amount per month. If Elaine loaned $1,525, how much interest will she
pay over a period of three months (in dollars)?

Every month, there is an 8% interest on 1,525, which is 0.08 x 1525 =
$122 per month. Elaine will pay 3 x 122 = $366 to the bank.


6. If in a certain jar there are X+1 black marbles and 2X+2 white marbles,
what is the probability of randomly pulling a white ball?
A
o
97
o
17

The total amount of balls in the jar is X + 1 + 2X + 2 = 3X + 3.
The probability of pulling a white ball is
3
2
)1(3
)1(2
33
22







X
X
X
X
or 0.667.
7. There are 30 students in a room. If 3 boys are taken out and now the
probability of randomly picking a boy is one third, what is the original
number of boys in the room?

After 3 boys are taken out, there’ll be 27 students in the room.
The probability of picking a boy now is 1/3 and so there are exactly 9
boys in the room. The original number of boys in the class is therefore
9+3 = 12.

8. If the sum of the first 4 out of 8 consecutive numbers is 40, what is the
sum of the rest?

Let the first 4 numbers be: X, X+1,X+2 and X+3.
Their sum is 40  4X + 6 = 40  4X = 34.
The rest of the numbers are X+4,X+5,X+6 and X+7.
The sum of those numbers is 4X + 4 + 5 + 6 + 7 = 4X + 22 = 56 and this
is the right answer.

9. If the points A(5, 5), B(11, 5), C(11, 12) and D(5, 12) are vertices of a
rectangle, what is the area of the rectangle?

Draw an axis system with the coordinates, as you can see a rectangle is
formed.
One side of the rectangle is (11 – 5 = 6) and the height is (12 – 5 = 7).
The area of the rectangle is 6 x 7 = 42.

10. 100 square feet of a basketball floor parquet costs 5 dollars and 25
cents. How much money will it cost to cover a court with the following
dimensions: 60 feet on 100 feet?

The area of 60 feet on 100 feet is 6,000 square feet.
If 100 square feet cost 5.25 dollars, 6,000 will cost
(6,000 / 100 = 60) x 5.25 = $315 and so the answer is 315.

11. The expression








4
13
4
112Q
is how much more than 3Q?

Simplify the expression by joining the two variables:
4
13112


Q

.

2
7
3
4
14
3
4
1412


QQ
Q
.
The expression is larger than 3Q by 7/2 or 3.5.

12. 62.5, 50, 40, …
In the sequence above, each term after the 1’st term is 20% less of the
term preceding it. What is the value of the 5’Th term of this sequence?

Each term in this sequence is 80% of the previous term.
40 is 80% of 50 and so the fourth term will be 0.8 x 40 = 32 and the fifth
term will therefore be 0.8 x 32 = 25.6 and this is the right answer.

SAT Quantitative test

6 chapters

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6 chapters of Mathematical Reasoning questions (25
questions each):

Every question answered and explained.

Chapter 1:


1. If 3X + 7 = 4, what is the value of (X – 2)
3
?
(A) -81
(B) -27
(C) 0
(D) 12
(E) 27

The best answer is B.
Solve: 3X + 7 = 4  3X = -3  X = -1.
(X – 2)
3
= (-3)
3
= -27 and so answer B is correct.


2. A, B, C and D are all different digits between 0 and 9.

If AB + DC = 7B (AB, DC and 7B are double digit numbers), what is the
value of C?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 5

The best answer is A.
Start adding from the right: B + C = B and so C = 0 since it can't be 10,
20 or anything more than 9.


3. If 3
7
= 9
2T
, what is the value of T?
(A) 0.5
(B) 1.5
(C) 1.75
(D) 2.25
(E) 2.5

The best answer is C.
3
7
= 9
2T
 3

7
= (3)
2 x

2T
 7 = 4T  T = 7/4 = 1.75.





4.




In the figure above, if the line segment AB is perpendicular to the x-axis
and has a length of 8, what is the value of s/r ?
(A) 0.25
(B) 0.5
(C) 0
(D) 1
(E) 2

The best answer is B.
If the line has a length of 8 and it’s parallel to the x-axis the coordinates
of point B will be (2, 1) and so S=1 and r=2.
The value of s/r = ½.

5. Everyday, Kevin divides $180 equally across different charity
organizations. On Sunday Kevin divided his money to 9 different
organizations, while on Monday, he divided his money to only 7.
How much more money (in dollars) did each organization receive on
Monday than on Sunday?
(A) 3.5
(B)
7
5
5

(C)
3
2
6

(D) 7.5
(E) 9

The best answer is B.
Calculate the amount that each organization received each day:
On Sunday: 180/9 = $20.
On Monday: 180/7 = $
7
5
25
, which is larger by
7
5
5

from Sunday and so B
is the right answer.




y
x
)9,2(A
),( srB
6. The income of a doctor is X times larger than that of a teacher. If we’ll
cut 20% of the doctor’s income and we’ll increase the teacher’s income
by 20% their income will be even. X =

(A) 1.5
(B) 2
(C) 3
(D) 2.5
(E) 3.5

The best answer is A.
Let the doctors income be D and the teachers income be T.
The doctors' income after a decrease is equal to the teachers' income after
an increase:
TD
TD
TD 5.1
10
12
10

8
100
120
100
80


And therefore X = 1.5.


7. Dorothy has 200 marbles. If 10% of the marbles are large and the rest
are small, how many small marbles should Dorothy remove so the portion
of the large marbles will be 20% of the total?
(A) 40
(B) 80
(C) 100
(D) 140
(E) 150

The best answer is C.
10% of the marbles are big, thus 20 marbles. The rest (200 – 20 = 180)
are small. We want 20 marbles to be 20% of the total and so the total
should be 100. In order for the total to be 100, 100 small marbles should
be removed and so the right answer is C.

8. A giant wheel with a radius of

130
, breaks loose from its axis and
starts rolling with out slipping on a flat surface. What is the distance that

the wheel will cross after three complete revolutions?
(A) 260
(B) 540
(C) 780
(D) 1040
(E) 2520

The best answer is C.
The circumference of the wheel is
260
130
22 


R
.
After three whole revolutions, the wheel will cross a distance of 260 x 3
= 780 and so C is the right answer.


9. For which of the following values of X will 5X + 8 be smaller than 14?
(A) 4
(B) 3
(C) 2
(D) 1.5
(E) 1

The best answer is E.
We want 5X + 8 < 14  5X < 6  X < 6/5 or X < 1.2
The only number that answers these criteria’s is answer E.

10. Which of the following numbers is smaller than 1/7 and larger than
1/8?
(A) 0.2
(B) 0.08
(C) 0.13
(D) 0.75
(E) 0.12

The best answer is C.
One number between 1/8 and 1/7 is 1/(7.5) =
15
2
2
15
1
5.7
1
 .
2/15 is like 20/150, which is approximately 0.133 and so C is the right
answer.


11. If
Y
Y
X



and both X and Y are integers, which of the following is
true?
(A) X = -Y
(B) X = -1
(C) X is positive
(D) X is negative
(E) X is a fraction


The best answer is D.
The first answer that pops into mind is that X is a fraction, but the
question says that X is an integer. The only way that X makes Y smaller
is if it is negative and so D is the right answer.


12. If
XX  532
, what is the value of X?

(A) 5
(B) 15
(C) 30
(D) 35
(E) 45

The best answer is C.
XX  532 can be written as: XX  532 . Divide both sides
by
X
to get: X30 and so X = 30.

13. If X is positive even number and Y is a positive odd number, which
of the following expressions is not even?

(A) (XY)
Y

(B) Y
2

(C) X
5

(D) Y
2
X
3

(E) 4Y

The best answer is B.
Pick up random numbers for X and Y: X=2 and Y=1.
The only odd answer is B, 1
2
= 1 and so this is the right answer.


14. A, B and C are integers. If the expression A + B + C is even and the
expression A – C is odd, which of the following can be said on B?

(A) odd
(B) even
(C) negative
(D) positive
(E) None of the above


The best answer is A.
Since A – C is odd, A + C is also odd (the sign doesn’t matter).
By adding B to A + C, the expression becomes even and therefore B must
be also odd and so A is the right answer.


15. How many square feet of marble are needed to cover a rectangular
floor that is 60 inches by 132 inches? (1 foot = 12 inches)
(A) 32
(B) 44
(C) 55
(D) 68
(E) 75

The best answer is C.
The area that is needed to be covered is 60 on 132 inches, in feet its
60/12 on 132/12, which is 5 feet on 11 feet and so the area is 55 and the
right answer is C.


16.

If M is the diameter of the circle and ACB is a right triangle at C, what is
the sum of X + Y + Z in degrees?
(A) 90
(B) 120
(C) 180
(D) 270
(E) 360

The best answer is C.
Since M is the diameter of the circle, Z as the inscribed angle, is 90
o
.
The sum of the angles in the ABC is 180
o
and so X + Y + 90 = 180 
X + Y = 90 and so X + Y + Z = 180
o
and so C is the answer.






M
C
B
A

X
Y
Z
17. On a blueprint, 3 cm represent 125 meters. If a road is 437.5 meters,
how many cm will represent it on the blueprint?
(A) 5
(B) 7.5
(C) 9
(D) 10.5
(E) 12

The best answer is D.
437.5 / 125 = 3.5. And therefore we should stick to the given proportion
and just multiply 3.5 by 3 cm to get 10.5 cm on the blueprint.


18. If 5
3X+2
= 125 and X
2Y – 1
= X
6
, what is the value of Y/X?
(A) 8
(B) 9.5
(C) 10
(D) 10.5
(E) 11

The best answer is D.

5
3X+2
= 125  5
3X+2
= 5
3
and so 3X + 2 = 3  X = 1/3.
X
2Y – 1
= X
6
 2Y – 1 = 6  Y = 7/2.
Y/X = (7/2)/(1/3) = 10.5.


19. In Pillsbury Island the weather during a 30 day month is distributed as
followed: 12 days of rain, 7 days of sunny weather and the rest of the
days have thunderstorms. When a randomly chosen tourist comes to the
island, what is the probability that there would be thunderstorms?
(A) 6/15
(B) ¼
(C) ¾
(D) 19/30
(E) 11/30
The best answer is E.
There are (30 – 12 – 7 = 11) days of thunderstorms in a month and so if a
day is chosen at random, there is a probability of 11/30 that there’ll be
thunderstorms.