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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 |
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%
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 |
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.
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 | Child | 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.
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.
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 | Child | 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.
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.
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 | Child | 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.
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.
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 | Child | 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.
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.
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.
● 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
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.
● 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
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.
● 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
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.
● 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
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.
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.
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.
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.
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.
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.
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.
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.
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.
Thu, 13 Aug 2020 19:11:14
addition of 3591 and 6972 is incorrect (used 6792 instead of 6972)
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
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.
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.
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.
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.
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TI-108
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