# UCAT Quantitative Reasoning Test #2

#### What is the series' next number?

13, 9, 14, 8, 15,

Correct answer: 7

Examine the distinctions between the terms, which are listed in brackets between the terms.

13 (-4) 9 (+5) 14 (-6) 8 (+7) 15…

The result of subtracting 8 from 15 should be the next term.

15-8=7.

#### What is the series' next number?

45, 15, 30, 30,10, 20,

Correct answer: 20

The series has a rule:

÷3, ×2, ×1….the cycle continues.

As a result of (30÷3=)10, and (10×2=)20, we have 20×1=20.

#### Clark is 15 years old, and his younger sister is the same age as him. When Clark turns 19, how old will his sister be?

Correct answer: 34

Clark's sister is twice his age, thus she is now 15*2=30 years old. In four years, Clark will be 19, which means his sister will be (30+4)=34.

#### There are 6,000 toilet sinks in a plumber's home. Over the next four days, he plans to install 20% of all sinks. How many toilet sinks will he install on each of the four days if he divides his work evenly?

Correct answer: 300

To begin, we must determine how many toilet sinks will be built over the next four days.

We can use the 10% shortcut to figure out what 20% of 6,000 is:

10% of 6,000 equals 600 (omit one 0), hence 20% equals 600*2=1,200.

Now, assuming the plumber intends to split his work evenly over four days, we simply divide 1,200 by 4.

1,200/4=300

#### A Bluetooth speaker will cost you at least $120. Its price increased by 20%, then by another $24. What is the overall price increase for this speaker in percentages?

Correct answer: 40%

The 10 percent -blocks trick can be used to find 20% of 120. 10%=12. As a result, (12×2)=24.

We get 120+24+24=$168 by adding $24.

We must subtract 120 from 168 to arrive at 48. This is the entire amount of money that has increased in value as a result of the price increase. We need to calculate how much 48 out of 120 is. We may gradually add units of 12 until we reach 48 because we already know what 10% of 120 is (12). Fortunately, we need 4 units of 12, which is 4 units of 10% = 40%.

Another option is to write a fraction (48/120) and then reduce or divide it by common divisors.

#### 3/4 cup sugar is required for an 18-cookie recipe. To make two dozen cookies with the same recipe, how much sugar would be required?

Correct answer: 1 cup

3/4 cup sugar is needed for 18 cookies.

We raised the amount of cookies by a factor of (24/18) when we made two dozen cookies. As a result, we need to multiply 3/4 by 24/18 to get the new sugar amount:

3/4×24/18=3×24/4×18= 1

#### Select the expression that best indicates the highest value:

Correct answer: 17/51

With a solid understanding of the 1-20 multiplication chart and fraction-to-decimal conversions, this question can be answered rapidly.

14/49 = divide by 7 to reach 2/7 ~ 0.14×2 ~0.28

15/50 = divide by 5 and get 3/10 = 0.3

17/51= divide by 17 and get 1/3 = 0.33

16/64 = divide by 16 and get = 1/4 = 0.25

#### Every year, a city hosts a comedy festival. In Year 1, the event lasted five weeks and a total of 123,545 tickets were sold. In Year 2, the event lasted for eight weeks, with average weekly ticket sales up by 25%. How many tickets were sold in year 2?

Correct answer: 247,090

Calculate the average weekly sales for the first year.

123,545 in 5 weeks

123,545/5 = 24709 a week

Calculate the sum based on the average weekly sales in Year 2:

Old Value x Multiplier = New Value

24,709 x 1.25 = 30,886.25

The festival lasted eight weeks, so:

30,886.25 x 8 = 247,090 tickets

#### For a limited time, Learning101 is giving a discount on their online Spanish course. They are giving you a 40% discount. You will receive an additional 10% discount on the new pricing if you pay in advance. In terms of a proportion of the original price, what is the cost of paying up front today?

Correct answer: 54%

Locate the first discount.

The new price is 0.6 times the full amount due to the 40% discount.

Look for a second discount.

Because there is a 10% discount, the price for paying in advance is 0.9 times the discounted price.

0.9 x 0.6 = 0.54 – 54%.

#### Town A's domestic fowl population is 20% that of Town B's domestic fowl population. Town C has 75% fowl population of Town A.

What is the domestic fowl population in Town B if there are 252 domestic fowl in Town C?

Correct answer: 1680

Using algebra, connect the population sizes:

Town A's population is referred to as: a

Town B's population is referred to as b.

Town A has a population that is 20 percent that of Town B:

a = 0.2b

Town C's population is referred to as c.

Town C has a population that is 75% that of Town A.

c = 0.75a

To find the value for B, use the value for C.

c = 252

so 0.75a = 252

a = 252/0.75

a = 336

0.2b = a

0.2b = 336

b = 1680

#### In 2017-18, the San Francisco Rams spent $285 million on "playing staff wages." The money they spent on "coaching staff wages" accounted for 15% of the total. These two numbers amounted for 75% of all employee wages.

To the nearest quarter million, what was the overall staff wage bill?

Correct answer: $437 million

Calculate the total wage for both the players and the staff.

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

Calculate the overall cost of the staff bill.

We need to calculate 100 / 75 of $327.75 million, which is 75 percent of the entire wage bill.

327.75 million x 100/75 = $437 million

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