1. Steven went from City X to City Z via City Y by car.

The distance from City X to City Y is

three-fourth the distance from City Y to City Z. The average speed from City X to City Y was
half as much as that from City Y to City Z. If the average speed for the entire travel was 49
km/hr, what was the average speed from City Y to City Z?
A. 39.2 km/hr
B. 42 km/hr
C. 63 km/hr
D. None of these

Answer: B. 42 km/hr

2. Frida reached a shopping mall by walk. She completes her shopping in 30 minutes. If her
walking speed is 10km/hr, she would return home at 7 pm. But, if she walks a little faster
with a speed of 15 km/hr, she would reach home by 6:30 pm. How much should be Frida’s
walking speed in order to reach home by 6:15 pm?
A. 15km/hr
B. 16 km/hr
C. 18 km/hr
D. 20 km/hr
Answer: D. 20 km/hr

3. In the figure given, a sector has an angle of 60 °. The portion shaded is what percent of
the complete sector given that OA = 3 cm and AB = 3 cm.

A. 20%
B. 25%
C. 30%
D. 50%

Answer: B. 25%

4. Andrew walks 3 miles North, 5 miles West, 6 miles South and 9 miles East. What is
distance covered by Andrew from his starting point?
A. √2 miles
B. √5 miles
C. 3 miles
D. 5 miles

Answer: D. 5 miles

5. Given that the area of a wheel is 100π cm2. How many centimeter will it travel if it makes
600 revolutions?
A. 20π cm
 B. 600π cm
C. 1200π cm
D. 60000π cm

6. Two vertical telephone poles which are 6 m and 3 m high respectively, stand 12 m apart.
A cable is connected from the top of 6m pole to some point on the ground between the
poles, and then to the top of the 8 m pole. How far is the point located from the 6 m pole if
the 15 m cable is used?
A. 7.54 m
B. 8 m
C. 4 m
D. 4.46 m

Answer: B.8 m

7. Andrew sells his camera for $371 and gains a profit of 6%. If he needs a profit of 8%, how
much should be the selling price of the camera?
A. $362
B. $378
C. $392
D. $416

Answer: B. $378

8. The cost price of three products X,Y and Z are in the ratio 3:4:5. X is sold at 10% gain and
Y is sold at a 7.5% loss. The overall gain or loss percent of X and Y is the same as the gain
or loss percent of all the three products taken together. Now what is the percentage of gain
or loss of Z?
A. 8.75% gain
B. 1.25% loss
C. 0
D. Cannot be determined

Answer: C. 0

9. Lucy is a wholesale dealer of dry fruits. She buys them from three different sellers at $10,
$8 and $6 per kilogram. She then mixes them in the ratio 3:4:5 by weight and sells at 50%
gain. What is the selling price per kilogram of the dry fruits?
A. $11.5
B. $10
C. $9.5
D. $8

Answer: A. $11.5

10. Brian travelled a certain distance at 8 kmph and returned to his starting point at 4kmph.
What is the average speed of Brian for the whole journey?
A. 3 ¾ kmph
B. 6 kmph
 C. 4 ¼ kmph
D. 5 ⅓ kmph

Answer: D. 5 ⅓ kmph

11. The marked price of an article exceeds the article’s cost price by a certain percentage
“x”. The ratio of “x” and the percentage of discount allowed on the same article is 3:2. If the
article is sold at the cost price, what is the percentage of discount?
A. 20%
B. 25%
C. 33 ⅓ %
D. 50%

Answer: D. 50%

12. Juliet drove from point A to point B at an average speed of 50 kmph and returned to
point A along the same route at average speed of 46 kmph. If her total driving time for the
journey was 4 hours, how many minutes did it take Juliet to drive from point B to point A?
A. 115 minutes
B. 120 minutes
C. 125 minutes
D. 130 minutes

Answer: C. 125 minutes

Directions for Qs 13 and 14

Study the below pie chart and bar chart carefully and answer the questions
13) If the percentage of cat owners in USA is increased by 5% per year over a period of four
years, what would be the resulting percentage?
A. 42.5%
B. 44%
C. 45%
D. 47.5%

Answer: 45%

14) If there are 4,500,000 cat owners in Thailand, how many of them own a Chausie?
A. 9900
B. 14850
C. 90000
D. 135000

Answer: A. 9900

15) The crew of a boat was increased by 32 per cent of its original number. They then ahd
33 men. How many men did they have initially?
A. 22
B. 23
C. 27
D. 25

1
16) Travelling by train is 2 2 times as fast as travelling by boat. How long would it take to go
600 km by boat if it takes 10 hours by train?

31
A. 3
hours
B. 25 hours
27
C. 2
hours
D. 15 hours
 1
17) A man took a loan for 1 3 years at an interest of 6%. At the end of the specified period,
he paid $432, which included the loan and the interest. How much did he originally borrow?
A. $397.60
B. $398
C.$400
D. $406.80

1
18) If a motor car travels 540 m in 18 second, how many kilometers does it go in of an
3
hour?
A.
B. 0.03 km
C. 0.9 km
D.

19) It takes 50 kg of cement to cover 10𝑚2. How many kg of cement will be needed to cover
a rectangular area 25 m by 10m ?
A. 250 kg
B. 1500 kg
C. 2000 kg
D. 1250 kg

20) The two cities A and B are separated by a distance of 3000 km. At 11 AM, the two trains
3
depart from the two cities. The speed of one train is 62 kilometres per hour, whereas the
5
4
speed of the other is 69 5 kilometres per hour. At 4 PM, how far apart will the two trains be?
A. 662 km
B. 2338 km
C. 2220 km
D. 1842 km

21) A brass bar of mass 75 kg is made of 45% zinc and the balance of copper. How many
kilogrammes of copper does it contain?
A. 55 kg
B. 41.25 kg
C. 33.75 kg
D. 0.6 kg

22) A family of three will divide $2000 among themselves in the ratio of 5:14:21. How much
lesser is the smallest share than the largest share?
A. $900
B. $800
C. $500
D. $750

23) If a chimney 18 m high casts a shadow 20 m long, how long a shadow would a chimney
27 m high cast?
A. 10 m
B. 25 m
C. 30 m
D. 36 m

24) How much would it cost to resurface a square plot 75 m long at a cost of 20 c a square
meter?
A. $6000
B. $1600
C. $1000
D. $1125

25) If you wish to convert a circular field that has a diameter of 56 m to a square field with
the same area, how long will a side of the square be?
A. 28 m
B. 36.8 m
C. 49.6 m
D. 46 m

26) You have a rope-encircled circular grazing field of diameter 96 m. A trotting track with a
circumference of 128 m is concentric with the field. If the trotting track needs to be repaved,
how much will it cost if the rate is $0.10 per square metre?
A. $426
B. $563.2
C. $826.4
D. $968.2

27) In making a speedometer, if a displacement equivalent to a 10𝑜 angle represented a

speed of 5 km/h, what angle would be needed to represent a speed of 30km/hr?
A. 10𝑜
B. 2𝑜
C. 60𝑜
D. 16𝑜

28) Brown owes $1200 and Jones $2500, but neither has enough money to pay his debts.
Brown says to Jones, ‘Lend me one-eighth of your bank account and I’ll pay my creditors.’
Jones says to Brown, ‘ Lend me one-ninth of yours and I’ll pay mine’ How much money does
Brown have?
A. $2400
B. $2100
C. $900
D. $1200

29) If a cuboid of dimensions 4 cm x 4 cm x 10 cm is placed inside a right circular cylinder of

diameter 6 cm and height 10 cm, what would be the volume of the unoccupied portion of the
cylinder?
A. (6𝜋 − 16) 𝑐𝑚3
B. (60𝜋 − 16)𝑐𝑚3
C. (90𝜋 − 160)𝑐𝑚3
D. (160 − 30𝜋)𝑐𝑚3

30) A retailer wishes to make 20% on shoes. At what price must he buy them in order to sell
them at $ 4.50 a pair?
A. $ 2.50
B. $ 4.25
C. $ 3.50
D. $ 3.75

31) An island is drawn to a scale of 1𝑐𝑚2 to 10 𝑘𝑚2 .What is the approximate area of the
island in 𝑘𝑚2 if each square in the grid has a length of 1 cm?

A. 240 𝑘𝑚2
B. 760 𝑘𝑚2
C. 480 𝑘𝑚2
D. 1000 𝑘𝑚2

32) In the Noosa National Park, John wants to go for a walk. He has two maps of the area,
but he is only allowed to take one because his sister needs the other one and they will be
travelling entirely opposite paths. The scales for Map X and Map Y are 1 centimetre on the
map to 500 m on the ground and 1 cm on the map to 250 m on the ground, respectively.
John will travel on foot only. The ideal map to use is...
A. Map X
B. Map Y
C. Both maps are equally suitable for walking
D. Without knowing John’s route, the ideal map cannot be chosen.

33) You recently received the house designs from an architect. You see that he has left out
the scale after looking at the plans. You are aware that the longest wall on the plan is 12.5
cm long, but its actual length is 25 metres. What is the scale of the architect's plan relative to
the ground?

A. 1 cm : 2 m
B. 0.25 cm : 1 m
C. 2 cm : 1 m
D. 1 cm : 4 m

34) 4 cm of ground is shown on a plan at a size of 1 cm. How much smaller would the area
of a circle in a plan be if a circle with a radius of 20 cm was drawn to scale?
A. 20 times smaller
B. 5 times smaller
C. 4 times smaller
D. 16 times smaller

35) A delivery van travels 20 kilometers at a speed of 50 kilometers per hour from office P to
office Q to deliver a package. How fast should the van travel on the return trip if the round-
trip travel time is supposed to be 40 minutes?
A. 55 km/hr
B. 60 km/hr
C. 65 km/hr
D. 75 km/hr

36) In March 2022, a kitten weighed 40 kg. In July 2022, the same kitten weighed 50 kg.
What was the percentage increase in the kitten's weight?
A. 75%
B. 25%
C. 50%
D. 33.33 %

37) Kevin exchanges money at the Post Office. He converts €325 and $351 into pounds.
What is the approximate percentage commission that the Post Office deducts before giving
Kevin £401.80?
Exchange Rates
£1 $ 1.50
£1 € 1.68
* Commission
Charged

A. 6%
B. 10%
C. 2%
D. 23%

38) Franklin bought a toy car as a gift for his friend’s birthday. He placed it in a cuboid box of
length 4 cm, breadth 6 cm and height 1 cm. He wants to wrap the box with a single sheet of
gift wrapping paper.
Which of the following dimensions of the paper would wrap the box completely without be
torn/cut?
A. Length -12 cm, Breadth- 6 cm
B. Length - 13 cm, Breadth - 4 cm
C. Length - 13 cm, Breadth - 4 cm
D. Length - 10 cm, Breadth - 6 cm

39) Chad had asked Paul to purchase three different types of ballpoint pen – Type A, Type B
and Type C.
Type A costs 50 cents
Type B costs $5.50
Type C costs $9.50.
He gave Paul $100 and told him to purchase 100 pens in any combination as long as the
amount spent is exactly $100 for 100 pens.
Which of the following cannot be true?

A. Out of the 100 pens, Paul had bought for $100, there were 5 Type C ballpoint pens.
B. Out of the 100 pens, Paul had bought for $100, there were 94 Type A ballpoint pens.
C. If Chad gave Paul only $5, Paul could buy only Type A ballpoint pens.
D. Out of the 100 pens, Paul had bought for $100, there were 5 Type B ballpoint pens.

40) An algebra test was conducted in a class of fewer than 30 students. 4 students failed the
test. Alex and Bob received a grade B on the test. 7 students received a grade C, whilst 2
students received a grade D. The rest of the class scored an A grade.
Which of the following must be true?
A. 7 students received a grade of A in the test.
B. There were 30 students in the class.
C. 14 students received a grade of B in the test.
D. Only one student failed in the test.

41) Charles walks 40 m Eastwards, then takes a left turn and walks 20 m. He then turns
right, walks 18 m, turns left and walks 24 m. Finally, Charles turns to the left and walks 12 m

Which of the following must be true about the direction in which Charles walks now?

A. Charles is walking in the East Direction

B. Charles is walking in the West Direction
C. Charles is walking in the North Direction
D. The direction in which Charles is walking cannot be determined

42) There is a website called “abcddef.com” that publishes challenging problems in math
each week. The members of the community would be submitting the answers. Once
submitted, a message showing the correct answer along with the percentage of people who
got the question right, will be appearing. Joe goes to this website, picks a challenging
problem and submits the correct answer. Now he see a message saying that his answer is
right and he also witnesses the percentage of people answering the question right update
from 50% to 51%. If Joe was the 1019th solver, how many members of the website ,
including Joe, attempted the same problem ? Assuming the percentage success of the
website’s users is rounded to the nearest integer and the website allows only one attempt
per user.
 A. 1019
B. 2219
C. 1173
D. 2017

43) A circle is inscribed in another circle without touching each other. The radius of the larger
circle is 13 cm and that of the smaller circle is 7 cm.If the least distance between their
circumference be 2 cm, then the distance between their centres is____________
A. 8 cm
B. 6 cm
C. 4 cm
D. 18 cm

44) A cylinder of radius 3 cm and height 21 cm has to be packed with a certain number of
cubes having side 3 cm. What is the required number of cubes to fit evenly into the cylinder?

A. 12
B. 10
C. 7
D. 9

45) Patricia has some amount with her to buy some items at the supermarket. She could buy
50 potatoes or 40 tomatoes. She holds back 10% of the initial amount she had, for auto
rickshaw expenses and buys 20 tomatoes and using the remaining amount, she purchases
potatoes. What is the possible number of potatoes she could have bought?

A. 36
B. 15
C. 20
D. 40

46) In a class , 40% of the students are boys and 75% of the boys had scored more than 90
in the final Maths exam. If 45% of the students scored more than 90 , what fraction of the
girls scored less than or equal to 90 in the exam?

2
A. 11
1
B.
4
1
C. 3
3
D. 4

47) A dark chocolate which is in the form of a sphere is placed in a box which is cubical in
shape with each side measuring 5 cm. The chocolate is placed such that it just fits in the
box. A fly waiting to taste the chocolate is sitting at one of the corners of the opened box.
What is the least distance it has to travel to reach the chocolate?
A. 2.5 𝑐𝑚
B. 2.5 (√3 − 1) cm
C. 5(√3 − 1) cm
D. 5(√2 − 1) cm

48. Michael got his first salary on Monday 30th March 2017. He chose to spend 20% of his
salary within the same week and kept the remaining amount in the bank. So on each
subsequent morning, he had 25% of the amount that he had at home the previous morning.
Finally, on the morning of 3rd April 2017 which is a Saturday, he had one dollar in his
pocket. What was the salary of Michael (in dollars)?
A. $256
B. $758
C. $1280
D. $2560

49. The external diameter, the length and the thickness of a hollow metal pipe is 8 cm, 21
cm and 1 cm respectively. If the density of the metal is 8𝑔 /𝑐𝑚3 , what is the weight of the
pipe in kilograms?
A. 2.59
B. 5.28
C. 3.69
D. 4.62

50) John loves tomatoes. He has been cultivating tomatoes in his garden. His garden is a
square in shape. Each tomato covers an area of one square centimeters in his garden. This
year is a prosperous year for John as he has been able to grow 131 tomatoes more than
what he had cultivated in the previous year. The shape of the garden still remains a square.
What is the total number of tomatoes John has cultivated this year in his garden?
A. 4225
B. 4096
C. 4356
D. Data Inadequate