Free Standardized Achievement Problem Solving Test Question and Answer
For the first x hours of grass cutting, Larry's Lawn Service will charge $w/hour. Thereafter, the company will charge $w + $2 for each additional hour of service. If z > x, how much extra will a homeowner be charged for a job that took z hours compared to one that only took w hours if x w z?
This issue can be resolved by choosing numbers:
We need x, w, and z. Pick x=3, w=4, and z=6.
The client gets charged $4/hour for the first three hours of a job that took four hours, and then $6/hour for the final hour. $4(3) plus $6(1) would be $12 plus $6, or $18 in total.
The customer gets charged $4/hour for the first three hours of a job that took six hours, and then $6/hour for the final three. $4(3) plus $6(3) would equal $12 plus $18 to equal $30 in total. The price difference is $12.
Let's enter the values we have in the expression: (w+2)(z-w) = (4+2)(6-4) = 6*2 = 12.
The algebraic answer is as follows:
If cutting the grass required z hours, the final cost would be: wx + (z-x)(w+2).
The total cost is wx + (w-x)(w+2) if the task of cutting the grass took w hours, where x w z.
The additional expense is:
[wx + (z-x)(w+2)] - [wx + (w-x)(w+2)]
= (w+2)[(z-x) – (w-x)]
= (w+2)(z-w)
Richard, Jared, and Matthew all purchased bouquets. The quantity of flowers Matthew bought was a single figure. Only one of the quantities of flowers that Matthew, Jared, and Richard bought could be divided by three. An even amount of flowers were purchased by one of them. Which of the following could be used to show how many flowers each person bought?
On this kind of question, the process of elimination is simpler. Let's examine the second criteria since every answer option has at least one single-digit number. We can rule out the following response options if just one of the numbers was divisible by three: (A), (C), and (D).
The presence of at least one even integer is the third prerequisite. Only option (E) contains an even number, 10, between (B) and (E).
What is the square root of.00000256's square root value?
Start by taking the square root of.00000256 to solve algebraically. The square root of 256 is known to be 16. In scientific language, we can express 0.00000256 as 256 x 10-8. So:
You can backsolve 04 x.04 =.0016 and.0016 x.0016 =.00000256 to confirm.
Backsolve your work to ensure accuracy:.004 x.004 =.000016. And .000016 x .000016 Equals .000000000256 (four more zeros) (four extra zeros).
At the jewelry store, Lady Edith purchased numerous necklaces, each of which cost sixteen dollars. Additionally, Lady Mary spent $20 on a number of bracelets. What is the average price of the necklaces Lady Edith and Lady Mary bought, if the ratio of necklaces Lady Edith bought to necklaces Lady Mary bought was 3 to 2?
These women bought 5 necklaces, 3 of which were owned by Lady Edith and 2 by Lady Mary. The entire money spent can be calculated using the following equation:
For every 5 necklaces, the total amount spent is 3(16) plus 2(20).
88 is the overall cost for each of the five necklaces.
We can easily calculate the average price of the necklaces by dividing 88 by 5. 88/5 = 17.6.
A yellow taxi cab traveled 2/3 miles per hour on average from Downtown to the Beachside and back. What was the average speed of the yellow taxi cab on the way to Beachside if the distance between Beachside and Downtown is one mile and the trip there took one and a half times as long as the trip back?
It's crucial to first comprehend what this question is trying to ask. The phrase "on the way to Beachside" refers to the route. The query inquires about the typical speed for a section of the entire journey. We'll need to know the length of time and distance of that segment of the journey in order to locate it.
Every three hours, 2 miles would be covered if the overall average pace was 2/3 of a mile per hour. The whole time must have been 3 hours because the overall distance was just 2 miles. If it took half as long to get there as it did to get back, it would take 2 hours to get there and 1 hour to get back for every 3 hours.
One mile takes two hours at the average speed of distance/time. The trip to Beachside was made at an average speed of 1/2 mph.
What percentage of three more than y is twice the value of x, if x and y are positive integers?
The answer to this query will determine the values for x and y. Say x is equal to 2. Four would be "twice the value of x." Say y is now equal to 5. "Three greater than y" is equal to eight. What percentage of 8 is 4 is the current query. We are aware that 4 equals 50% of 8.
The right solution will also result in 50% when we enter our values into the available answer choices: (200x/(y + 3) = 200(2) / (5) + 3 = 400/8 = 50.
Meredith jogged at an average speed of six miles per hour to the top of the hill. She returned down the same path. She was relieved to find that the descent was swifter, and her average speed increased to 14 miles per hour. How many miles, roughly, is the route one way if the entire run took Meredith exactly an hour to complete and she did not stop at any points?
Time = Speed/Distance Uphill travel time is equal to D/6. Time spent descending equals D/14. Time Spent = 1 hour. To solve for D, we can write the equation shown below: Time spent traveling uphill plus time spent traveling downward equals total time.
What is the percentage of profit or loss made on the sale of each pair of shoes, assuming each pair of shoes cost the same amount of money and each pair of shoes sold for the same amount of money, if the total cost of 20 pairs of shoes equals the total revenue made from the sale of 25 pairs of shoes?
Profit/Loss% = (Sales Price - Cost Price) / Cost Price x 100 is the formula you need to know. The stem informs us that 20 cents equals 25 cents, or 4 cents equals 5 cents, so the sales price to cost price ratio is 4/5.
To make our Profit/Loss% calculation easier to understand, divide each term by the cost price: Profit/Loss Percentage = (S/C - C/C) times 100
P/L% = (S/C - 1) times 100 For this issue, we are aware that S/C equals 4/5. Thus, we can connect and resolve:
P/L% = (4/5 – 1) x 100
P/L% = (-1/5) x 100
A circle with the center P has the rectangle LMNO engraved in it. What is the approximate circumference of the circle if the width of the rectangle is 8 times its length and the distance between P and side LM is 3?
We must determine a circle's radius before we can determine its circumference.
A rectangle has the area lw. Here, it is stated that lw equals 8w. Thus, the length is eight. Additionally, we know that P is 3 from LM, indicating that the rectangle's length must be 6.
The hypotenuse of a right triangle with other two sides that are each half the length and half the width of the rectangle is the radius of the circle, LP. We don't need to use the Pythagorean theorem because the triplet is a traditional Pythagorean triplet (3:4:5).
Fill in the radius in the circumference formula: C = 2πr. C = 2*π*5. The circumference is roughly 10, which is a value little above 30.
The two circles' centers, X and P, are the same. Circle P is inside Circle Q. What is the difference between Circle Q's diameter and Circle P's diameter if Circle Q's circumference is four times that of Circle P, and Circle P's radius is three?
P has a diameter of 6 if its radius is 3. 2r times 6 is the circumference. The circumference of Q is four times that of P. The circumference of Q is 24 + 2r. Q must have a radius of 12 and a diameter of 24.
24 – 6 = 18 is the difference between the diameters.
Clarissa spent the entire day exploring Britain. Starting from her hotel, Clarissa boarded a bus that made its way through a 30-mile stretch of the countryside at an average pace of 15 miles per hour. The bus then made a lunch stop in London before continuing its three-hour tour of the city's attractions at a 10 mph speed. The bus finally departed the city and made a direct 40-mile trip back to the motel. After leaving London, Clarissa arrived at her accommodation in exactly two hours. What was the approximate average speed of the bus throughout the trip?
Let's examine how we can use the D = R x T method to discover the missing information. We know that we will need to find the Total Distance and the Total Time in order to determine the "Average Rate" of the bus. For the initial leg of the journey, we know that T = 2 hours because 30 miles equals 15 mph times T. D Equals 30 miles for the middle portion of the journey because we know that D = 10 mph times three hours. For the final leg of the journey, we know that R = 20 mph because 40 miles equals R x 2 hours. We can now calculate the total time and distance. 100 miles is the total distance (30 miles + 30 miles + 40 miles). Total Time is equal to 2 hours, 3 hours, and 2 hours, or 7 hours. The Average Rate is therefore 14.28 mph (100 miles per hour).
Nine medical professionals are managing many clinical studies at a medical research facility. Three physicians are engaged in a clinical trial with precisely two other physicians, while six physicians are engaged in a clinical trial with precisely one other physician. What is the likelihood that two doctors who are randomly chosen from the lab will NOT be collaborating on a clinical trial?
The likelihood that the second person would be one of their partners would be 2/8 if the first person we selected was from the second group (probability = 3/9). This time, the numerator is 2, as each member of the second group has two partners rather than one. 3/9*2/8 = 6/72 = 1/12.
We will add these probabilities since choosing the first person from either of these outcomes (the first group OR the second group) results in the outcome we want. 1/12 + 1/12 = 2/12 = 1/6.
The likelihood that the two doctors are not collaborating is therefore 1 - 1/6 = 5/6.
In a 200-member university club, there are 50 fewer Political Science majors than there are International Relations majors. How many club members are majoring in international relations if one-fifth of the club members are neither political science nor international relations majors and no club member is majoring in both fields?
Let P represent the total number of political science majors and R represent the total number of majors in international relations. Since "one fifth of the legislators are neither," there are 40 legislators that fall under this category (1/5 * 200). Consequently, the number of Poly-Sci majors and IR majors is 200 - 40 = 160, or P + R = 160. P = 4R - 50 results from converting the sentence "the number of Poly-Sci majors is 50 less than 4 times the number of IR majors" into an equation.
This results from plugging this into the equation P + R = 160:
4R – 50 + R = 160
5R – 50 = 160
5R = 210 \sR = 42
There is growth at the City Opera House. The opera theater is currently located on a rectangular city block with a total volume of 9600 ft. What would the additional volume be if the extended Opera House was 2.5 times as long, broad, and deep as the original structure?
Volume is calculated as length, width, and height. LWH = 9600 is the building's original volume. 2.5L x 2.5W x 2.5H, or (lwh) x 2.5 x 2.5 x 2.5 = 15.625, will be the new footage (lwh). The new volume will be 15.625(9600) = 150,000 since lwh = 9600.
Which of the following integers contains the most digits that are unique?
5/7 = .7142…. There are already more distinct digits than four, which is more than any other number in the answer options. Keep in mind that there are only ten digits available for each placeholder in a number: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Unique refers to something that is distinct from the other numerals.
The diameter of Circle B was doubled by 1.8. What was the area increased by, roughly speaking?
This is an excellent question to which you can add your own values. Say the initial radius was 10, for example. Since r2 = (10)2 = 100, the initial area would be equal to that. The new radius would be 18 and the new area would be equal to r2 = (18)2 = 324 if the diameter rose by 80%.
The difference, 324 minus 100, equals 224. a growth of 224/100, or around 225%.