# UCAT Quantitative Reasoning Test #5

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#### For pre-made protein drinks, a health and wellness store uses the following coding scheme. They are rated according to how many grams of protein are in each smoothie. The quantity of each item they currently have in stock is mentioned. When they are not on sale, drinks with more protein are typically more expensive. Every third week, the ProtoShake brand offers promotions with up to 75% off the regular price. What percentage of the drinks on hand include shakes with less than 15 grams of protein?

Correct! Wrong!

Explanation:
A value's percentage of the whole is taken into account in proportions:
In this case, the quantity supplied that contains less than 15g of protein as a proportion of the overall quantity stocked is relevant:
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 public event was organized by a medical school society to promote medicine. To offset expenditures and collect money for charity, they imposed prices. Children under 10 are not allowed. Adults or youngsters may make up groups. The event is attended by a family consisting of a father (49), and his three kids (10, 12, and 15). All four of them attend the CPR introduction, and as the kids played with the surgical robot model, the father learnt how to stitch. They spent how much money at the conference?

Correct! Wrong!

Explanation:
Calculate the cost of the family's ticket purchases:
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 blunder: Note that only the father attended the suturing session and that only the kids attended the robotics session. If the price of these were flipped, the answer would be £57.00, and if you assumed that everyone in the group attended every session, the answer would be £91.75.

#### For pre-made protein drinks, a health and wellness store uses the following coding scheme. They are rated according to how many grams of protein are in each smoothie. The quantity of each item they currently have in stock is mentioned. When they are not on sale, drinks with more protein are typically more expensive. Every third week, the ProtoShake brand offers promotions with up to 75% off the regular price. After a workout, a weightlifter wants a beverage with precisely 25g of protein. How many drinks is he allowed to have?

Correct! Wrong!

Explanation:
The table lists the number of drinks that contain 25g or more of protein, but it doesn't say how many of them contain 25g.
As a result, the information provided in the data does not adequately address this topic.
Review the lesson material on Cannot Tell in QR as a top tip because this is a question that cannot be answered and cannot tell is the proper response.

#### A public event was organized by a medical school society to promote medicine. To offset expenditures and collect money for charity, they imposed prices. Children under 10 are not allowed. Adults or youngsters may make up groups. The following year, prices are raised by 15% for individuals, groups, and children, respectively. What is the cost difference for a family of four to attend a simulated surgery with just two adults and two kids?

Correct! Wrong!

Explanation: Calculate the new price and the resulting 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
The family consists of two parents and two children, thus the disparity will be twice.
Common error: Always match the proper change to the correct value when two percentage differences are provided. The answer would be £3.16 if the adult price increased by 12 percent and the child price increased by 15 percent.

#### A public event was organized by a medical school society to promote medicine. To offset expenditures and collect money for charity, they imposed prices. Children under 10 are not allowed. Adults or youngsters may make up groups. Two parents (a mother, 45, and her partner, 34), the mother's 16-year-old child, and the couple's twins, 10, make form a separate family. How much would it cost each of them to take the suturing course alone?

Correct! Wrong!

Explanation:
Determine the family's composition:
There are two kids and three grownups. They form a group of five, and as a result, five of them are eligible for the group discount.
Calculate how much each individual payment would be:
£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 lower when purchased as a group; the bullet points show that both adults and children can create groups.

#### Twenty percent of the domestic avian population is found in Town X compared to Town Y. In comparison to Town X, Town Z has 75% fewer domestic birds. What is the domestic fowl population in Town Y if there are 252 domestic fowl in Town Z?

Correct! Wrong!

Explanation:
Algebraically connect the population sizes:
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
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 error: Keep in mind that you must divide by 0.75 rather than multiply by 1.25 in order to find 100 percent of a value if you only know 75 percent of it.

#### A public event was organized by a medical school society to promote medicine. To offset expenditures and collect money for charity, they imposed prices. Children under 10 are not allowed. Adults or youngsters may make up groups. Whether a child or an adult participates, the cost of executing the suturing procedure is the same. There is a profit margin of 65% on the adult ticket. What is the child ticket's profit margin?

Correct! Wrong!

Explanation:
Find the child ticket's profit:
The costs must account for 35 percent of the adult ticket's 65 percent profit margin. 0.35 x 10 = £3.50
This is predetermined between adults and youngsters, according to the question.
This means that the profit on a child ticket is: 8 – 3.5 = 4.5
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: Use the whiteboard and your mental calculator to complete as many of these questions as you can. Without having to type the calculations into the calculator, you may perform the 0.35 x 10 and the 8 - 3.5, saving time.

#### The owner of a convenience store examines his Saturday receipts to determine the typical number of things purchased. What was the typical number of purchases?

Correct! Wrong!

Explanation:
This is a question of weighted means. It is possible to transform the frequencies into weights.
Count all the items to determine their 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
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

#### In 2017–18, the San Francisco Rams spent \$285 million on "playing staff wages." 15% of that was additional money they spent on "coaching staff wages." These two sums made up a total of 75% of the staff's salaries. How much money, to the nearest quarter million, did the staff's entire wage bill come to?

Correct! Wrong!

Explanation:
Calculate the total playing and staff salaries.
\$285,000,000 x 1.15 = \$327.75 million.
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

#### This is the income for a medium-to-large Australian company. All figures are reported in Australian dollars. Writing had a profit margin of 52% in March while teaching had a profit margin of 40%. Which one of teaching or writing earned a bigger profit in March, and by what percentage, based on the revenue from the table?

Correct! Wrong!

Explanation:
Find each one's profit:
Teaching: 0.4 x 130,000 = \$52,000
Writing: 0.52 x 101,000 = \$52,520
Calculate the difference in percentage between the two:
52,520/52000 = 1.01
Therefore, writing has a higher profit by 1%.

#### This is the income for a medium-to-large Australian company. All figures are reported in Australian dollars. In the three months shown in the table, how much of this company's teaching revenue was generated in February?

Correct! Wrong!

Explanation:
Find the entire amount of teaching income:
120 + 145 + 130 = 395
Calculate the revenue for February as a percentage of that:
145/395 = 0.367… = 37% to the nearest percentage point

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