QR Simple Arithmetic

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Simple Arithmetic

Simple Arithmetic

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A health and wellbeing shop has the following coding system for pre-made protein drinks. They are graded by the protein content in grams per shake. They have listed the number of each that they have in stock.

Drinks with more protein tend to be priced at a higher level when they are not on special offer. The brand ProtoShake runs deals every third week with up to 75% off their normal price.

Code	Protein (g/shake)	Number of bottles
BK1	<10	10
BK2	10-14.9	17
BK3	15-24.9	12
BK4	25+	41

// @todo

1. What proportion of the drinks stocked have fewer than 15g of protein in the shake?

A. 12.50%

B. 30.75%

C. 33.75%

D. 66.25%

E. 69.25%

Explanation

Answer: C

Explanation:

1. Find the number of drinks stocked with this protein and thus the proportion:

Proportions consider a value as a percentage of the total:
For this question, it is the number stocked with less than 15g of protein as a percentage of the total number stocked:

There are 10 with <10g protein and 17 with 10-14.9g:

10 + 17 = 27

There are 80 in total:
10 + 17 + 12 + 41 = 80

27/80 = 0.3375 = 33.75%

Post Comment

Drinks with more protein tend to be priced at a higher level when they are not on special offer. The brand ProtoShake runs deals every third week with up to 75% off their normal price.

Code	Protein (g/shake)	Number of bottles
BK1	<10	10
BK2	10-14.9	17
BK3	15-24.9	12
BK4	25+	41

// @todo

2. A weightlifter wants to have a drink with exactly 25g of protein after his session. How many of the drinks can he have?

A. 12

B. 35

C. 41

D. 53

E. Cannot tell

Explanation

Answer: E

Explanation:

The table provides information on the number of drinks with 25g + of protein but there is no information about how many of these have 25g. Therefore, there is insufficient information in the data provided to answer this question.

Top Tip: Review the lesson content on Cannot Tell in QR – this is a question which cannot be answered and so cannot tell is the correct option.

Post Comment

A medical school society ran a public event for the promotion of medicine. They charged prices to cover the costs and raise money for charity.

Workshop	Adult (≥16 years)	Child (10 to 15 years)	Group (5 people or more)
CPR introduction	£7.00	£5.50	£6.50
Learn to suture	£10.00	£8.00	£9.10
Watch a simulated surgery	£6.50	£5.00	£5.75
Play with a model surgical robot	£9.50	£8.25	£9.00
Listen to a pioneering GP	£6.50	£5.00	£5.25

Under 10s are not permitted.
Groups can be made up of adults or children.

// @todo

3. A family made up of a father (49) and his three children (10, 12 and 15) attend the event. All four go to the CPR introduction, and the father learned to suture whilst all the children played with the model surgical robot. How much did they spend at the conference?

A. £23.50

B. £34.75

C. £57.00

D. £58.25

E. £91.75

Explanation

Answer: D

Explanation:

1. Work out the tickets the family purchased and their cost:

For the CPR intro: 1 x Adult and 3 x Child
1 x £7 + 3 x £5.50 = £23.50
For the Learn to Suture: 1 x Adult
1 x £10 – £10
For playing with a robot: 3 x Child
£8.25 x 3 = £24.75

The total is: £23.50 + £10 + £24.75 = £58.25

Common trap: Notice that only the father went to the suturing session and only the children went to the robotics one. If you switched the price of these, this would be answer C and if you stated that all of the group went to each session, the answer would be E.

Post Comment

A medical school society ran a public event for the promotion of medicine. They charged prices to cover the costs and raise money for charity.

Workshop	Adult (≥16 years)	Child (10 to 15 years)	Group (5 people or more)
CPR introduction	£7.00	£5.50	£6.50
Learn to suture	£10.00	£8.00	£9.10
Watch a simulated surgery	£6.50	£5.00	£5.75
Play with a model surgical robot	£9.50	£8.25	£9.00
Listen to a pioneering GP	£6.50	£5.00	£5.25

Under 10s are not permitted.
Groups can be made up of adults or children.

// @todo

4. A separate family consists of two parents (a mother aged 45 and her partner aged 34), the mother’s 16-year-old child and the couple’s ten-year-old twins. What is the cheapest price for all of them to attend just the suturing course?

A. £46.00

B. £45.70

C. £45.50

D. £44.00

E. Cannot tell

Explanation

Answer: C

Explanation:

1. Work out who the family consists of:

There are 3 adults and 2 children. Notice that they form a group of 5 and 5 people can access the group discount.

2. Work out how much it would be to pay individually:

£10 x 3 + 8 x 2 = £46.00

3. Work out how much it would be to pay as a group:
5 x 9.1 = £45.50 – a lower price.

Common trap:Notice that the price is cheaper as a group – the bullet points reveal that groups can be formed of both adults and children.

Post Comment

A medical school society ran a public event for the promotion of medicine. They charged prices to cover the costs and raise money for charity.

Workshop	Adult (≥16 years)	Child (10 to 15 years)	Group (5 people or more)
CPR introduction	£7.00	£5.50	£6.50
Learn to suture	£10.00	£8.00	£9.10
Watch a simulated surgery	£6.50	£5.00	£5.75
Play with a model surgical robot	£9.50	£8.25	£9.00
Listen to a pioneering GP	£6.50	£5.00	£5.25

Under 10s are not permitted.
Groups can be made up of adults or children.

// @todo

5. The cost of running the suturing is the same regardless of whether it is a child or an adult participating. The adult ticket includes a profit margin of 65%. What is the profit margin for the child ticket?

A. 68.8%

B. 60.8%

C. 58.2%

D. 56.0%

E. 54.0%

Explanation

Answer: D

Explanation:

1. Find the profit for the child ticket:

If the adult ticket has a profit margin of 65%, the costs must represent 35%
0.35 x 10 = £3.50
The question states that this is fixed between adults and children.

This means that the profit on a child ticket is:
8 – 3.5 = 4.5

2. Find this as a percentage of the child price:

4.5/8 = 0.56 – 56%

Common trap:Note that 8 – 3.5 = 4.5 not 5.5 – this slip would lead to Answer option A.

Timing Tip: Try to do as many of these questions using mental maths and the whiteboard as possible. You could do the 0.35 x 10 and the 8 – 3.5 without typing them into the calculator, saving precious time.

Post Comment

A medical school society ran a public event for the promotion of medicine. They charged prices to cover the costs and raise money for charity.

Workshop	Adult (≥16 years)	Child (10 to 15 years)	Group (5 people or more)
CPR introduction	£7.00	£5.50	£6.50
Learn to suture	£10.00	£8.00	£9.10
Watch a simulated surgery	£6.50	£5.00	£5.75
Play with a model surgical robot	£9.50	£8.25	£9.00
Listen to a pioneering GP	£6.50	£5.00	£5.25

Under 10s are not permitted.
Groups can be made up of adults or children.

// @todo

6. The following year, prices are increased for adults and groups by 15% and for children by 12%. What is the difference in price for a family of two adults and two children attending just to watch a simulated surgery?

A. Cannot Tell

B. £1.53

C. £1.58

D. £3.06

E. £3.16

Explanation

Answer: E

Explanation:

1. Find the new price and thus the increase:

New price = Old price x Multiplier
Adults: 1.15 x 6.50 = £7.48
Children 1.12 x 5 = £5.60

The difference is:
7.48 – 6.50 = £0.98
5.60 – 5 = £0.60
(0.98 + 0.6) x 2 = 1.58 x 2 = £3.16

Common trap: Be careful to note that the family is made up of two adults and two children so the difference will be doubled.

Common trap: When there are two percentage differences mentioned make sure that you match the correct change to the correct value. A 12% increase in the adult price and a 15% increase in the child price would give answer D.

Post Comment

// @todo

7. The domestic fowl population in Town X is 20% of the domestic fowl population in Town Y. The population of domestic fowl in Town Z is 75% of that in Town X. If the domestic fowl population in Town Z is 252, what is the domestic fowl population in Town Y?

A. 67

B. 336

C. 1575

D. 1650

E. 1680

Explanation

Answer: E

Explanation:

1. Link the population sizes algebraically:

Call the population in Town X: a
Call the population in Town Y: b
The population in Town X is 20% the population in Town Y:
a = 0.2b
Call the population in Town Z: c
The population in Town Z is 75% the population in Town X
c = 0.75a

2. Use the value for C to find the value for B
c = 252
so
0.75a = 252
a = 252/0.75
a = 336
0.2b = a
0.2b = 336
b = 1680

Common trap: Note that to find 100% of a value from knowing 75% of it, you have to divide by 0.75 rather than multiplying by 1.25.

Post Comment

● Hermione is writing comprehension passages and questions for Ron’s homework solutions company. She is paid AUD$0.07 per word in the passage and the same amount per word for the questions.

● Questions are required to be a minimum of 10% of the total length.

● The company reinvests 15% of profits from the previous year into the creation of new questions. Hermione is part of a team of 12 writers, all headed up by their manager Luna.

● She keeps a track of the passages she writes in May in the following table. She categorises them into groupings based on the combined length of the passages and questions in the ranges below.

Word Range	Frequency
0 – 500	2
500 – 1000	4
1000 – 2000	3
2000 – 3000	5
3000 – 5000	1

AUD$1 = £0.54 GBP = USD $0.69

// @todo

8. In July, she wrote a story of 1800 words. What is the minimum length of the question section?

A. 100

B. 180

C. 200

D. 360

E. Cannot Tell

Explanation

Answer: C

Explanation:

1. Set up an equation for the length

Let us call the length of the question section X.

The total length will be the length of the story + the question section.

This gives 1800 + X.

The total length has to be a minimum of 10x the length of the question section.

This means it has to be a minimum of 10X

2. Solve for X

10X = 1800 + X

9X = 1800

X = 200

This means the answer is C.

Common trap: Note that the question section has to be 1/10th of the total length rather than 1/10th of the length of the story. This means it has to be slightly longer than 180 words.

Post Comment

● Hermione is writing comprehension passages and questions for Ron’s homework solutions company. She is paid AUD$0.07 per word in the passage and the same amount per word for the questions.

● Questions are required to be a minimum of 10% of the total length.

● The company reinvests 15% of profits from the previous year into the creation of new questions. Hermione is part of a team of 12 writers, all headed up by their manager Luna.

● She keeps a track of the passages she writes in May in the following table. She categorises them into groupings based on the combined length of the passages and questions in the ranges below.

Word Range	Frequency
0 – 500	2
500 – 1000	4
1000 – 2000	3
2000 – 3000	5
3000 – 5000	1

AUD$1 = £0.54 GBP = USD $0.69

// @todo

9. Hermione wants to purchase a Mecbook Wind for USD$1250. She only wants to write 5000-word passages (including questions). How many would she have to complete to be able to afford the laptop?

A. 2

B. 3

C. 4

D. 5

E. 6

Explanation

Answer: E

Explanation:

1. Find the price in AUD

AUD$1 = USD$0.69

Divide USD$1250 by AUD$0.69 to find the price in AUD

1250 / 0.69 = AUD$1811.19…

2. Find the number of words she needs to write to reach this and thus the number of books:

She gets paid 0.07 per word so:

1811.19 / 0.07 = 25879…

She is writing 5000-word passages:

25879/5000 = 5.17…

She can’t write part of a 5000-word passage so she will have to write 6 to be able to afford the book.

Common Trap: Remember that she is paid in AUD but purchasing in USD.

Top Tip: Always check the wording of the question – it specifically states she would have to write full passages so round up. 5 would not be sufficient to pay for it but 6 is.

Post Comment

● Hermione is writing comprehension passages and questions for Ron’s homework solutions company. She is paid AUD$0.07 per word in the passage and the same amount per word for the questions.

● Questions are required to be a minimum of 10% of the total length.

● The company reinvests 15% of profits from the previous year into the creation of new questions. Hermione is part of a team of 12 writers, all headed up by their manager Luna.

● She keeps a track of the passages she writes in May in the following table. She categorises them into groupings based on the combined length of the passages and questions in the ranges below.

Word Range	Frequency
0 – 500	2
500 – 1000	4
1000 – 2000	3
2000 – 3000	5
3000 – 5000	1

AUD$1 = £0.54 GBP = USD $0.69

// @todo

10. Hermione is headhunted by a rival firm offering her a 25% pay rise. If she writes an average of 12500 words a month for three months, to the nearest penny, how much more would she earn with the rival firm than her current one?

A. £354.38

B. £364.38

C. £452.81

D. £462.81

E. £656.25

Explanation

Answer: A

Explanation:

1. Find the additional amount per word and thus the amount in 3 months in AUD.

25% more than AUD$0.07
0.07 x 0.25 = AUD$0.0175

She writes 12500 words for 3 months.
0.0175 x 12500 x 3 = AUD$656.25

2. Convert this into pounds:

AUD$1 = 0.54 so

AUD$656.25 x 0.54 = £354.38

Common trap:Make sure to do the correct conversion – Option C is the answer if you convert using the figure for USD and E is the answer if you forget entirely to convert into pounds.

Post Comment

● Hermione is writing comprehension passages and questions for Ron’s homework solutions company. She is paid AUD$0.07 per word in the passage and the same amount per word for the questions.

● Questions are required to be a minimum of 10% of the total length.

● The company reinvests 15% of profits from the previous year into the creation of new questions. Hermione is part of a team of 12 writers, all headed up by their manager Luna.

● She keeps a track of the passages she writes in May in the following table. She categorises them into groupings based on the combined length of the passages and questions in the ranges below.

Word Range	Frequency
0 – 500	2
500 – 1000	4
1000 – 2000	3
2000 – 3000	5
3000 – 5000	1

AUD$1 = £0.54 GBP = USD $0.69

// @todo

11. In May, Hermione’s passages were all at the middle of the categories in which they were classed. For example, she wrote 2 passages of 250 words. To the nearest 100 words, what was her average passage length in May?

A. 1600

B. 1400

C. 1200

D. 1000

E. 800

Explanation

Answer: A

Explanation:

1. Identify this is a weighted means question and calculate the weights

This is a weighted means question which means the mean is the sum of the weight for each value multiplied the number of words.

The weight can be calculated by the frequency of a passage of a certain length divided by the total number of passages.

In total there were: 2 + 4 + 3 + 5 + 1 = 15 passages

The weightings are therefore:

Word Range	Weight
0 – 500	2/15
500 – 1000	4/15
1000 – 2000	3/15
2000 – 3000	5/15
3000 – 5000	1/15

2. Multiply these by the middle of the word range for each:

Passage Length	Weight	Passage x Weight
250	2/15	500/15
750	4/15	3000/15
1500	3/15	4500/15
2500	5/15	12500/15

The sum is therefore: (500 + 3000 + 4500 + 12500 + 4000)/15 = 24500/15

This gives a mean of 24500/15 = 1633… = 1600 words to the nearest hundred

Timing Tip: Keeping the numbers as top-heavy fractions until the final step will save time.

Post Comment

Number of Items	Frequency
1	65
2	75
3	22
4	33
5	55

A shopkeeper goes through his Saturday receipts to find the average number of items bought in his convenience store.

// @todo

12. What was the average number of items bought?

A. 2.0

B. 2.2

C. 2.4

D. 2.6

E. 2.8

Explanation

Answer: E

Explanation: This is a weighted means question. The frequencies can be converted into weights.

1. Find the total number of items and thus the weights:

65 + 75 + 22 + 33 + 55 = 250.

Weights are a measure of the frequency of a value in comparison to the total number of frequencies:

For 1 item the weight is therefore 65/250
For 2 items: 75/250
For 3 items: 22/250
For 4 items; 33/250
For 5 items: 55/250

2. Multiply the number of items by their weights.

1 x 65/250 + 2 x 75/250 + 3 x 22/250 + 4 x 33/250 + 5 x 55/250 = 688/250

688/250 = 2.752 which is 2.8

Common trap: Keep the numbers as fractions until the final step – this means that you will use exact values rather than introducing rounding which might lead to an incorrect answer.

Post Comment

San Francisco Rams’ spending on “playing staff wages” was $285 million in 2017-18. The additional money they spent on “coaching staff wages” was 15% of that. Combined, these two amounts made up 75% of all staff wages.

// @todo

13. What was the approximate total staff wage bill to the nearest quarter million?

A. $42.75 million

B. $109.25 million

C. $327.75 million

D. $409.75 million

E. $437 million

Explanation

Answer: E

Explanation:

1. Find the combined playing and staff wages.

$285,000,000 x 1.15 = $327.75 million.

2. Find the total staff bill.

$327.75 million represents 75% of the total wage bill so we need to find 100 / 75 of it.

327.75 million x 100/75 = $437 million

Common Trap: Option D is the result of a common mistake. When you have 75% of something, you don’t simply increase the answer by one-quarter.

Post Comment

Advertisement Prices

Cielo Deportes hold the TV rights for a number of high profile sports. Their premium product is the rights to the Primero Ligue – the top tier of football in the country. They also have the rights to the Secundo Ligue.

The table below shows Prices for an advert during football matches in the Primero and Secundo Ligue on TV and Radio.

Length of Advert (seconds)	TV (£)	Radio (£)
5	1372	843
15	3591	2270
30	6972	4025

For a Secundo Ligue match, there is a buy-one-get-one-half-price on adverts of the same length.

// @todo

14. For a top tier game, how much more would it be to purchase two 5s TV ads and a 15s TV ad than one 15s Radio ad and one 30s radio ad?

A. £30

B. £40

C. £2249

D. £2259

E. £2269

Explanation

Answer: B

Explanation:

1. Find the price for two 5s and a 15s adverts on TV.

A 5s ad is £1372 and a 15s ad is £3591.
2 x £1372 + £3591 = £6335

2. Find the price for the 15s and 30s Radio adverts and thus the difference.
£2270 + £4025 = £6295

The difference between the two figures is:
£6335 – £6295 = £40.

Top Tip: Don’t be put off by answers options very different to the one you think is the correct answer. In this case, they were around the value you would get if mixed up the lengths between radio and television.

Post Comment

Advertisement Prices

The table below shows Prices for an advert during football matches in the Primero and Secundo Ligue on TV and Radio.

Length of Advert (seconds)	TV (£)	Radio (£)
5	1372	843
15	3591	2270
30	6972	4025

For a Secundo Ligue match, there is a buy-one-get-one-half-price on adverts of the same length.

// @todo

15. Dan initially wanted two 15 s TV adverts for a Secundo Ligue game. He then decides to get one 15 s and one 30 s TV advert. How much more did he spend, to the nearest pound?

A. 3200

B. 3201

C. 5176

D. 5177

E. 5176.50

Explanation

Answer: D

Explanation: The key to answering this question comes from remembering the discount.

1. Work out how much he would have initially paid.

From the bullet point below the table, we know that there is a 50% discount on the second 15s advert, so the calculation is:
1.5 x 3591 = £5386.50

2. Work out how much he will pay now and the difference between the two:

He now purchases one of each, both at full price so:

£3591 + £6972 = £10,563.

Find the difference between the two:

£10563 – £5386.50 = £5176.50 so
£5177 to the nearest pound.

Common trap: Always read the bullet points below a table – they will change the situation. If he hadn’t got a discount on the two adverts of a similar amount, the calculation would give £3381.

Post Comment

N Medicmind Tutor

Thu, 13 Aug 2020 19:11:14

addition of 3591 and 6972 is incorrect (used 6792 instead of 6972)

kate Medicmind Tutor

Thu, 27 Aug 2020 10:17:05

can this be updated, it takes so long to figure out whether i am actually correct or not based on these explanations when the data is not correct

Advertisement Prices

The table below shows Prices for an advert during football matches in the Primero and Secundo Ligue on TV and Radio.

Length of Advert (seconds)	TV (£)	Radio (£)
5	1372	843
15	3591	2270
30	6972	4025

For a Secundo Ligue match, there is a buy-one-get-one-half-price on adverts of the same length.

// @todo

16. Jaime’s takeaway took out a 5s ad on the local radio covering a game. She received 250 additional orders with an average value of £17.50. Her average profit margin is 25%. Did the profit from the additional orders exceed the amount she spent on the advert and by how much?

A. Yes – she made £250.75

B. Yes – She made £278.25

C. Yes – she made £3532.

D. No – She lost £250.75

E. No – She lost £278.25

Explanation

Answer: A

Explanation:

1. Find the amount of additional income and thus profit she made from the advert.

250 x £17.50 = £4375

She has a 25% profit margin so:

£4375 x 0.25 = £1093.75

2. Take away the amount she spent on the advert:

£1093.75 – £843 = £250.75 profit.

Top tip: Make sure that you read the full question. Answer C is found by assuming that all the £17.50 is profit rather than just 25% of it.

Post Comment

Advertisement Prices

The table below shows Prices for an advert during football matches in the Primero and Secundo Ligue on TV and Radio.

Length of Advert (seconds)	TV (£)	Radio (£)
5	1372	843
15	3591	2270
30	6972	4025

For a Secundo Ligue match, there is a buy-one-get-one-half-price on adverts of the same length.

// @todo

17. A new TV executive increases the price of a 30 second TV ad to £12,565.20. What percentage increase does this represent?

A. 65%

B. 165%

C. 75%

D. 80%

E. 180%

Explanation

Answer: D

Explanation: The easiest way to answer this is through the multiplier method.

1. Find the new value (£12,565.20) and the original value (£6972)

New value: £12,565.20
Original Value: £6972

2. Divide the new value by the original value to find the multiplier:

12565.2 / 6972 = 1.8 = 80% increase

Top Tip: Using the multiplier saves time. Just remember that it is the decimal you would put in your calculator. This means that 1.80 shows a 80% increase not an 180% increase.

Post Comment

Simple Arithmetic Review Screen

Instructions

Below is a summary of your answers. You can review your questions in three (3) different ways.

The buttons in the lower right-hand corner correspond to these choices:

1. Review all of your questions and answers.
2. Review questions that are incomplete.
3. Review questions that are flagged for review. (Click the 'flag' icon to change the flag for review status.)

You may also click on a question number to link directly to its location in the exam.

Simple Arithmetic Section

Final Answer Review Screen

Instructions

This review section allows you to view the answers you made and see whether they were correct or not. Each question accessed from this screen has an 'Explain Answer' button in the top left hand side. By clicking on this you will obtain an explanation as to the correct answer.

At the bottom of this screen you can choose to 'Review All' answers, 'Review Incorrect' answers or 'Review Flagged' answers. Alternatively you can go to specific questions by opening up any of the sub-tests below.

Simple Arithmetic Section

TI-108

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QR Simple Arithmetic

Your Score: + Band

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Section Breakdown

Simple Arithmetic

Explanation

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Explanation

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Explanation

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Explanation

Simple Arithmetic Review Screen

Instructions

Simple Arithmetic Section

Final Answer Review Screen

Instructions

Simple Arithmetic Section

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What is your preferred phone number?

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