# UCAT Quantitative Reasoning Test #4

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#### 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? Correct! Wrong!

Explanation:
Annual tax paid within 4th bracket = (£1,900 x 12) – £17,890 = £4,910
Income within 4th bracket = £4,910 / 0.28 = £17,535.71 (2dp)
Post-tax Salary = (£87,850 + £17,535.71) – £22,800 = £82,585.71 (2dp) = £82,590 to the nearest £10

#### 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). Benny makes a monthly tax payment of £1,450. What is his taxable income per year? Correct! Wrong!

Explanation:
Annual tax = £1,450 x 12 = £17,400, i.e. in 3rd tax bracket
Tax paid within 3rd bracket = £17,400 – £4,990 = £12,410
Income within 3rd bracket = £12,410 / 0.25 = £49,640
Total income = £36,250 + £49,640 = £85,890

#### 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). 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? Correct! Wrong!

Explanation:
Old tax = £4,990 + [ 25% x (£80,000 – £36,250) ] = £15,927.50
New tax = £17,890 + [ 28% x (£90,000 – £87,850) ] = £18492
Increase = £18492 – £15927.50 = £2564.50

#### The table displays the total tax (\$) paid on the taxable income for the year. 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. Lennie's annual salary is \$63,000. How much tax does she pay on her income? Correct! Wrong!

Explanation:
Total Tax = \$6,579.20 + [ 22% x (\$63,000 – \$44,120) ]
= \$6,579.20 + (22% x \$1,880) = \$6,579.20 + \$4,154
= \$10,732.80

#### The table displays the total tax (\$) paid on the taxable income for the year. 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. \$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? Correct! Wrong!

Explanation:
Annual Tax = \$6,579.20 + [ 22% x (\$50,000 – \$44,120) ]
= \$6,579.20 + (22% x \$5,880) = \$6,579.20 + \$1,293.60 = \$7,872.80 Average tax rate = 7,872.80 / 50,000 x 100 = 16% (2sf)

#### The table displays the total tax (\$) paid on the taxable income for the year. 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. Sylvia's yearly salary is \$23,158. How much tax does she pay on her income? Correct! Wrong!

Explanation:
Total Tax = \$1,440 + [ 16% x (\$23,158 – \$12,000) ]
= \$1,440 + (16% x \$11,158) = \$1,440 + \$1,785.28
= \$3,225.282.80

#### The table displays the total tax (\$) paid on the taxable income for the year. 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. 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? Correct! Wrong!

Explanation:
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
Old tax = \$1,440 + [ 16% x (\$38,000 – \$12,000) ] = \$5,600
New tax = \$1,584 + [ 16% x (\$38,000 – \$13,200) ] = \$5,552 (\$48 lower)

#### 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. 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? Correct! Wrong!

Explanation:
Calculate the average speed using the units' conversions to meters and seconds.
1 hour = 60 minutes = 60 x 60 seconds = 3600 s
10 km = 10,000 m
So in metres per second:
10000 / 3600 = 2.777… = 2.8 m/s
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.

#### 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. 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? Correct! Wrong!

Explanation:
Calculate his previous and current costs, then calculate the difference in percentage.
The supper deal and coffee were his previous expenses:
2.75 + 3.00 = £5.75
His new costs are:
1.50
Use the formula:
Multiplier = New Value / Old Value
Multiplier = 1.50 / 5.75 = 0.26….

0.26… = 74% percentage decrease – Option C.
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.
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.

#### ● All figures in the table are in kilograms. ● 1 ml water = 1g Which of the subsequent claims is factually incorrect? Correct! Wrong!

Explanation:
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.
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.

#### ● All figures in the table are in kilograms. ● 1 ml water = 1g 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? Correct! Wrong!

Explanation:
1. Find the mass of coffee used in each ratio:
90% was used at a ratio of 1:18:
0.9 x 200,000 = 180,000
10% was used at a ratio of 1:20
0.1 x 200,000 = 20,000
2. Find the volume of coffee produced:
Find the volume of coffee made from this mass:
1g = 1ml
180,000 was used in the ratio 1:18 so:
180,000 x 18 = 3,240,000Kg so 3,240,000L
20,000 was used in the ratio 1:20 so:
20,000 x 20 = 400,000Kg so 400,000L
3,240,000 + 400,000 = 3,640,000L – D.
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.