IKMC 2027 - Grades 7-8 - Self-study SET 11 - Thematic Batch 3

Question 1

$55554\cdot55556-55551\cdot55559=$

1. 1
2. 5
3. 9
4. 15
5. 25

Question 2

Frank buys a strange clock at a flea market. It has only a minute hand and a display showing the angle between the hour and minute hands. What time does the illustrated clock show?

1. 4:10 a.m.
2. 6:10 a.m.
3. 7:10 a.m.
4. 9:10 a.m.
5. 10:10 a.m.

Question 3

A shop discounts all products by 30%. Its “favourite products” receive a further 20% discount. What is the final percentage discount on those products?

1. 30%
2. 44%
3. 50%
4. 55%
5. 60%

Question 4

Two trains travel towards each other. One is 350 m long and travels at 60 km/h; the other is 420 m long and travels at 50 km/h. What is the distance, in metres, from the point where their fronts meet to the point where their tails meet?

1. 50
2. 70
3. 100
4. 120
5. 140

Question 5

If $\frac ab=\frac cd$ and $c\ne0$, which expression below is not true?

Interpret the question as asking which formula does not follow in general.

1. $\frac ba=\frac dc$
2. $a^2d^2=b^2c^2$
3. $\frac ac=\frac bd$
4. $\frac ad=\frac bc$
5. $\frac{a+b}{b}=\frac{c+d}{d}$

Question 6

The number 2014 has all its digits less than 5, and its smallest digit is 0. How many four-digit numbers have this property?

1. 144
2. 244
3. 256
4. 324
5. Another answer

Question 7

Find $2\cdot\frac1{100}+3\cdot\frac1{1000}+4\cdot\frac1{10000}$.

1. 0.234
2. 0.432
3. 0.0234
4. 0.0432
5. All the above answers are wrong

Question 8

How many four-digit integers can be formed from the four digits of 2017?

Use each given digit exactly once.

1. 6
2. 9
3. 16
4. 18
5. 24

Question 9

The sum of the perimeters of the shaded regions in the figure is $64\pi$ units. What is the sum of the radii of the three circles?

1. 8
2. 24
3. 32
4. 48
5. Cannot be determined

Question 10

The figure shows a maritime flag. Each side is divided into three equal segments. What is the ratio of the white area to the grey area?

1. 1 : 1
2. 1 : 2
3. 1 : 3
4. 1 : 4
5. 2 : 3

Question 11

An apple shop receives 22 baskets of apples each day. There are three varieties, and each basket contains apples of just one variety. Find the largest N such that among the 22 baskets there are always at least N baskets of one variety.

1. 5
2. 6
3. 7
4. 8
5. 9

Question 12

In the five-pointed star shown, find angle A.

1. $35^\circ$
2. $42^\circ$
3. $51^\circ$
4. $65^\circ$
5. $100^\circ$

Question 13

Trapezoid ABCD has AB parallel to CD and AB=3CD. Point E lies on ray AB with B the midpoint of AE. Find the area of triangle AED if triangle ECD has area 3.5 square units.

1. 14
2. 21
3. 28
4. 31
5. 35

Question 14

Which of the following products is greatest?

1. $444\times7777$
2. $777\times4444$
3. $555\times6666$
4. $888\times3333$
5. $999\times2222$

Question 15

Ank glues 7×7×7 unit cubes into a large cube. Before the glue dries, Ank removes some unit cubes to make three tunnels between opposite faces, as shown. When the glue dries, Ank immerses the shape in paint. How many remaining small cubes have exactly one painted face?

1. 144
2. 120
3. 148
4. 216
5. 124

Question 16

One sixth of the audience at a children's cinema are adults. Two fifths of the children are boys. What percentage of the whole audience are girls?

1. 1/2
2. 1/3
3. 1/4
4. 1/5
5. 2/5

Question 17

Seven workers work in a factory with four different production lines. Each day only four workers attend, each operating one line. Any three workers may be absent together. Training one worker on one line costs 100 dollars. What is the smallest training cost that ensures every line can operate every day?

1. 700 dollars
2. 1000 dollars
3. 1300 dollars
4. 1600 dollars
5. 2000 dollars

Question 18

Ann, Bill, Cynthia and Della each have one of four pets: a dog, a cat, a fish or a hamster. Ann has neither the dog nor the fish; Bill has neither the dog, the fish nor the hamster. Who has the hamster?

Use the source convention that the four different pets are assigned one each to the four children.

1. Ann
2. Bill
3. Cynthia
4. Della
5. Cannot be certain

Question 19

Three workers, Charlie, Aley and Michael, have different ages. They enter a restaurant and each orders a dish. We know:
– Charlie is either the oldest or the youngest.
– Aley is older than the person who orders chicken rice.
– The person who orders fish rice is younger than the person who orders fried noodles.
– Charlie orders chicken rice or Michael orders fried noodles.
What does Aley order?

Original printed choices: A) Fish rice; B) Chicken rice; C) Fried noodles; D) Fish rice or fried noodles; E) Chicken rice or fried noodles

Editorial task: Explain the literal model, the source method and any necessary correction.

Question 20

Which picture shows the illustrated object viewed directly from above?

1. Figure A from the source
2. Figure B from the source
3. Figure C from the source
4. Figure D from the source
5. Figure E from the source