Sixty divided by three equals twenty. The difference between seven and two is five; eight times five equals forty. Their sum is sixty. Then subtracting four times three (twelve) gives sixty minus twelve which equals forty-eight.

Price after tax of 10% is 110 dollars, hence 110% represents 110 dollars, therefore 100% represents $100, also meaning the item is 100 dollars before tax.

Since price of item is 2/3 of a original number,

100/(2/3)=150, which is the original number.

1 hour and 45 minutes equals 1.75 hours, and 1 hour and 30 minutes equals 1.5 hours. Let the original speed be V. Then V multiplied by 1.75 equals the same distance as (V plus five) multiplied by 1.5.

Setting up the equation:

1.75V = 1.5(V + 5)
= 1.5V + 7.5

Subtracting 1.5V yields
0.25V = 7.5, so V equals thirty kilometers per hour.

Students in only drama equal 22 – 14, which is eight. Students in only sports equal 28 – 14, which is 14. The difference is 14 – 8, which equals 6.

Let F be the father’s age and (60 – F) be the sum of the children’s ages.

Five years ago:

• Father’s age was F – 5.
• The children’s total age was (60 – F) – 10, as both children were 5 years younger, which simplifies to 50 – F.

The condition states: F – 5 = 2 × (50 – F)

Now, solve for F:

1. F – 5 = 100 – 2F
2. Add 2F to both sides: 3F – 5 = 100
3. Add 5 to both sides: 3F = 105
4. Divide both sides by 3: F = 35

Thus, the father’s age is 35.

Calculate the total number of outfits for Mark by multiplying the number of shoes and hats:
Mark’s outfits = 5 × 3 = 15.

Calculate the total number of outfits for Laura:
Laura’s outfits = 4 × 4 = 16.

Compare the totals:
Since 16 (Laura) is 1 more than 15 (Mark), Laura has 1 more outfit than Mark.

Convert each container’s volume to milliliters:

Container A: 2 L 320 mL = (2 × 1000) + 320 = 2320 mL
Container B: 750 mL (already in mL)
Container C: 1 L 890 mL = (1 × 1000) + 890 = 1890 mL
Container D: 0.55 L = 0.55 × 1000 = 550 mL
Find the total volume by adding all the milliliters:
Total = 2320 + 750 + 1890 + 550 = 5510 mL

Compute the average volume by dividing the total by 4:
Average = 5510 mL ÷ 4 = 1377.5 mL

Convert the average back into liters and milliliters:
1377.5 mL = 1 L (1000 mL) + 377.5 mL

Answer: Option A – 1 L 377.5 mL.

Let the number of red marbles be R. Then the number of blue marbles is R – 20. Let the number of green marbles be G.

Since the total number of marbles is 84, we have:
R + (R – 20) + G = 84
2R + G = 104

The probability of drawing a blue marble is given as (R – 20)/84, and it equals 2/7. So:
(R – 20)/84 = 2/7
Multiply both sides by 84:
R – 20 = (2/7) × 84
Since (2/7) × 84 = 24, we get:
R – 20 = 24
Therefore, R = 44.

Substitute R = 44 into Equation 1:
2(44) + G = 104
88 + G = 104
G = 104 – 88 = 16.
Number of Green Marbles is 16

Let the width be w. Since the length is 3 times the width, the length is 3w.
The perimeter of the rectangle is given by 2(w + 3w) = 8w, and we know this equals 100 cm.
So, 8w = 100, which means w = 12.5 cm.
The length is 3w = 3 × 12.5 = 37.5 cm.
When the rectangle is divided into 4 congruent rectangles by cutting halfway along both the width and the length, each smaller rectangle has:
• Width = 12.5 ÷ 2 = 6.25 cm
• Length = 37.5 ÷ 2 = 18.75 cm
The perimeter of one smaller rectangle is 2(6.25 + 18.75) = 2 × 25 = 50 cm.

When dividing any integer by 12, the possible remainders range from 0 to 11.
Since we’re focusing on even numbers, the remainders must also be even.
Identifying even remainders:

The even numbers between 0 and 11 are: 0, 2, 4, 6, 8, and 10.
Verifying each option:

Option A: 0, 2, 4, 6, 8, 10
This includes all possible even remainders when an even number is divided by 12.
Option B: 0, 1, 2, 3, 4, 5
This includes both even and odd remainders.
Option C: 1, 3, 5, 7, 9, 11
This includes only odd remainders.
Option D: 2, 4, 6, 8, 10, 12
This includes an invalid remainder (12) since remainders must be less than the divisor.
Option E: 0, 2, 4, 6, 8, 10, 12
This also includes an invalid remainder (12).

We analyze the sum of five numbers chosen from {4, 7, 9, 11, 12, 15}.

Step 1: Minimum and Maximum Sums
The smallest possible sum: 4 + 7 + 9 + 11 + 12 = 43
The largest possible sum: 7 + 9 + 11 + 12 + 15 = 54
Since 43 is the minimum sum and 54 is the maximum sum, the sum can be both below and above 45, meaning option (5) is incorrect.

Step 2: Checking Multiples of 5
The sum can be 43, 45, 47, 49, 51, 54, etc.
45 is a multiple of 5, meaning the sum is not always a multiple of 5, so option (1) is incorrect.
Step 3: Checking Even Totals
The sum of five numbers depends on how many evens and odds we choose.
The numbers 4, 12 are even, while 7, 9, 11, 15 are odd.
Since choosing five numbers always includes at least three odd numbers, the sum can be either odd or even, so option (2) is incorrect.
Step 4: Checking Multiples of 4
The sum can be 43, 45, 47, 49, 51, 54, etc.
Among these, 54 is a multiple of 4, meaning the sum can be a multiple of 4, so option (3) is correct.
Step 5: Checking Multiples of 3
The possible sums are 43, 45, 47, 49, 51, 54.
45, 51, and 54 are all multiples of 3, meaning the sum can be a multiple of 3, so option (4) is incorrect.

Step 1: Understanding the Quadrilateral
Since the quadrilateral has no parallel sides, it is not a parallelogram, trapezium, or rectangle.
Since it has exactly two right angles, it is not a kite or a rhombus (which usually have zero or two lines of symmetry).
A quadrilateral with two right angles and no parallel sides is usually an irregular quadrilateral, such as a trapezium with two right angles and uneven non-parallel sides.
The fact that one diagonal is longer than the other further confirms that the quadrilateral is not symmetric.

Step 2: Checking for Lines of Symmetry
A line of symmetry divides the shape into two identical mirror halves.
Since the shape has unequal opposite sides and different diagonal lengths, it cannot be folded onto itself along any axis.
This means the quadrilateral has 0 lines of symmetry.

Step 1: Let the total number of seeds be x.
First section: 1/3 of x → Seeds planted = x/3

Remaining seeds: x – x/3 = 2x/3

Second section: 1/2 of the remaining seeds → Seeds planted = (1/2) × (2x/3) = x/3

Remaining seeds: (2x/3) – (x/3) = x/3

Third section: 1/4 of the remaining seeds → Seeds planted = (1/4) × (x/3) = x/12

Remaining seeds: (x/3) – (x/12) = (4x/12) – (x/12) = 3x/12 = x/4

Fourth section: The farmer has 10 seeds left, meaning x/4 = 10.

Step 2: Solve for x
x/4 = 10
Multiply both sides by 4:
x = 40

Let the number of red discs be R.
Then the number of blue discs is R + 4, and the number of yellow discs is 2R.
The total number of discs is given by:
R + (R + 4) + 2R = 4R + 4.
Set up the equation with the total provided:
4R + 4 = 40.
Solve for R:
4R = 36
R = 9.
Now, the number of blue discs = 9 + 4 = 13.
Therefore, the probability of selecting a blue disc = number of blue discs / total discs = 13/40.

Let
A = price of a sandwich (with GST)
B = price of a salad (with GST)
C = price of a smoothie (with GST)

We are given:
A + C = 8.80
B + C = 7.70
A + B + C = 11.55

Notice that subtracting (A + C) from (A + B + C) gives B:
B = (A + B + C) − (A + C) = 11.55 − 8.80 = 2.75

Similarly, subtracting (B + C) from (A + B + C) gives A:
A = (A + B + C) − (B + C) = 11.55 − 7.70 = 3.85

Thus, the total cost of a sandwich and a salad is:
A + B = 3.85 + 2.75 = 6.60

First convert each pack to kilograms and calculate cost per kg:

A: 2.00 kg → 18.00 ÷ 2.00 = 9.00 dollars per kg

B: 750 g = 0.75 kg → 6.75 ÷ 0.75 = 9.00 dollars per kg

C: 450 g = 0.45 kg → 4.95 ÷ 0.45 = 11.00 dollars per kg

D: 1.20 kg → 11.28 ÷ 1.20 = 9.40 dollars per kg

E: 3.20 kg → 26.88 ÷ 3.20 = 8.40 dollars per kg

The lowest cost per kilogram is 8.40 dollars per kg, so the best value is Option E.

First, convert the actual distance to metres:   Actual distance = 12 km 45 m = (12 × 1000) + 45 = 12000 + 45 = 12045 m

Next, convert the incorrectly recorded distance to metres: Incorrect distance = 45 km 12 m = (45 × 1000) + 12 = 45000 + 12 = 45012 m

Find the difference by subtracting the actual distance from the incorrect distance:   Difference = 45012 m – 12045 m = 32967 m

Since Vancouver is 8 hours behind London, when it is 7:15 AM in Vancouver, London’s time is 7:15 AM + 8 hours = 3:15 PM.
New Delhi is 5 hours and 30 minutes ahead of London. Therefore, add 5 hours and 30 minutes to London’s time: 3:15 PM + 5:30 = 8:45 PM.
Thus, when it is 7:15 AM in Vancouver, the time in New Delhi is 8:45 PM.

Let the number of stickers Mia has be x.
Then Liam has 6x stickers and Noah has 2x stickers.
According to the problem, the difference between Liam’s and Noah’s stickers is 24. That is, 6x – 2x = 4x = 24.
Solve for x: 4x = 24 gives x = 6.
The ratio of Liam’s stickers to Noah’s stickers is (6x)/(2x) = 6/2 = 3.
Thus, Liam has 3 times as many stickers as Noah. The correct answer is 3.

Represent the four possible orientations as a cycle in clockwise order:
Index 0: North-East
Index 1: South-East
Index 2: South-West
Index 3: North-West

The arrow starts facing south-west, which corresponds to index 2.

The arrow makes 76 quarter-turns clockwise. Since 76 is divisible by 4, there is no net change. It remains at index 2 (south-west).

Next, it makes 55 quarter-turns anti-clockwise. Since 55 divided by 4 gives remainder 3, subtract 3 quarter turns from the current index: which is equivalent to index 3. The arrow is now facing north-west.

Finally, it makes 89 quarter-turns clockwise. Since 89 divded by 4 gives remainder 1, add 1 quarter turn to the current index:
This corresponds to north-east.

Thus, after all the turns, the arrow is facing north east.

Let the father’s age be represented as 10a + b, where a is the tens digit and b is the ones digit. Reversing the digits gives 10b + a. According to the problem,

10b + a = (10a + b) + 36.

Subtract 10a + b from both sides:

(10b – b) – (10a – a) = 36
9b – 9a = 36

Divide by 9:

b – a = 4.                        (1)

We are also given that the product of the digits is 12:

a × b = 12.                        (2)

Now, list the pairs of single-digit numbers whose product is 12:

2 and 6 (2 × 6 = 12)
3 and 4 (3 × 4 = 12)
Next, check which pair satisfies equation (1): b – a = 4.
For the pair 2 and 6:
6 – 2 = 4, which fits.
For the pair 3 and 4:
4 – 3 = 1, which does not fit.

Thus, a = 2 and b = 6.
The ones digit of his age is therefore 6.

Marcus wins a round whenever his spin is higher than Jordan’s spin. We can break it down by looking at each possible outcome for Marcus:

• When Marcus spins a 1 (which happens 2 times), he cannot win because no number is lower than 1.
• When Marcus spins a 2 (4 times), he wins only if Jordan’s spin is a 1. Since Jordan has three 1s overall, at most three rounds with a 2 from Marcus can beat a 1 from Jordan. Thus, wins from spinning 2 = 3.
• When Marcus spins a 3 (3 times), his spin beats any Jordan spin of 1 or 2. Jordan’s combined count for 1s and 2s is 3 + 3 = 6. This is more than enough to cover all three rounds where Marcus spins a 3, so wins from spinning 3 = 3.
• When Marcus spins a 4 (3 times), his spin wins against any Jordan spin of 1, 2, or 3. Jordan’s combined count for 1s, 2s, and 3s is 3 + 3 + 4 = 10, which easily covers the three rounds with a 4 from Marcus. Thus, wins from spinning 4 = 3.

Adding these up: 0 (from 1s) + 3 (from 2s) + 3 (from 3s) + 3 (from 4s) = 9 rounds.

Let the number of tickets sold on Monday be x.
• Tuesday’s tickets = (2/3) × x
• Wednesday’s tickets = half of Tuesday’s = (1/2) × (2/3 × x) = (1/3) × x
• Thursday’s tickets = 150

The total tickets sold are:
x + (2/3)x + (1/3)x + 150 = 600

Combine like terms for Monday, Tuesday, and Wednesday:
x + (2/3)x + (1/3)x = x + x = 2x

So the equation becomes:
2x + 150 = 600

Subtract 150 from both sides:
2x = 450

Divide both sides by 2:
x = 225

Thus, 225 tickets were sold on Monday.

Step 1: Find the sum in the numerator.
1/3 + 2/5 + 3/7 = 122/105
Step 2: Compute the denominator.
1/2 – 1/8 = 3/8
Step 3: Divide the numerator by the denominator.
(122/105) / (3/8) = 976/315 = 3 31/315 ≈ 3.1

Thus, the value is closest to 3.1.

Assume Alex is at point 0. Since Alex and Chris are 350 m apart, let Chris be at point 350. Given that Alex and Ethan are 950 m apart, Ethan is at point 950.

Step 2 – Determine Bella’s position:
Bella lives between Alex and Chris. Let the distance from Alex to Bella be x. Then the distance from Bella to Chris is 350 – x. We are told that Bella lives 1.5 times as far from Alex as from Chris, so:
x = 1.5 × (350 – x)
Solve for x:
x = 525 – 1.5x
2.5x = 525
x = 210
So, Bella is at point 210 and her distance from Chris is 350 – 210 = 140 m.

Step 3 – Locate Diana’s house:
Since Bella and Diana are equally distant from Chris, Diana must be 140 m away from Chris. Because the order is Alex, Bella, Chris, Diana, Ethan, Diana is to the right of Chris. Thus, Diana’s position is:
350 + 140 = 490 m

Step 4 – Find the distance from Diana to Ethan:
Distance from Diana to Ethan = Ethan’s position – Diana’s position = 950 – 490 = 460 m

Let x be the whole number.

Step 1 – Use the first condition:
7x – 2 < 100
Add 2 to both sides: 7x < 102
Divide by 7: x < 102/7, which is approximately 14.57
Since x is a whole number, the maximum possible value is 14.

Step 2 – Use the second condition:
5x + 8 > 60
Subtract 8 from both sides: 5x > 52
Divide by 5: x > 52/5, which is 10.4
Since x is whole, the minimum possible value is 11.

Step 3 – Identify all possible values:
x can be 11, 12, 13, or 14.

Step 4 – Find the sum:
11 + 12 + 13 + 14 = 50

Let C be the weight of the empty container and F be the weight of the flour when the container is completely full.

From the problem, when the container is 3/4 full:
C + (3/4)F = 350

And when it is 1/4 full:
C + (1/4)F = 190

Subtract the second equation from the first:
[C + (3/4)F] – [C + (1/4)F] = 350 – 190
(3/4 – 1/4)F = 160
(1/2)F = 160
F = 320 grams

Now, substitute F = 320 into the second equation to find C:
C + (1/4)*320 = 190
C + 80 = 190
C = 110 grams

Finally, determine the weight when the container is 5/8 full:
Total weight = C + (5/8)F
= 110 + (5/8)*320
= 110 + 200
= 310 grams

Step 1: Identify Emma’s departure and arrival times
Emma takes the third ferry from Eastport to Westhaven.
Departure: 13:25
Arrival: 14:10

Step 2: Identify the next ferry from Westhaven to Eastport
The next ferry from Westhaven to Eastport departs at 15:15 and arrives at 16:00.

Step 3: Calculate her time in Westhaven
She arrives at 14:10 and departs at 15:15.
Time spent in Westhaven: 15:15 – 14:10 = 1 hour 5 minutes.

The three interior angles of any triangle add up to 180 degrees.

Add the given angles: 50 + 60 = 110.

Subtract from 180: 180 − 110 = 70.

Answer: 70° (Choice A)

To solve this, we need to find the smallest number that is divisible by 1, 2, 3, 4, and 5.
This is the Lowest Common Multiple (LCM) of 1, 2, 3, 4, and 5.

Step 1: Prime Factorization
1 = 1
2 = 2
3 = 3
4 = 2²
5 = 5
Step 2: Find the LCM
The LCM takes the highest powers of all prime numbers present:

LCM(1, 2, 3, 4, 5) = 2² × 3 × 5 = 60

So, the smallest number of marbles Alice could have is 60

Step 1: Find the side length of the original square
The area of the original square is 900 cm².
Since area = side × side, the side length is 30 cm (since 30 × 30 = 900).

Step 2: Find the area of the first smaller square
Each side is reduced to one-third, so the new side length is 30 ÷ 3 = 10 cm.
The area of this square is 10 × 10 = 100 cm².

Step 3: Find the area of the second smaller square
Each side is further reduced to one-half, so the new side length is 10 ÷ 2 = 5 cm.
The area of this square is 5 × 5 = 25 cm².

The speed of the train = 108 km/h
The speed of the bus = 72 km/h
Time = 24 seconds
Step 1: Convert the speeds to meters per second
To convert from km/h to m/s, we use the conversion factor:
1 km/h = 5/18 m/s.

Train speed in m/s:
108 × (5/18) = 30 m/s

Bus speed in m/s:
72 × (5/18) = 20 m/s

Step 2: Calculate the distance each has traveled in 24 seconds
Distance traveled by the train:
Distance = Speed × Time = 30 m/s × 24 seconds = 720 meters

Distance traveled by the bus:
Distance = Speed × Time = 20 m/s × 24 seconds = 480 meters

Step 3: Find the difference
The difference in the distance traveled by the train and the bus is:
720 meters – 480 meters = 240 meters.

Final Answer:
The faster train has moved 240 meters more than the slower bus during the 24 seconds.

Step 1: Determine each person’s work rate.

Ramiro works from 8:45 am to 9:30 am, which is 45 minutes.
His work rate is 1 job per 45 minutes, or 1/45 of the job per minute.

Naomi works from 8:30 am to 9:00 am, which is 30 minutes.
Her work rate is 1 job per 30 minutes, or 1/30 of the job per minute.

Step 2: Find their combined work rate when working together.

Add the two rates: 1/45 + 1/30.
To add, find a common denominator.
1/45 can be written as 2/90 and 1/30 as 3/90.
Together, they work at (2/90 + 3/90) = 5/90, which simplifies to 1/18 of the job per minute.
Step 3: Determine the time needed when working together.

The time taken to complete the whole job is the reciprocal of their combined rate.
That is, time = 1 / (1/18) = 18 minutes.
Step 4: Calculate the finishing time on Wednesday.

They start at 8:40 am. Adding 18 minutes gives:
8:40 am + 18 minutes = 8:58 am.

First, calculate the percentage increase for each species.

For the maggots:

They increased from 10 to 100.
The increase is 100 – 10 = 90.
The percentage increase is (90 ÷ 10) × 100 = 900%.
For the ants:

They increased from 20 to 50.
The increase is 50 – 20 = 30.
The percentage increase is (30 ÷ 20) × 100 = 150%.
Now, compare the two percentages.

The maggots increased by 900%, while the ants increased by 150%.
The difference in percentage increase is 900% – 150% = 750% greater maggots growth.

Step 1 – Determine the lap time for each vehicle.
Convert speeds to km per minute by dividing by 60.
• Car: 80 km/h = 80/60 = 4/3 km/min
• Motorcycle: 72 km/h = 72/60 = 1.2 km/min
• Bicycle: 48 km/h = 48/60 = 0.8 km/min

Now, compute the lap time (time = distance ÷ speed):
• Car’s lap time = 2 km ÷ (4/3 km/min) = 2 × (3/4) = 1.5 minutes
• Motorcycle’s lap time = 2 km ÷ 1.2 km/min = 1.6667 minutes (or exactly 100 seconds)
• Bicycle’s lap time = 2 km ÷ 0.8 km/min = 2.5 minutes

Step 2 – Convert the lap times to seconds for easier comparison.
• Car: 1.5 minutes = 90 seconds
• Motorcycle: 1.6667 minutes = 100 seconds
• Bicycle: 2.5 minutes = 150 seconds

Step 3 – Find the least common multiple (LCM) of the lap times in seconds.
Factor each time into primes:
• 90 = 2 × 3² × 5
• 100 = 2² × 5²
• 150 = 2 × 3 × 5²

The LCM is given by the highest powers of each prime:
• For 2: highest power is 2²
• For 3: highest power is 3²
• For 5: highest power is 5²
So, LCM = 2² × 3² × 5² = 4 × 9 × 25 = 900 seconds

Step 4 – Convert 900 seconds back to minutes:
900 seconds ÷ 60 = 15 minutes

Thus, all three will meet again at the starting point after 15 minutes.