UCAT Quantitative Reasoning Test #4 — Questions and Answers
Question 1: The table displays the total tax paid (in pounds) on the taxable income for the year. <br> For instance, someone with a £30,000 annual taxable income will pay £895 plus 15% of (£30,000 - £8,950). <br> Maria pays income tax of £1,900 each month. What is her annual pay, net of taxes, to the closest £10? How much of her monthly income should she save, roughly speaking?
- £84,590
- £82,590 (Correct answer)
- £85,590
- £86,590
Correct answer: £82,590
Explanation: <br> Annual tax paid within 4th bracket = (£1,900 x 12) – £17,890 = £4,910 <br> Income within 4th bracket = £4,910 / 0.28 = £17,535.71 (2dp) <br> Post-tax Salary = (£87,850 + £17,535.71) – £22,800 = £82,585.71 (2dp) = £82,590 to the nearest £10
Question 2: The table displays the total tax paid (in pounds) on the taxable income for the year. <br> For instance, someone with a £30,000 annual taxable income will pay £895 plus 15% of (£30,000 - £8,950). <br> Benny makes a monthly tax payment of £1,450. What is his taxable income per year?
- £72,840
- £81,540
- £68,490
- £85,890 (Correct answer)
Correct answer: £85,890
Explanation: <br> Annual tax = £1,450 x 12 = £17,400, i.e. in 3rd tax bracket <br> Tax paid within 3rd bracket = £17,400 – £4,990 = £12,410 <br> Income within 3rd bracket = £12,410 / 0.25 = £49,640 <br> Total income = £36,250 + £49,640 = £85,890
Question 3: The table displays the total tax paid (in pounds) on the taxable income for the year. <br> For instance, someone with a £30,000 annual taxable income will pay £895 plus 15% of (£30,000 - £8,950). <br> Beth receives a promotion at work, and her pre-tax pay increases from £80,000 to £90,000. How big of a difference is there in the tax she pays?
- £2564.50 (Correct answer)
- £1359.50
- £2672.00
- £10335.50
Correct answer: £2564.50
Explanation: <br> Old tax = £4,990 + [ 25% x (£80,000 – £36,250) ] = £15,927.50 <br> New tax = £17,890 + [ 28% x (£90,000 – £87,850) ] = £18492 <br> Increase = £18492 – £15927.50 = £2564.50
Question 4: The table displays the total tax ($) paid on the taxable income for the year. <br> For instance, a person with a $30,000 annual taxable income will pay $1,440 in addition to $12,000 + 16 percent of that amount. <br> Lennie's annual salary is $63,000. How much tax does she pay on her income?
- $9,600
- $5,593.00
- $12,660.00
- $10,732.80 (Correct answer)
Correct answer: $10,732.80
Explanation: <br> Total Tax = $6,579.20 + [ 22% x ($63,000 – $44,120) ] <br> = $6,579.20 + (22% x $1,880) = $6,579.20 + $4,154 <br> = $10,732.80
Question 5: The table displays the total tax ($) paid on the taxable income for the year. <br> For instance, a person with a $30,000 annual taxable income will pay $1,440 in addition to $12,000 + 16 percent of that amount. <br> $50,000 is Daniel's taxable income per year. What is the average income tax rate he pays over the course of his full paycheck, to the closest percent?
- 15%
- 16% (Correct answer)
- 17%
- 18%
Correct answer: 16%
Explanation: <br> Annual Tax = $6,579.20 + [ 22% x ($50,000 – $44,120) ] <br> = $6,579.20 + (22% x $5,880) = $6,579.20 + $1,293.60 = $7,872.80 <b r> Average tax rate = 7,872.80 / 50,000 x 100 = 16% (2sf)
Question 6: The table displays the total tax ($) paid on the taxable income for the year. <br> For instance, a person with a $30,000 annual taxable income will pay $1,440 in addition to $12,000 + 16 percent of that amount. <br> Sylvia's yearly salary is $23,158. How much tax does she pay on her income?
- $3,241.28
- $2,778.96
- $4,096.28
- $3,225.28 (Correct answer)
Correct answer: $3,225.28
Explanation: <br> Total Tax = $1,440 + [ 16% x ($23,158 – $12,000) ] <br> = $1,440 + (16% x $11,158) = $1,440 + $1,785.28 <br> = $3,225.282.80
Question 7: The table displays the total tax ($) paid on the taxable income for the year. <br> For instance, a person with a $30,000 annual taxable income will pay $1,440 in addition to $12,000 + 16 percent of that amount. <br> The lower and upper limits of each income tax bracket rise by 10% over the course of a year. How does Emma's annual tax payment of $38,000 on her salary vary as a result?
- It ends up $48 higher than before
- It ends up $48 lower than before (Correct answer)
- It ends up $96 higher than before
- It ends up $96 lower than before
Correct answer: It ends up $48 lower than before
Explanation: <br> The tax paid at the top of the bottom bracket's lowest bracket becomes $13,200, and the lowest upper bound becomes 12% x 13,200 = $1,584 <br> Old tax = $1,440 + [ 16% x ($38,000 – $12,000) ] = $5,600 <br> New tax = $1,584 + [ 16% x ($38,000 – $13,200) ] = $5,552 ($48 lower)
Question 8: For the past six weeks, Henry has maintained this daily plan while working from home. It runs from Monday through Friday. Sundays and Saturdays have always been his days off from work. <br> He leaves the house at 7 a.m. and arrives back at 8 a.m. What was his average speed over the course of his 10 km run, to the nearest 0.1 m/s?
- 2.6 m/s
- 2.5 m/s
- 2.8 m/s (Correct answer)
- 10 m/s
Correct answer: 2.8 m/s
Explanation: <br> Calculate the average speed using the units' conversions to meters and seconds. <br> 1 hour = 60 minutes = 60 x 60 seconds = 3600 s <br> 10 km = 10,000 m <br> So in metres per second: <br> 10000 / 3600 = 2.777… = 2.8 m/s <br> A common snare is that all of the answers are given in m/s. Be careful not to choose the answer 10 km/h hastily because he has been running at 10 km/h.
Question 9: Henry has followed this daily pattern while working from home for the past six weeks, Monday through Friday. He has never worked on Saturdays and Sundays. <br> When he had an office job, Henry would buy a Tescbury's meal deal for lunch for £3.00 and a coffee for £2.75 on the way in. These were all of his expenses. He no longer drinks coffee in the morning and calculates that a portion of his cooked lunch costs £1.50. What is his cost reduction % throughout a workweek?
- 26%
- 25%
- 75%
- 74% (Correct answer)
Correct answer: 74%
Explanation: <br> Calculate his previous and current costs, then calculate the difference in percentage. <br> The supper deal and coffee were his previous expenses: <br> 2.75 + 3.00 = £5.75 <br> His new costs are: <br> 1.50 <br> Use the formula: <br> Multiplier = New Value / Old Value <br> Multiplier = 1.50 / 5.75 = 0.26…. <br> <br> 0.26… = 74% percentage decrease – Option C. <br> Timing Tip: In UCAT Quantitative Reasoning, percentage reduction is one of the most frequently evaluated skills. Learn how to use the multiplier method to save time. <br> It is not necessary to calculate the numbers for five days' worth of purchases because the percentage difference will be the same for one day as it will be for five.
Question 10: ● All figures in the table are in kilograms. <br> ● 1 ml water = 1g <br> <br> Which of the subsequent claims is factually incorrect?
- Except for one year, restaurants drank more coffee.
- Cafés’ coffee use increased by 10% each year. (Correct answer)
- Every year, more coffee is consumed overall.
- Hotel utilization of coffee beans increased by about 3.7% between 2012–13 and 2013–14.
Correct answer: Cafés’ coffee use increased by 10% each year.
Explanation: <br> The rise between 2010-11 and 2011-12 was 200,000/180,000 = 1.11, which is an increase of 11.1% rather than 10.1%. Other figures represent 10% increase, but not during the initial time. <br> Timing Tip: Options that only mention one category should be prioritized first since they only call for the analysis of a single subset of data.
Question 11: ● All figures in the table are in kilograms. <br> ● 1 ml water = 1g <br> <br> The optimal ratio for coffee preparation is 1:18 for coffee bean mass to water mass. In cafes in 2011–12, this ratio was utilized to process 90 percent of the coffee beans that were consumed. 1:20 was the mass ratio for coffee beans to water in the remaining samples. How many litres of coffee were served by cafes in 2011–12, assuming that coffees just contain water and coffee?
- 3,276,000 L
- 3,600,000 L
- 3,640,000 L (Correct answer)
- 4,000,000 L
Correct answer: 3,640,000 L
Explanation: <br> 1. Find the mass of coffee used in each ratio: <br> 90% was used at a ratio of 1:18: <br> 0.9 x 200,000 = 180,000 <br> 10% was used at a ratio of 1:20 <br> 0.1 x 200,000 = 20,000 <br> 2. Find the volume of coffee produced: <br> Find the volume of coffee made from this mass: <br> 1g = 1ml <br> 180,000 was used in the ratio 1:18 so: <br> 180,000 x 18 = 3,240,000Kg so 3,240,000L <br> 20,000 was used in the ratio 1:20 so: <br> 20,000 x 20 = 400,000Kg so 400,000L <br> 3,240,000 + 400,000 = 3,640,000L – D. <br> Common Trap: Remember that not all of the coffee will be made in the 1:18 ideal ratio. If this were true, the answer would be 3,640,000 L.
UCAT Quantitative Reasoning Test #4
The table displays the total tax paid (in pounds) on the taxable income for the year.
For instance, someone with a £30,000 annual taxable income will pay £895 plus 15% of (£30,000 - £8,950).
Maria pays income tax of £1,900 each month.
What is her annual pay, net of taxes, to the closest £10? How much of her monthly income should she save, roughly speaking?