ECAA 2019 Economics Admissions Assessment D563/11

Each region in the country of Bolandia sets its own tax rate which applies to the whole of an individual's annual income.

Below is a table showing tax information relating to six different people.

Who pays the same amount of tax in a year as Tim?

• A.Neil
• B.Veronica
• C.David
• D.Amy
• E.Roz

Answer: C

Below is a greyscale image of the flag of Canada. The flag consists of two red strips on the left and the right, a white square in the middle, and a red maple leaf in the centre.

[diagram not to scale]

The width of the white square is twice as large as the width of a red strip. The red maple leaf occupies a quarter of the square in the middle.

What is the ratio of red to white in the flag?

• A.1:1
• B.2:1
• C.3:2
• D.5:3
• E.5:4

Answer: D

The following table compares five selected commuting routes in different European countries with respect to the length of the journey and the monthly cost of a season ticket as a percentage of average monthly wages.

comparison of selected commuting routes

On average, the commuters of which route spend the lowest proportion of their wages per kilometre of the route?

• A.Luton–London
• B.Brandenburg–Berlin
• C.Karis–Helsinki
• D.Uppsala–Stockholm
• E.Drogheda–Dublin

Answer: C

The bar chart shows the total numbers of tickets sold for a concert over three nights.

Premium tickets are more expensive than Standard tickets.

Which one of the following statements is correct?

• A.The highest total sales income was for Thursday.
• B.The highest total sales income was for Friday.
• C.The highest total sales income could have been for Thursday or Friday.
• D.The highest total sales income could have been for Thursday or Saturday.
• E.The highest total sales income could have been for Friday or Saturday.

Answer: E

• A.2
• B.4
• C.5
• D.6
• E.10

Answer: B

The table below shows the amount of waste recycled each year, in thousands of tonnes, over a three-year period in 20 countries.

What is the biggest percentage increase in recycling in the table from year 1 to year 3?

• A.50%
• B.75%
• C.100%
• D.150%
• E.200%

Answer: E

Peter has drawn two diagrams showing information about the two cars owned by his parents:

Which one of the following statements is not correct?

• A.The more expensive car is newer.
• B.The cheaper car is bigger.
• C.The older car is slower.
• D.The newer car is bigger.
• E.The slower car is smaller.

Answer: B

A digital display consists of seven segments which light up in different combinations to produce digits. For example, to display the digit '1' the two right-hand segments light up as shown:

The display is used to show, in sequence, each of the digits 1 to 9.

What is the maximum and minimum number of times that any one segment lights up during this sequence?

• A.A
• B.B
• C.C
• D.D
• E.E

Answer: C

Sandi is planning a trip to the old city of Pordson. She wants to stay for four nights in order to visit all of the attractions, and one of the nights must be the Saturday so that she can attend a special music concert.

The table below shows the prices per night and details of the deals for the five main hotels in Pordson.

Deals:
3F2: Stay 2 nights and get the 3rd night free
SFSHP: Stay Friday and get the Saturday night half price.
50%: 50% discount on all stays of 3 or more nights.
4FP3: Stay 4 nights and get the cheapest night free.
CBK: €50 discount on stays of 3 or more nights.

What is the minimum that Sandi will need to spend on a hotel bill for her stay in Pordson?

• A.€110
• B.€120
• C.€140
• D.€145
• E.€160

Answer: C

In March, 20 people voted for the position of chair of a committee. There were three potential candidates: Andrew, James and Roger.

In April, 11 of these people changed their votes, as follows:

3 people changed their vote from Andrew to James
2 people changed their vote from James to Roger
5 people changed their vote from Andrew to Roger
1 person changed their vote from Roger to James

Which one of these bar charts could not show the number of votes for the three candidates in March and April?

• A.Chart A
• B.Chart B
• C.Chart C
• D.Chart D
• E.Chart E

Answer: C

Alex and Sue are playing a game with a set of nine cards, numbered from 1 to 9. A 3 × 3 grid of cards is dealt onto the table. The cards for the next round have just been dealt and are as shown below.

The first player chooses two cards and scores the difference between the two numbers. The second player then chooses two cards from the seven that are left and scores the average of the two numbers. The highest score wins the round. Both players must choose cards that are either horizontally or vertically next to each other in the grid.

For this round of the game Alex has to decide whether to play first or second. She wants to make sure that she wins the round. If she has more than one possible winning move then she wants to achieve the highest score possible.

What should Alex choose to do?

• A.play first and choose the 1 and 8
• B.play first and choose the 3 and 9
• C.play first and choose the 6 and 7
• D.play first and choose the 7 and 9
• E.play second

Answer: E

The single ferry to Pepper Island starts each day from mainland Seatown and crosses to the island port of Kaysville. It runs back and forth from 9:30 am to 4:10 pm on Saturdays, Sundays and Bank Holidays, and from 10:30 am to 2:20 pm from Monday to Friday.

*highlighted days = Bank Holidays

Each crossing takes 50 minutes. Between crossings, there is a 10-minute stopover for cleaning and refuelling. This is extended to 20 minutes on Saturdays, Sundays and Bank Holidays to allow for the increased cleaning requirements.

What is the maximum number of crossings the ferry can make in May?

• A.140
• B.144
• C.154
• D.166
• E.186

Answer: B

Nathan is making a pair of trousers for his young son. The diagram shows the pattern for one piece. Four such pieces are needed.

[diagram not to scale showing a shape with max width 15cm and height 38cm]

For simplicity he assumes that he will need a 15cm × 38 cm rectangle for each piece. The material comes in three widths with prices as shown:

Material may be bought in lengths which are exact multiples of 10 cm.

What is the lowest price he can pay?

• A.42p
• B.56p
• C.60p
• D.66p
• E.80p

Answer: B

Arthur plans to modernise his bathroom. His design requires a 1600 mm × 700 mm bath. He wants side grips to help him get out of the bath, and because he doesn't want to choose the taps before ordering the bath he must have one which doesn't have pre-drilled tap holes.

A list from the bath catalogue is shown below:

How much will Arthur save by choosing the cheapest steel bath that fits his requirements rather than the cheapest acrylic bath that fits his requirements?

• A.£2
• B.£3
• C.£4
• D.£10
• E.£18

Answer: C

The Head of Year 6 is planning an end-of-term treat for her students. The pie chart represents the numbers of votes cast by the children for each of the five possible outings.

Which one of the following rows (A–E) could show the actual number of votes cast by the children for each of the options?

• A.A
• B.B
• C.C
• D.D
• E.E

Answer: E

The drawing below shows an allotment shed.

[diagram not to scale]

The four outside wood surfaces of the shed, including the door, need to be painted with three coats of paint. It takes 4 minutes to paint 1 square metre.

I have two identical sheds to paint and will take just one 20-minute tea break.

How long will it take to paint the two sheds?

• A.36 minutes
• B.1 hour and 48 minutes
• C.2 hours and 8 minutes
• D.3 hours and 36 minutes
• E.3 hours and 56 minutes

Answer: E

A school party consisting of 4 teachers and 20 students is visiting the theatre. Of the students, 8 are aged 15 years and 12 are aged 16 years. The following table shows the entry prices to the theatre.

What is the least amount that the school party must pay for entry to the theatre?

• A.$525
• B.$530
• C.$545
• D.$550
• E.$560

Answer: A

Consider the following net, which forms a hexagonal prism:

Which one of the following nets will form an identical prism?

• A.A
• B.B
• C.C
• D.D
• E.E

Answer: C

• A.Tuesday
• B.Wednesday
• C.Thursday
• D.Friday
• E.Saturday

Answer: D

A 250 g bag of mixed nuts lists the contents on the packet as follows:

As they are my favourite, I eat all the almonds in the packet and then re-weigh it. I find that the almond content was the minimum it could have been whilst being consistent with the labelling.

What is the largest possible peanut content of the nuts remaining in the bag after I have eaten the almonds?

• A.40%
• B.48%
• C.50%
• D.57%
• E.60%

Answer: C

• A.$x = 2\left(\frac{y+1}{3}\right) - 1$
• B.$x = 2\left(\frac{y+1}{3}\right) + 1$
• C.$x = 2\left(\frac{y+1}{3}\right)^2 - 1$
• D.$x = 2\left(\frac{y+1}{3}\right)^2 + 1$
• E.$x = 3\left(\frac{y+1}{2}\right)^2 - 1$
• F.$x = 3\left(\frac{y+1}{2}\right)^2 + 1$
• G.$x = \left(\frac{2(y+1)}{3}\right)^2 - 1$

Answer: C

• A.£4.00
• B.£4.32
• C.£5.00
• D.£5.62
• E.£6.40
• F.£6.72

Answer: E

• A.$x < -1$ or $x > 0$
• B.$-1 < x < 0$
• C.$x < -9$ or $x > -1$
• D.$-9 < x < -1$
• E.$x < -9$ or $-1 < x < 0$
• F.$-9 < x < -1$ or $x > 0$

Answer: F

• A.$\sqrt{2}$
• B.$\frac{5\sqrt{2}}{4}$
• C.$\frac{7\sqrt{2}}{4}$
• D.$\frac{7\sqrt{2}}{2}$
• E.$4\sqrt{2}$
• F.$\frac{9}{2}\sqrt{2}$
• G.$8\sqrt{2}$

Answer: C

• A.4
• B.8
• C.16
• D.72
• E.80

Answer: B

• A.$x = 3^{5-k}$
• B.$x = 3^{5+k}$
• C.$x = 5^{3-k}$
• D.$x = 5^{3+k}$
• E.$x = 3^5 - k$
• F.$x = 3^5 + k$
• G.$x = 5^3 - k$
• H.$x = 5^3 + k$

Answer: C

• A.3
• B.4
• C.5
• D.6
• E.7

Answer: B

• A.$k < -4$ or $k > 4$
• B.$-4 < k < 4$
• C.$k < 0$ or $k > 4$
• D.$0 < k < 4$
• E.$k \le -16$ or $k > 16$
• F.$-16 < k < 16$
• G.$-6 < k < 6$
• H.$k < -6$ or $k > 6$

Answer: A

• A.$n = \frac{3p-1}{9p-1}$
• B.$n = \frac{3p+1}{9p-1}$
• C.$n = \frac{1}{1-9p}$
• D.$n = \frac{1}{9p-1}$
• E.$n = \frac{4p-1}{16p-1}$
• F.$n = \frac{4p+1}{16p-1}$
• G.$n = \frac{1}{1-16p}$
• H.$n = \frac{1}{16p-1}$

Answer: E

• A.$\frac{20}{7}$
• B.$-\frac{2\sqrt{30}}{7}$
• C.$-\frac{2\sqrt{3}}{7}$
• D.$\frac{2\sqrt{3}}{7}$
• E.$\frac{2\sqrt{30}}{7}$
• F.$\frac{20}{7}$

Answer: E

• A.27:125
• B.54:125
• C.81:125
• D.27:250
• E.81:250

Answer: A

• A.0
• B.$\frac{1}{4}$
• C.$\frac{3}{4}$
• D.1
• E.3
• F.6

Answer: E

• A.1
• B.7
• C.$\log_{10}12$
• D.$\log_{10} \left( \frac{12}{49} \right)$
• E.$\frac{\log_{10}12}{\log_{10}7}$
• F.$\frac{1}{\log_{10}7}$

Answer: E

• A.none of them
• B.1 only
• C.2 only
• D.3 only
• E.1 and 2 only
• F.1 and 3 only
• G.2 and 3 only
• H.1, 2 and 3

Answer: B

• A.0
• B.$\frac{3}{2}$
• C.$\frac{5}{6}$
• D.$\frac{8}{3}$
• E.$\frac{247}{48}$

Answer: D

The expression $(ax + b)(cx + d)$ is expanded, where a, b, c and d are real numbers.

Consider the following three conditions:

condition 1: $b = -d$

condition 2: $ad = -bc$

condition 3: $a = c = 1$ and $b = -d$

Which of these conditions is/are sufficient for the expansion of $(ax + b)(cx + d)$ to equal $px^2 + q$, for all x, where p and q are real numbers?

• A.A
• B.B
• C.C
• D.D
• E.E
• F.F
• G.G
• H.H

Answer: D