A. The quantity on the left is greater
B. The quantity on the right is greater
C. Both are equal
D. The relationship cannot be determined without further information
SOLVE
1. The average of four numbers is 36
à The sum of the same four numbers 140
2. n is an integer >0
à (1/n + n) 2
3.
à The diagonal of a rectangle Half the perimeter of the same rectangle
4. x + y = 5 & y - x = 3
à x y
5.
à The distance between the points with rectangular coordinates (0,5) and (0,10)
The distance between the points with rectangular coordinates (1,8) and (-3,5)
6.
à + 7 √(36 + 49)
7. A fair coin is tossed three times
à The chances of getting 3 heads The chances of getting no heads
8.
à The percentage of the multiples of 2 that are also multiples of 5
The percentage of the multiples of 5 that are also multiples of 2
9.
à The area of a right angled triangle with sides 6,8 and 10
Twice the area of a right angled triangle with sides 3,4 and 5
10.
JL = KM
à JK LM
SOLUTION
1. A 2. D 3. B 4. B 5. C
6. B 7. C 8. B 9. A 10. C
SOLVE
1. The greatest prime factor of 36 The greatest prime factor of 48
2. AB is a diagonal of the circle. All triangles above the diagonal in the diagram are equal in area.
All triangles below the diagonal are equal in area.
Total area of the triangles above AB. Total area of the triangles below AB.
3. The beach resort is 2 kilometers from the city and the sports complex is 10 kilometers from the city.
The city, resort and sports complex all lie at sea level.
The distance from the beach resort to the sports complex. 7 kilometers
4.
Discount in dollars on $60 at the rate of 4 percent
Discount in dollars on $40 at the rate of 6 percent
5. Twice an odd integer greater than 6 Three times an odd integer greater than 2
6. The rate of a certain chemical reaction doubles for every 10 degree rise in temperature.
Twice the rate at 10° Half the rate at 30°
7. y/x q/p
8. Fred is now 10 years older than George was 5 years ago
Fred's age 5 years ago George's age now
9. x4 / 4 / (x / 4)410. The sum of the even numbers from 2 to 100 inclusive 52 x 50
SOLUTION
1. C 2. B 3. A 4. C 5. D
6. C 7. A 8. C 9. D 10. B
SOLVE
1. 28 116
2. n is an even integer
The remainder when n is divided by 3 The remainder when n is divided by 53. The number of students in class A is 10 less than twice the number of students in class B.
There are x students in class B.
à The number of students in class A 2x - 10
4. x² - 12x + 35 = 0
X 12
5. The list price of a television set is t dollars
The price of the TV in a sale offering a 15 percent discount 0.85t dollars
6. 7/8 > x > 5/6
X 6/7
7. AB is parallel to ED; BCE and ACD are line segments
length of BC Length of CA
8. 10mm = 1 cm
The area of a square with sides of 1cm 10 times the area of a square with sides of 1mm
9. A is a point on the circle and BC is a chord but not a diameter of the circle
X 90
10. x is positive
x19 / x20SOLUTION
1. A 2. D 3. C 4. B 5. C
6. D 7. D 8. A 9. D 10. D
SOLVE
1. Ravi has more than twice the number of marbles that Sita and Tim have together.
The number of marbles that Ravi has
Three times the number that Sita and Tim have together.
2. x y
3. In a class of 32 students 75 per cent are girls. 50 per cent of the students study French.
The number of girls who study French 7
4. Pedro travels by bus to school at an average speed of 40 kilometers per hour.
He is driven home by the same route in a friend's car at an average speed of 50 kilometers per hour.
Average speed for both legs of the journey 45
5. Lines l, m and n are parallel. Angle ABC = 90
x + y 90
6. Area of a rectangle of perimeter 10 Area of a triangle with base 6 and height 3
7. Two dice have sides numbered 1 to 6.
When these two dice are rolled the score is the sum of the numbers on the upper faces.
The probability of a score of 3 The probability of a score of 2
8.
The distance between the tips of the hour and minute hands of a clock at nine o'clock
The distance between the tips of the hour and minute hands of the same clock at nine thirty.
9. Point P has the coordinates (3,7) and point Q has the coordinates (-7,3) on the same rectangular coordinate plane.
Distance from the origin (0,0) to point P Distance from the origin to point Q
10. (x - 4)(x + 3) = 0
x - 3 0
SOLUTION
1. D 2. A 3. A 4. B 5. C
6. B 7. A 8. B 9. C 10. D
SOLVE
1. Let a¤b be defined as a² - b + a
2¤3 3
2. The profit from a business is to be divied in the ratio 4 to 5 between X and Y respectively.
The money X receives when the profit is $153 $70
3. The sum of all the positive integer divisors of 15 8
4. The lengths of two sides of a triangle are 4 and 6
The length of the third side 10
5. A 10-foot plank of wood is cut to give three equal lengths with a shorter length left over.
The length of one of the equal pieces 3 feet
6. 28 percent of the students in Class A study German, 14 percent in Class B study German
The percentage of Class A and B combined that study German 20 percent
7. O is the centre of the circle, and angle POQ is a right angle
MN/PQ 2/1
8. xy ≠ 0
x²y² ( - xy)²
9. Figure not to scale. Angles QPS and QRS are right angles. QR = 3 , RS = 4, and PS = 2
Side PQ 5
10. ♣x = x² - 1
(♣3)(♣4) ♣11
SOLUTION
1. C 2. B 3. A 4. B 5. D
6. D 7. B 8. C 9. B 10. C
SOLVE
1. 9 less than 4x = 39
x 10
2. k² = 4; km = 6
k m
3. 3 x 10³ + 2 x 10² + 10 321 x 10
4. A rectangle has area 30
Perimeter of this rectangle 25
5. Farm X is 8 miles due west of farm Y, and farm Z is 7 miles due north of farm Y
Distance between X and Z 10 miles
6. This question and the next refer to the following definition
For all non-negative numbers
x ¤ = x + 1
(9 ÷ 3)¤ 9¤ ÷ 3¤
7. Refer to the data from the previous question
p and q are non-negative integers
(p + q)¤ p + q¤
8. Figure not to scale. The figure is composed of squares.
The larger squares are each of area 49. The area of each small square is 4
x 3
9. n > 0
n50 n550
10. a is an external angle; b is an internal angle
The sum of the exterior angles of the figure The sum of the interior angles of the figure
SOLUTION
1. A 2. D 3. C 4. D 5. A
6. A 7. C 8. C 9. D 10. B
SOLVE
1. -1 (-1) -1 +(-1)
2. 75,410 rounded to the nearest hundred 75,410 rounded to the nearest thousand
3. ABCD is a rectangle
The length of the curved path from A to C 5
4. Twice the volume of a cube of side 1 Volume of a cube of side 2
5. x, y and z are consecutive integers and xyz = 0
z 0
6.
The time it would take to drive 80 miles at an average speed of 60 miles per hour
The time it would take to drive 60 miles at an average speed of 45 mile an hour
7. 1/3 4/5 6/7 2/9 3/11
The smallest fraction shown The product of the greatest fraction shown and 2/3
8. 45 per cent of n = 60
90 per cent of n 120
9.
The number of integers between 50 and 100 which are multiples of 3
The number of integers between 10 and 81 which are multiples of 4
10. Note figure not to scale
Twice area of triangle ABC Area of triangle DBC
SOLUTION
1. A 2. A 3. A 4. B 5. D
6. C 7. B 8. C 9. B 10. D
SOLVE
1. x is 3 less than y
x + 5 y + 2
2. p + q = 3, and p-q = 6
q 0
3. A circle and a line lie in the same plane.
The greatet possible number of points that are on both the circle and the line. 2
4. Three boxes contain 20, 25 and 27 sweets respectively.
The least no of sweets that need to be transferred so that there is an equal no in each box.
5
5. The sum of all the integers from -10 to 12 inclusive. 23
6. There are 28 students in a class all born in 1990
The probability that all their birthdays are in February
The probability that all their birthdays fall on a Friday
7. C is the midpoint of segment AE and AB < DE
BC CD
8. This question and the next refer to the following:
The graph shows the sales figures for a certain company in five consecutive years.
Percentage increase in sales from 1989 to 1991
Percentage fall in sales from 1991 to 1993
9. Refer to the previous question
The mean (average) of the 5 annual sales figures
The median of the 5 annual sales figures
10. n is a positive integer; p = 8 x 9 x 11 x n
The remainder when p is divided by 6 The remainder when p is divided by 33
SOLUTION
1. C 2. B 3. C 4. B 5. C
6. B 7. A 8. A 9. B 10. C
SOLVE
1. ab = 0
a 0
2. -1 < x < 0
x³ x5
3. The average of four numbers is 30. The average of three of these numbers is 20.
The value of the fourth number 60
4. AC > CB > AB
b a
5. The line containing point A is rotated 90 degrees anticlockwise about the origin, O.
The y coordinate of point A before rotation. The y coordinate of point A after rotation.
6. Points x and y lie on line l
The number of points on line l that are twice as far from x as from y 2
7. r is the radius of circle C. s is the circumference of circle C.
6r s
8. Total savings on 40 gallons of fuel bought at $1.152 per gallon instead of $1.245 $3.70
9. The cost of hiring props for the school play was to be shared by 8 students. 4 more students decide to share the cost. The new cost per person is $2 less.
Total cost of hiring props $50
10. A bag contains only red, white and blue balls. One third of the balls are red, one fifth of the balls are white. One ball is to be selected at random.
Probability of drawing a white ball Probability of drawing a blue ball
SOLUTION
1. D 2. B 3. C 4. A 5. C
6. C 7. B 8. A 9. B 10. B
SOLVE
1. In triangle ABC, Angle ABC =59, angle ACB = 61
The length of side AB The length of side BC
2. Each of six sectors of a circle is assigned a number such that the numbers in any two adjacent sectors add up to 15
x 8
3. 5 less than 4x = 27
x 9
4. Rob has more money than Paul. Paul has more money than Vinny and Sam has more money than Toni. Toni has less money than Rob but more money than Paul.
Total amount that Vinny and Sam have together
Total amount that Rob and Toni have together
5. The area of one face of a rectangular block is 16 and the area of an adjacent face is 20.
Volume of the block 100
6. The average (arithmetic mean) of four numbers is 20. The sum of three numbers is 60
The fourth number 20
7. The x coordinate of point P The y coordinate of point P
8. 4 < x < 8 , and 3 < y < 7
x - y 5
9. The sum of all integers from -6 to 30 inclusive The sum of all integers from 7 to 30 inclusive
10. Note: figure not to scale. Lines l and m are parallel
AB / AD DC / CB
SOLUTION
1. A 2. C 3. B 4. D 5. D
6. C 7. B 8. B 9. C 10.D