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#### Jed has more than twice as many strawberries as Dianna, but only half as many as Lisa. If Dianna has ‘a' number of strawberries, how many strawberries do Jed, Dianna, and Lisa have in terms of ‘a'?

Correct! Wrong!

Dianna has 'a' strawberries, we know. From the given statement in the question, Jed has 2a+2 strawberries. Lisa has twice as many strawberries as Jed, so she has 4a+4 strawberries. When we add these up, we get 4a+4+2a+2+a = 7a +6.

#### Milk should be thinned to a 3:2 ratio of milk to water. The milkman accidentally added water, resulting in 8 liters of milk that is half water and half milk. What must he add to correct the proportions of the mixture?

Correct! Wrong!

Remember that the final milk-to-water ratio must be 3:2. Now, according to the scenario in the question, we have eight liters of solution with four liters of milk and four liters of water, for a 2:2 ratio. To make it 3:2, we add 2 liters of milk. This results in a total of 6 liters milk and 4 liters water, or a 6:4 ratio that can be simplified to 3:2.

#### A rectangle's width is 2/3 times its length. What is the perimeter of this rectangle if the length is calculated to be 9?

Correct! Wrong!

Because the width of the rectangle is 2/3 of its length, which is 9, the width is 6. As a result, the perimeter is 6+6+9+9 = 30. (The perimeter of a rectangle is calculated by adding the lengths of each of its sides.)

#### A line l passes through the point and is parallel to the y-axis (2,3). What are the gradient (m) and x-intercept?

Correct! Wrong!

Correct answer: m= ∞ , x= (2,0)

Because the given line is parallel to the y-axis and the y-axis slope is infinite, its slope is also infinite. Because the line is defined by x=2, its x intercept will be 2 as well because all of its points are of the form (2,y).

#### What is the equation of the new parabola formed by shifting y = x2 three units to the positive y-axis?

Correct! Wrong!

Correct answer: y = x2 + 3

As the parabola is shifted above, the value of y changes, so we increase y, i.e. the entire function, by 3 units. As a result, y=x2+3

#### A sphere with a diameter of 1 unit is enclosed in a cube with sides of 1 unit each. Find the remaining unoccupied volume inside the cube.

Correct! Wrong!

Using the formula length^3, we can calculate the volume of a cube. We then subtract the volume of the sphere from it to get the empty volume. 1*1*1=1 is the volume of a cube. The volume of the sphere is (4/3)* π *(radius)^3. By plugging in the values, we get (4/3)* π *(0.5) ^3. This is equal to pi/6. When the two are subtracted, the result is 1- π /6.

#### If a triangle's greatest side is A, and the other two sides are B and C. What is the connection between them?

Correct! Wrong!

The largest side is greater than the sum of the two smaller sides and less than the difference of the two smaller sides. As a result, option A is the correct answer.

#### The City Opera House is growing. The city block containing the opera house is currently rectangular in shape, with a total volume of 9600 feet. What is the new volume if the expanded Opera House is 2.5 times as long, wide, and deep as the original structure?

Correct! Wrong!

The volume is equal to the product of the length, width, and height. The original volume of the building is equal to lwh = 9600. The new dimensions are 2.5l x 2.5w x 2.5h, or (lwh) x 2.5 x 2.5 x 2.5 = 15.625(lwh). Given that lwh = 9600, the new volume is 15.625(9600) = 150,000.

#### In a university of 200 people, the number of Psychology majors is 50 less than four times that of Computer Science majors. How many club members are Computer Science majors if one-fifth of the club members are neither Psychology nor Computer Science majors, and no club member is majoring in both Psychology and Computer Science?

Correct! Wrong!

Let P represent the number of Psychology majors and C represent the number of Computer Science majors." One-fifth of the legislators are neither, for a total of 1/5 *200 = 40 legislators. As a result, there are 200 – 40 = 160 Psychology and Computer Science majors, or P + C = 160. According to the clause, the number of Psychology majors is 50 less than 4 times that of Computer Science majors." "P = 4C – 50 is the result of plugging these values into an equation.

#### If the total cost of 20 pairs of shoes is equal to the total revenue generated by the sale of 25 pairs of shoes, what is the percentage of profit or loss made on each pair of shoes sold, assuming each pair of shoes costs the same dollar amount and is sold for the same dollar amount?

Correct! Wrong!

Profit/Loss % = (Sales Price – Cost Price) / Cost Price x 100 is the key formula here. The stem tells us that 20c = 25s, or 4c = 5s, so the sales price to cost price ratio is 4/5.

Let's simplify our Profit/Loss % formula by dividing each term by its cost:
Profit/Loss % = (S/C – C/C) x 100

P/L% = (S/C – 1) x 100 We know that S/C = 4/5 for this problem. So we can plug in and solve:
P/L% = (4/5 – 1) x 100
P/L% = (-1/5) x 100
P/L% = -20% loss

#### Rose spent the entire day sightseeing in the Great Britain. Rose boarded a bus from her hotel and traveled 30 miles through the countryside at an average speed of 15 miles per hour. The bus then stopped in London for lunch before continuing on a three-hour tour of the city's sights at a speed of ten miles per hour. Finally, the bus exited the city and drove the 40 miles back to the hotel. Rose arrived at her hotel exactly two hours after she left London. What was the average rate of the bus for the entire journey?

Correct! Wrong!

To calculate the "Average Rate" of the bus, we know we need to know the Total Distance and Total Time, so let's see how we can use the D = R x T formula

For the first leg of the journey, we know that 30 miles = 15mph x T, so T = 2 hours.
For the middle section of the journey, we know that D = 10mph x 3 hours, so D = 30 miles.
For the final leg of the journey, we know that 40 miles = R x 2 hours, so R = 20mph.

We can now calculate the Total Distance and Total Time.
Distance total = 30 miles + 30 miles + 40 miles = 100 miles. Time total = 2 hours + 3 hours + 2 hours = 7 hours. So the average rate is 100 miles per hour divided by 7 hours equals 14.28mph. The closest approximation is A.

#### Joy spent \$16 on each of the necklaces she purchased at the jewelry store. Princess also purchased a number of necklaces for \$20 each. What is the average cost of the necklaces Joy and Princess bought if the ratio of the number of necklaces Joy bought to the number of necklaces Princess bought is 3 to 2?

Correct! Wrong!

For every 5 necklaces purchased by these ladies, 3 are Joy's and 2 are Princess'. We can use the following equation to calculate the total amount spent:

Total Amount Spent for every 5 Necklaces = 3(16) + 2(20).
88 = Total Amount Spent for each of the 5 necklaces

To calculate the average price of the necklaces, divide 88 by 5. 88/5 = 17.6.

#### Josh, Daniel, and Clark all purchased flowers. Josh purchased a single digit number of flowers. Only one of the flowers purchased by Josh, Daniel, and Clark was divisible by 3. The number of flowers purchased by one of them was an even number. Which of the following could represent the number of flowers purchased by each person?

Correct! Wrong!

On this type of question, the process of elimination is more convenient. Let's look at the second requirement now that all of the answer choices contain at least one single-digit number. If only one of the numbers was divisible by 3, we can eliminate the following answer choices: (A), (C), and (D) (D).

#### Given two positive integers x and y, what percentage of three more than y is twice the value of x?

Correct! Wrong!

This is an excellent question for determining x and y values. Assume x = 2. “Twice the value of x” equals 4. Assume that y = 5. “Three more than y” equals 8. The question now is: what percentage of 8 is 4? We know that 4 equals half of 8.

When we enter our values into the answer choices, the correct answer will also yield 50%: (200x/(y + 3) = 200(2)/(5) + 3 = 400/8 = 50.

#### Which of the following is greater than 1/2?

Correct! Wrong!

Converting all fractions to decimals is one way to deal with them. In this case, all that is required is to determine which is greater than 0.5. Otherwise, to determine which is greater than 1/2, multiply the numerator by the denominator and see if the result is greater than the denominator. In answer B, doubling the numerator yields 8, which is greater than 7.

#### What is the average (arithmetic mean) of all tens from 10 to 190 inclusive?

Correct! Wrong!

You could add all multiples of 10 (10 + 20 + 30....+190) and divide by the number of terms (19). Or you could realize that the average of an evenly spaced series of numbers equals the value of the middle term (or the average of the two middle terms if the number of terms is an odd number). The tenth term in the series is the middle term out of 19 = 100.

#### A metal cubical block weighs 6 pounds. How much heavier will a cube of the same metal be if its sides are twice as long?

Correct! Wrong!

If you double the sides of a cube, the surface area ratio of the old and new cubes is 1:4. The volume ratio of the old and new cubes will be 1:8. Volume is proportional to weight. As a result, if the first weighs 6 pounds, the second weighs 6x8 pounds = 48.

#### A fence is to be built with 6 inch wide posts separated by 5 feet lengths of chain. Which of the following cannot be the length of a fence in feet if it begins and ends with a post? (1 foot = 12 inches)

Correct! Wrong!

There will be one more post than there are chains on the fence. (For example, P-c-P-c-P). As a result, the total length must be a multiple of the chain length plus one post (5.5) plus one post extra. Length = (5.5n + 0.5), where n is any positive whole number. If n=3, length=17; if n=5, length=28, and so on, but there is no whole number that equals 35.

#### A die is rolled, followed by a coin toss. What is the probability that the die will show an even number AND the coin will show a tail?

Correct! Wrong!

First, we can compute the two individual probabilities.
Prob (as determined by the die) = 3/6 = 1/2 (2,4 and 6 out of 1,2,3,4,5 and 6)
Second, Prob(even AND tail) is P(even) x P(tail) = 1/2 x 1/2.

#### Company XYZ manufactures toy trucks for a shopping mall at a cost of \$7.00 per truck for the first 500 trucks and \$5.00 per truck after that. What was Company XYZ's gross profit if 600 trucks were produced and sold for \$15.00 each?

Correct! Wrong!

We must understand that Gross Profit = Revenue — Total Cost.

There are 600 trucks manufactured. The first 500 trucks, according to the question, cost \$7.00 each. As a result, the total cost of the first 500 trucks is \$7.00 x 500 = \$3500. The remaining 100 trucks cost \$5.00 each for a cost of \$5.00. 100 = \$500.

Add these up to get the price of the 600 trucks:
\$3500 + \$500 = \$4000

Because the selling price remains constant, calculating the total profit is simplified:
\$15.00 x 600 = \$9000

Because we now have both revenue and total cost, the answer to the question of gross profit is
\$9000 — \$4000 = \$5000.

#### Ryan bought a guitar that was originally \$290 but was discounted by \$27. How much of a discount did Ryan get on the guitar?

Correct! Wrong!

27 is slightly less than 29, which is 10% of \$290. As a result, 9 percent is the best approximation.

#### In a Math exercise, Mike solves problems 74 to 125. How many problems does he solve?

Correct! Wrong!

To determine how many problems are in the series, take the difference and add one.
125 - 74 = 51; 51 + 1 =52

#### In a sports club of 30 members, 17 play basketball, 19 soccer, and 2 do not play at all. How many members participate in both basketball and soccer?

Correct! Wrong!

Because two members do not participate in either sport, there are 28 members who participate in one or both. Let the number who play both be n. Total (28) will consist of only badminton players (17 - n), tennis players (19 - n), and those who play both (n).
28 = (17 - n) + (19 - n) + n
28 = 36 - n ; n = 8

#### Solve the average of four tenths and five thousandths.

Correct! Wrong!

Four tenths = 0.4
Five thousandths = 0.005
(0.4 + 0.005)/2 = 0.2025 is the average.

Correct! Wrong!