SAT problem solving

SAT problem solving

SAT problem solving practice test 01

1 Of the following, which is greater than ½ ?

4 A cubical block of metal weighs 6 pounds How much will another cube of the same

metal weigh if its sides are twice as long?

5 In a class of 78 students 41 are taking French, 22 are taking German Of the students

taking French or German, 9 are taking both courses How many students are not enrolled

9 Amy has to visit towns B and C in any order The roads connecting these towns with

her home are shown on the diagram How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?

1 Which of the following could be a value of x, in the diagram above?

A 10

B 20

C 40

D 50

E any of the above

2 Helpers are needed to prepare for the fete Each helper can make either 2 large cakes

per hour, or 35 small cakes per hour The kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed How many helpers are required?

3 Jo's collection contains US, Indian and British stamps If the ratio of US to Indian

stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US

4 A 3 by 4 rectangle is inscribed in circle What is the circumference of the circle?

5 Two sets of 4 consecutive positive integers have exactly one integer in common The

sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?

A 4

B 7

C 8

D 12

E it cannot be determined from the information given

6 If f(x) = (x + 2) / (x-2) for all integers except x=2, which of the following has the

7 ABCD is a square of side 3, and E and F are the mid points of sides AB and BC

respectively What is the area of the quadrilateral EBFD ?

9 After being dropped a certain ball always bounces back to 2/5 of the height of its

previous bounce After the first bounce it reaches a height of 125 inches How high (in inches) will it reach after its fourth bounce?

10 n and p are integers greater than 1

5n is the square of a number

75np is the cube of a number

The smallest value for n + p is

A 14

B 18

C 20

D 30

E 50

1 The distance from town A to town B is five miles C is six miles from B Which of the

following could be the distance from A to C?

C II and III only

D I and III only

E I, II and III

7 For how many integer values of n will the value of the expression 4n + 7 be an integer

greater than 1 and less than 200?

8 In the above correctly worked addition sum, A,B,C and D represent different digits,

and all the digits in the sum are different What is the sum of A,B,C and D?

9 12 litres of water are poured into an aquarium of dimensions 50cm length, 30cm

breadth, and 40cm height How high (in cm) will the water rise?

10 Six years ago Anita was P times as old as Ben was If Anita is now 17 years old, how

old is Ben now in terms of P ?

3 One side of a triangle has length 8 and a second side has length 5 Which of the

following could be the area of the triangle?

4 A certain animal in the zoo has consumed 39 pounds of food in six days If it continues

to eat at the same rate, in how many more days will its total consumption be 91 pounds?

5 A perfect cube is an integer whose cube root is an integer For example, 27, 64 and 125

are perfect cubes If p and q are perfect cubes, which of the following will not necessarily

8 A dress on sale in a shop is marked at $D During the discount sale its price is reduced

by 15% Staff are allowed a further 10% reduction on the discounted price If a staff member buys the dress what will she have to pay in terms of D ?

9 All the dots in the array are 2 units apart vertically and horizontally What is the length

of the longest line segment that can be drawn joining any two points in the array without passing through any other point ?

10 If the radius of the circle with centre O is 7 and the measure of angle AOB is 100,

what is the best approximation to the length of arc AB ?

1 Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day

on Tuesday and Thursday She does not work on Saturday and Sunday She earns $324 per week How much does she earn in dollars per hour?

2 ABCD is a parallelogram BD = 2 The angles of triangle BCD are all equal What is

the perimeter of the parallelogram?

I n is odd

II n + 1 cannot be a prime number

III (n + 2) divided by 7 has remainder 2

5 A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2

How many of the smaller cubes have paint on exactly 2 sides?

6 Line l contains the points (3,1) and (4,4).

If line m is a different line, parallel to line l in the same coordinate plane, which of the following could be the equation of line m?

7 In the figure above the square has two sides which are tangent to the circle If the area

of the circle is 4a²π, what is the area of the square?

8 A triangle has a perimeter 13 The two shorter sides have integer lengths equal to x and

x + 1 Which of the following could be the length of the other side?

10 Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts water The painter has

by mistake added water so that he has 6 litres of paint which is half water and half paint What must he add to make the proportions of the mixture correct?

A 1 litre paint

B 1 litre water

C ½ litre water and one litre paint

D ½ litre paint and one litre water

E ½ litre paint

1 Which of the following can be used to illustrate that not all prime numbers are odd?

4 A piece of ribbon 4 yards long is used to make bows requiring 15 inches of ribbon for

each What is the maximum number of bows that can be made?

5 How many numbers between 200 and 400 meet one or both of the conditions given in

the two statements below?

Statement 1: The number begins with 3

Statement 2: The number ends with 3

7 PQRS is a parallelogram and ST = TR What is the ratio of the area of triangle QST to

the area of the parallelogram?

8 A picture is copied onto a sheet of paper 8.5 inches by 10 inches A 1.5 inch margin is

left all around What area in square inches does the picture cover?

9 The table shows the results of a poll which asked drivers how many accidents they had

had over the previous 5 years What is the median number of accidents per driver?

3 Two equal circles are cut out of a rectangle of card of dimensions 16 by 8 The circles

have the maximum diameter possible What is the approximate area of the paper

remaining after the circles have been cut out?

5 x = y - (50/y), where x and y are both > 0

If the value of y is doubled in the equation above, the value of x will

A decrease

B stay the same

C increase four fold

D double

E increase to more than double

6 Which of the following could be a solution of the equation │x│ = │4x - 3│

7 The number of degrees that the hour hand of a clock moves through between noon and

2.30 in the afternoon of the same day is

8 Jeff takes 20 minutes to jog around the race course one time, and 25 minutes to jog

around a second time What is his average speed in miles per hour for the whole jog if the course is 3 miles long?

9 A and B are equidistant from the line l How many circles can be drawn with their

centres on line l and that pass through both A and B?

10 A wheel has a diameter of x inches and a second wheel has a diameter of y inches

The first wheel covers a distance of d feet in 100 revolutions How many revolutions does the second wheel make in covering d feet?

2 The price of a cycle is reduced by 25 per cent The new price is reduced by a further 20

per cent The two reductions together are equal to a single reduction of

5 BCD is a line segment and Angle BAC = ¼ Angle ACB ; Angle ACD = ?

A 140

B 100

C 120

D 60

E it cannot be determined from the information given

6 Which of the following integers is in the solution set of │1 – 3x│ < 5 ?

7 In a certain village, m litres of water are required per household per month At this

rate, if there are n households in the village, how long (in months) will p litres of water last?

A p /mn

B mn / p

C mp / n

10 Radius of circle center O is 3 times the radius of circle center C.

Angle ACB = Angle POQ

If the shaded area of circle C is 2 then what is the area of the shaded part of circle O ?

3 If x and y are integers, and 3x + 2y = 13, which of the following could be the value of

4 In triangle ABC, AD = DB , DE is parallel to BC, and the area of triangle ABC is 40

What is the area of triangle ADE ?

A 10

B 15

C 20

D 30

E it cannot be determined from the information given

5 If n > 0 , which of the following must be true?

6 If the slope of a line is ½ and the y-intercept is 3, what is the x-intercept of the same

7 6 people meet for a business lunch Each person shakes hands once with each other

person present How many handshakes take place?

9 In a sports club with 30 members, 17 play badminton and 19 play tennis and 2 do not

play either How many members play both badminton and tennis?

10 Rectangle ABCD has a perimeter of 26 The half circle with diameter AD has an area

of 8π What is the perimeter of the part of the figure that is not shaded?

1 Courier charges for packages to a certain destination are 65 cents for the first 250

grams and 10 cents for each additional 100 grams or part thereof What could be the weight in grams of a package for which the charge is $1.55 ?

A 100

B 90

C 80

D 70

E cannot be determined from the information

3 If x / y is an integer, which of the following statements must be true?

A both x and y are integers

(2) multiply the sum by 3

(3) subtract x + y from the product

6 If the equation of a line p in the coordinate plane is y = 3x + 2, what is the equation of

line q which is a reflection of line p in the x-axis?

8 The first term in a sequence is 1 and the second term is 5 From the third term on each

term is the average (arithmetic mean) of all preceding terms What is the 25th term in the sequence?

9 The solid brick shown is made of small bricks of side 1 When the large brick is

disassembled into its component small bricks, the total surface area of all the small bricks

is how much greater than the surface area of the large brick?

1 A straight fence is to be constructed from posts 6 inches wide and separated by lengths

of chain 5 feet long If a certain fence begins and ends with a post, which of the following

could not be the length of the fence in feet? (12 inches = 1 foot)

2 A circular logo is enlarged to fit the lid of a jar The new diameter is 50 per cent larger

than the original By what percentage has the area of the logo increased?

4 Half the people on a bus get off at each stop after the first, and no one gets on after the

first stop If only one person gets off at stop number 7, how many people got on at the first stop?

5 The slope of the line passing through the point (5,5) is 5/6 All of the following points

could be on the line except

6 For a wall of a given material and of a fixed surface area, the rate of heat loss by

conduction through the wall is inversely proportional to the thickness (T) of the wall, and directly proportional to the temperature difference (d) across the wall The rate of heat loss could be given by which of the following expressions?

8 Refer to the table provided in the previous question.

The difference between the median and the mode of the number of children per family is

A I only

B II only

C I and II only

D I and III only

E II and III only

10 At what point does the graph of 5x + 4y = 12 intersect the y-axis?

1 6 pints of a 20 percent solution of alcohol in water are mixed with 4 pints of a 10

percent alcohol in water solution The percentage alcohol in the new solution is

2 ASB is a quarter circle PQRS is a rectangle with sides PQ = 8 and PS = 6 What is the

length of the arc AQB ?

A 5π

B 10π

4 Which of the following describes the relationship between A and B as shown in the

pairs of numbers in the table above?

5 The total weight of a tin and the cookies it contains is 2 pounds After ¾ of the cookies

are eaten, the tin and the remaining cookies weigh 0.8 pounds What is the weight of the empty tin in pounds?

6 Which of the following pairs of angles must be equal?

A a and e only

B a and e, and c and d only

C c and d only

D d and e only

E c and d and d and e only

7 The average bonus per employee was

8 Refer to the chart from the previous question.

If median bonus amount = m, mean bonus amount = n, and modal bonus amount = p, which of the following represents the correct ordering of m, n and p?

10 The graph shows a quadratic function with a minimum at (-1,1)

If f(a) = f(1), which if the following could be the value of a?