1. Two years ago, Arthur gave each of his five children 20 percent of his fortune to invest in any way they saw
fit. In the first year, three of the children, Alice, Bob, and Carol, each earned a profit of 50 percent on their
investments, while two of the children, Dave and Errol, lost 40 percent on their investments. In the second
year, Alice and Bob each earned a 10 percent profit, Carol lost 60 percent, Dave earned 25 percent in profit,
and Errol lost all the money he had remaining. What percentage of Arthur's fortune currently remains?
A. 93
B. 97
C.100
D. 107
E. 120
2. A car dealership has 40 cars on the lot, 30% of which are silver. If the dealership receives a new shipment of
80 cars, 40% of which are not silver, what percent of the total number of cars are silver?
A.35
B.37.5
C.45
D.47.5
E.50
3. Paul's income is 40% less than Rex's income, Quentin's income is 20% less than Paul's income, and Sam's
income is 40% less than Paul's income. If Rex gave 60% of his income to Sam and 40% of his income to
Quentin, Quentin's new income would be what fraction of Sam's new income?
A.11/12
B.13/17
C.13/19
D.12/19
E.11/19
4. A school’s annual budget for the purchase of student computers increased by 60% this year over last year. If
the price of student computers increased by 20% this year, then the number of computers it can purchase
this year is what percent greater than the number of computers it purchased last year?
A.33.33
B. 40
C. 42
D. 45
E. 48
F. 50
G. 60
5.Boomtown urban planners expect the city’s population to increase by 10% per year over the next two years.
If that projection were to come true, the population two years from now would be exactly double the
population of one year ago. Which of the following is closest to the percent population increase in Boomtown
over the last year?
6.A retailer bought a shirt at wholesale and marked it up 80% to its initial retail price of $45. By how many
more dollars does he need to increase the price to achieve a 100% markup?
A. 6
B. 7.5
C. 8
D. 9
E. 10.5
7. A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile. How much, in
dollars, would it cost 3 people to travel x miles if he decides to give them a 50% discount?
A. 3xr / 2
B. 3x / 200r
C.3r / 200x
D.3xr / 200
E. xr / 600
F. 300
8. Bob just filled his car's gas tank with 20 gallons of gasohol, a mixture consisting of 5% ethanol and 95%
gasoline. If his car runs best on a mixture consisting of 10% ethanol and 90% gasoline, how many gallons of
ethanol must he add into the gas tank for his car to achieve optimum performance?
A. 9/10
B. 1
C. 10/9
D. 20/19
E. 2
9. Which of the following values is closest to 1/3 + 0.4 + 65%?
A. 1.1
B. 1.2
C. 1.3
D. 1.4
E. 1.5
10. A certain tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride.
The proportion of sodium chloride in the tank is 40% by volume and the capacity of the tank is 24 gallons. If
the water evaporates from the tank at the rate of 0.5 gallons per hour, and the amount of sodium chloride
stays the same, what will be the concentration of water in the mixture in 2 hours?
A.43
B. 50
C.52
D.54
E.56
F. 60
G. 64
11.The useful life of a certain piece of equipment is determined by the following formula: u =(8d)/h2, where u is
the useful life of the equipment, in years, d is the density of the underlying material, in g/cm3, and h is the
number of hours of daily usage of the equipment. If the density of the underlying material is doubled and the
daily usage of the equipment is halved, what will be the percentage increase in the useful life of the
equipment?
12.If m > 0, y > 0, and x is m percent of 2y, then, in terms of y, m is what percent of x?
A.y/200
B.2y
C.50y
D. 50/y
E. 5000/y
13.x% of y is increased by x%. What is the result in terms of x and y?
A. 100xy + x
B. xy + x/100
C. 100xy + x/100
D. 100xy + xy/100
E. xy(x + 100)/10000
14.The manufacturer’s suggested retail price (MSRP) of a certain item is $60. Store A sells the item for 20
percent more than the MSRP. The regular price of the item at Store B is 30 percent more than the MSRP, but
the item is currently on sale for 10 percent less than the regular price. If sales tax is 5 percent of the
purchase price at both stores, what is the result when the total cost of the item at Store B is subtracted from
the total cost of the item at Store A?
A. $0
B. $0.63
C. $1.80
D.$1.89
E.$2.10
15. Two years ago, Sam put $1,000 into a savings account. At the end of the first year, his account had accrued
$100 in interest bringing his total balance to $1,100. The next year, his account balance increased by 10%. At
the end,of the two years, by what percent has Sam's account balance increased from his initial deposit of
$1,000?
A.19%
B.20%
C.21%
D.22%
E.25%
16. The price of a certain painting increased by 20% during the first year and decreased by 15% during the
second year. The price of the painting at the end of the 2-year period was what percent of the original price?
A. 102%
B.105%
C.120%
D.135%
E.140
17.If an item that originally sold for z dollars was marked up by x percent and then discounted by y percent,
which of the following expressions represents the final price of the item?
A. [10,000z + 100z(x – y) – xyz]/10000
B. [10,000z + 100z(y – x) – xyz]/10000
C.[100z(x – y) – xyz]/10000
D. [100z(y – x) – xyz]/10000
E. 10000 / [x – y]
18.A clock store sold a certain clock to a collector for 20 percent more than the store had originally paid for the
clock. When the collector tried to resell the clock to the store, the store bought it back at 50 percent of what
the collector had paid. The shop then sold the clock again at a profit of 80 percent on its buy-back price. If
the difference between the clock's original cost to the shop and the clock's buy-back price was $100, for how
much did the shop sell the clock the second time?
A. $270
B. $250
C. $240
D. $220
E. $200
19.90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary
make up 40% of the total school population of x students, what is x?
A. 125
B. 150
C. 225
D. 250
E. 500
20.Cindy has her eye on a sundress but thinks it is too expensive. It goes on sale for 15% less than the original
price. Before Cindy can buy the dress, however, the store raises the new price by 25%. If the dress cost $68
after it went on sale for 15% off, what is the difference between the original price and the final price?
A. $0.00
B.$1.00
C. $3.40
D. $5.00
E. $6.80
1. Percentage problems involving unspecified amounts can usually be solved more easily by using the number 100. If Arthur's fortune was originally $100, each of his children received $20.
Let's see what happened to each $20 investment in the first year:
Alice: $20 + $10 profit = $30
Bob: $20 + $10 profit = $30
Carol: $20 + $10 profit = $30
Dave: $20 - $8 loss = $12
Errol: $20 - $8 loss = $12
We continue on with our new amounts in the second year:
Alice: $30 + $3 profit = $33
Bob: $30 + $3 profit = $33
Carol: $30 - $18 loss = $12
Dave: $12 + $3 profit = $15
Errol: $12 - $12 = 0
At the end of two years, $33 + $33 + $12 + $15 = $93 of the original $100 remains.
The correct answer is A.
Let's see what happened to each $20 investment in the first year:
Alice: $20 + $10 profit = $30
Bob: $20 + $10 profit = $30
Carol: $20 + $10 profit = $30
Dave: $20 - $8 loss = $12
Errol: $20 - $8 loss = $12
We continue on with our new amounts in the second year:
Alice: $30 + $3 profit = $33
Bob: $30 + $3 profit = $33
Carol: $30 - $18 loss = $12
Dave: $12 + $3 profit = $15
Errol: $12 - $12 = 0
At the end of two years, $33 + $33 + $12 + $15 = $93 of the original $100 remains.
The correct answer is A.
2. This is a weighted average problem; we cannot simply average the percentage of silver cars for the two batches because each batch has a different number of cars.
The car dealership currently has 40 cars, 30% of which are silver. It receives 80 new cars, 60% of which are silver (the 40% figure given in the problem refers to cars which are not silver). Note that the first batch represents 1/3 of the total cars and the second batch represents 2/3 of the total cars. Put differently, in the new total group there is 1 first-batch car for every 2 second-batch cars.
We can calculate the weighted average, weighting each percent according to the ratio of the number of cars represented by that percent:
Weighted average = (1(30%) + 2(60%))/3 =50%
Alternatively, you can calculate the actual number of silver cars and divide by the total number of cars. 40(0.3) + 80(0.6) = 12 + 48 = 60. 60/120 = 50%.
The correct answer is E.
The car dealership currently has 40 cars, 30% of which are silver. It receives 80 new cars, 60% of which are silver (the 40% figure given in the problem refers to cars which are not silver). Note that the first batch represents 1/3 of the total cars and the second batch represents 2/3 of the total cars. Put differently, in the new total group there is 1 first-batch car for every 2 second-batch cars.
We can calculate the weighted average, weighting each percent according to the ratio of the number of cars represented by that percent:
Weighted average = (1(30%) + 2(60%))/3 =50%
Alternatively, you can calculate the actual number of silver cars and divide by the total number of cars. 40(0.3) + 80(0.6) = 12 + 48 = 60. 60/120 = 50%.
The correct answer is E.
Notice that Paul’s income is expressed as a percentage of Rex’s and that the other two incomes are expressed as a percent of Paul’s. Let’s assign a value of $100 to Rex’s income. Paul’s income is 40% less than Rex's income, so (0.6)($100) = $60. Quentin’s income is 20% less than Paul's income, so (0.8)($60) = $48. Sam’s income is 40% less than Paul's income, so (0.6)($60) = $36. If Rex gives 60% of his income, or $60, to Sam, and 40% of his income, or $40, to Quentin, then: Sam would have $36 + $60 = $96 and Quentin would have $48 + $40 = $88. Quentin’s income would now be $88/$96 = 11/12 that of Sam's.
The correct answer is A.
The correct answer is A.
Let’s denote the formula for the money spent on computers as pq = b, where
p = price of computers
q = quantity of computers
b = budget
We can solve a percent question that doesn’t involve actual values by using smart numbers. Let’s assign a smart number of 1000 to last year’s computer budget (b) and a smart number 100 to last year’s computer price (p). 1000 and 100 are easy numbers to take a percent of.
This year’s budget will equal 1000 × 1.6 = 1600
This year’s computer price will equal 100 × 1.2 = 120
Now we can calculate the number of computers purchased each year, q = b/p
Number of computers purchased last year = 1000/100 = 10
Number of computers purchased this year = 1600/120 = 13 1/3 (while 1/3 of a computer doesn’t make sense it won’t affect the calculation)
p q b This Year p=100, q=10, b= 1000
Last Year p=120, q=13 1/3,b=1600
The question is asking for the percent increase in quantity from last year to this year =
(new – old)X100/old =33.33%increase
This question could also have been solved algebraically by converting the percent increases into fractions.
Last year: pq = b, so q = b/p
This year: (6/5)(p)(x) = (8/5)b
If we solve for x (this year's quantity), we get x = (8/5)(5/6)b/p or (4/3)b/p
If this year's quantity is 4/3 of last year's quantity (b/p), this represents a 33 1/3% increase.
The correct answer is A.
p = price of computers
q = quantity of computers
b = budget
We can solve a percent question that doesn’t involve actual values by using smart numbers. Let’s assign a smart number of 1000 to last year’s computer budget (b) and a smart number 100 to last year’s computer price (p). 1000 and 100 are easy numbers to take a percent of.
This year’s budget will equal 1000 × 1.6 = 1600
This year’s computer price will equal 100 × 1.2 = 120
Now we can calculate the number of computers purchased each year, q = b/p
Number of computers purchased last year = 1000/100 = 10
Number of computers purchased this year = 1600/120 = 13 1/3 (while 1/3 of a computer doesn’t make sense it won’t affect the calculation)
p q b This Year p=100, q=10, b= 1000
Last Year p=120, q=13 1/3,b=1600
The question is asking for the percent increase in quantity from last year to this year =
(new – old)X100/old =33.33%increase
This question could also have been solved algebraically by converting the percent increases into fractions.
Last year: pq = b, so q = b/p
This year: (6/5)(p)(x) = (8/5)b
If we solve for x (this year's quantity), we get x = (8/5)(5/6)b/p or (4/3)b/p
If this year's quantity is 4/3 of last year's quantity (b/p), this represents a 33 1/3% increase.
The correct answer is A.
This problem can be solved most easily with the help of smart numbers. With problems involving percentages, 100 is typically the ‘smartest’ of the smart numbers.
If we assume that today’s population is 100, next year it would be 1.1 × 100 = 110, and the following year it would be 1.1 × 110 = 121. If this is double the population of one year ago, the population at that time must have been 0.5 × 121 = 60.5. Because the problem seeks the “closest” answer choice, we can round 60.5 to 60.
In this scenario, the population has increased from 60 to 100 over the last year, a net increase of 40 residents. To determine the percentage increase over the last year, divide the net increase by the initial population: 40/60 = 4/6 = 2/3, or roughly 67%.
For those who prefer the algebraic approach: let the current population equal p. Next year the population will equal 1.1p, and the following year it will equal 1.1 × 1.1p = 1.21p. Because the question asks for the closest answer choice, we can simplify our algebra by rounding 1.21p to 1.2p. Half of 1.2p equals 0.6p. The population increase would be equal to 0.4p/0.6p = 0.4/0.6 = 2/3, or roughly 67%.
.
If we assume that today’s population is 100, next year it would be 1.1 × 100 = 110, and the following year it would be 1.1 × 110 = 121. If this is double the population of one year ago, the population at that time must have been 0.5 × 121 = 60.5. Because the problem seeks the “closest” answer choice, we can round 60.5 to 60.
In this scenario, the population has increased from 60 to 100 over the last year, a net increase of 40 residents. To determine the percentage increase over the last year, divide the net increase by the initial population: 40/60 = 4/6 = 2/3, or roughly 67%.
For those who prefer the algebraic approach: let the current population equal p. Next year the population will equal 1.1p, and the following year it will equal 1.1 × 1.1p = 1.21p. Because the question asks for the closest answer choice, we can simplify our algebra by rounding 1.21p to 1.2p. Half of 1.2p equals 0.6p. The population increase would be equal to 0.4p/0.6p = 0.4/0.6 = 2/3, or roughly 67%.
.
To solve this problem, first find the wholesale price of the shirt, then compute the price required for a 100% markup, then subtract the $45 initial retail price to get the required increase.
Let x equal the wholesale price of the shirt. The retailer marked up the wholesale price by 80% so the initial retail price is x + (80% of x). The following equation expresses the relationship mathematically:
x + 0.80x = 45
1.8x = 45
x = 45/1.8
x = 450/18
x = 25
Since the wholesale price is $25, the price for a 100% markup is $50. Therefore the retailer needs to increase the $45 initial retail price by $5 to achieve a 100% markup.
The correct answer is E.
Let x equal the wholesale price of the shirt. The retailer marked up the wholesale price by 80% so the initial retail price is x + (80% of x). The following equation expresses the relationship mathematically:
x + 0.80x = 45
1.8x = 45
x = 45/1.8
x = 450/18
x = 25
Since the wholesale price is $25, the price for a 100% markup is $50. Therefore the retailer needs to increase the $45 initial retail price by $5 to achieve a 100% markup.
The correct answer is E.
Explanation for Question 7:We can solve this as a VIC (Variable In answer Choices) and plug in values for x and r.
R, cents per person per mile,= 10
X, # of miles,= 20
Since there are 3 people, the taxi driver will charge them 30 cents per mile.
Since they want to travel 20 miles, the total charge (no discount) would be (30)(20) = 600.
With a 50% discount, the total charge will be 300 cents or 3 dollars.
If we plug r = 10 and x = 20 into the answer choices, the only answer that yields 3 dollars is D.
The correct answer is D.
R, cents per person per mile,= 10
X, # of miles,= 20
Since there are 3 people, the taxi driver will charge them 30 cents per mile.
Since they want to travel 20 miles, the total charge (no discount) would be (30)(20) = 600.
With a 50% discount, the total charge will be 300 cents or 3 dollars.
If we plug r = 10 and x = 20 into the answer choices, the only answer that yields 3 dollars is D.
The correct answer is D.
Bob put 20 gallons of gasohol into his car's gas tank, consisting of 5% ethanol and 95% gasoline.
ethanol=1gallon, gasoline=19gallon
Assume after adding x gallon of ehtanol to the given mixture, the mixture will contain 10% of ethanol
therefore, X/(20+X)=1/10
X=10/9
The correct answer is C.
ethanol=1gallon, gasoline=19gallon
Assume after adding x gallon of ehtanol to the given mixture, the mixture will contain 10% of ethanol
therefore, X/(20+X)=1/10
X=10/9
The correct answer is C.
Noting that 65% is very close to 2/3, we may approximate the original expression as follows:
1/3 + 0.4 + 65% = Original expression
1/3 + 0.4 + 2/3 = Close approximation
1 + 0.4
1.4
The correct answer is D
1/3 + 0.4 + 65% = Original expression
1/3 + 0.4 + 2/3 = Close approximation
1 + 0.4
1.4
The correct answer is D
First, let’s find the initial amount of water in the tank:
Total mixture in the tank =1/4 × (capacity of the tank) = (1/4) × 24 = 6 gallons
Concentration of water in the mixture = 100% – (concentration of sodium chloride) = 100% – 40% = 60%
Initial amount of water in the tank = 60% × (total mixture)= 0.6 × 6 = 3.6 gallons
Next, let’s find the amount and concentration of water after 2 hours:
Amount of water that will evaporate in 2 hours = (rate of evaporation)(time) = 0.5(2) = 1 gallon
Remaining amount of water = initial amount – evaporated water = 3.6 – 1 = 2.6 gallons
Remaining amount of mixture = initial amount – evaporated water = 6 – 1 = 5 gallons
Concentration of water in the mixture in 2 hours = (remaining water/remaining mixture) × 100%
which equals: (2.6/5) × 100% = 52%
The correct answer is C.
Total mixture in the tank =1/4 × (capacity of the tank) = (1/4) × 24 = 6 gallons
Concentration of water in the mixture = 100% – (concentration of sodium chloride) = 100% – 40% = 60%
Initial amount of water in the tank = 60% × (total mixture)= 0.6 × 6 = 3.6 gallons
Next, let’s find the amount and concentration of water after 2 hours:
Amount of water that will evaporate in 2 hours = (rate of evaporation)(time) = 0.5(2) = 1 gallon
Remaining amount of water = initial amount – evaporated water = 3.6 – 1 = 2.6 gallons
Remaining amount of mixture = initial amount – evaporated water = 6 – 1 = 5 gallons
Concentration of water in the mixture in 2 hours = (remaining water/remaining mixture) × 100%
which equals: (2.6/5) × 100% = 52%
The correct answer is C.
One of the most effective ways to solve problems involving formulas is to pick numbers. Note that since we are not given actual values but are asked to compute only the relative change in the useful life, we can select easy numbers and plug them into the formula to compute the percentage increase. Let’s pick d = 3 and h = 2 to simplify our computations:
Before the change: d = 3, h = 2; u = (8)(3)/22 = 24/4 = 6
After the change: d = (2)(3)= 6, h =2/2 =1; u = (8)(6)/12 = 48
Finally, percent increase is found by first calculating the change in value divided by the original value and then multiplying by 100:
(48 – 6)/6 = (42/6) = 7
(7)(100) = 700%
The correct answer is D.
Before the change: d = 3, h = 2; u = (8)(3)/22 = 24/4 = 6
After the change: d = (2)(3)= 6, h =2/2 =1; u = (8)(6)/12 = 48
Finally, percent increase is found by first calculating the change in value divided by the original value and then multiplying by 100:
(48 – 6)/6 = (42/6) = 7
(7)(100) = 700%
The correct answer is D.
Since there are variables in the answer choices, as well as in the question stem, one way to approach this problem is to pick numbers and test each answer choice. We know that x is m percent of 2y, so pick values for m and y, then solve for x.
y = 100
m = 40
x is m percent of 2y, or x is 40 percent of 200, so x = (0.40)(200) = 80.
So, for the numbers we are using, m is what percent of x? Well, m = 40, which is half of x = 80. Thus, m is 50 percent of x. The answer choice that equals 50 will be the correct choice.
(A) y/200 = 100/200 = 0.5 WRONG
(B) 2y = (2)(100) = 200 WRONG
(C) 50y = (50)(100) = 5000 WRONG
(D) 50/y = 50/100 = 0.5 WRONG
(E) 5000/y = 5000/100 = 50 CORRECT
y = 100
m = 40
x is m percent of 2y, or x is 40 percent of 200, so x = (0.40)(200) = 80.
So, for the numbers we are using, m is what percent of x? Well, m = 40, which is half of x = 80. Thus, m is 50 percent of x. The answer choice that equals 50 will be the correct choice.
(A) y/200 = 100/200 = 0.5 WRONG
(B) 2y = (2)(100) = 200 WRONG
(C) 50y = (50)(100) = 5000 WRONG
(D) 50/y = 50/100 = 0.5 WRONG
(E) 5000/y = 5000/100 = 50 CORRECT
The easiest way to solve this problem is to use the VIC method of substituting actual numbers for x and y. The problem asks us to take x% of y and increase it by x%. Since we are dealing with percentages, and the whole (y) is neither given to us nor asked of us, let's set y = 100 and x = 10. Note that this is a variation on the typical method of picking small numbers in VIC problems.
10% of 100 is 10. Increasing that 10 by 10% gives us 10 + 1 = 11.
Therefore 11 is our target number.
Let's test each answer choice in turn to see which of them matches our target number.
The correct answer is E.
10% of 100 is 10. Increasing that 10 by 10% gives us 10 + 1 = 11.
Therefore 11 is our target number.
Let's test each answer choice in turn to see which of them matches our target number.
The correct answer is E.
First, determine the total cost of the item at each store.
Store A:
$60 (MSRP) + $12 (+ 20% mark-up = 0.20 × $60) = $72.00 (purchase price)
$72.00 (purchase price) + $3.60 (+ 5% sales tax = 0.05 × $72) = $75.60 (total cost)
Store B:
$60 (MSRP) + $18 (+ 30% mark-up = 0.30 × $60)= $78.00 (regular price)
$78.00 (regular price)– $7.80 (–10% sale = –0.10 × $78) = $70.20 (current purchase price)
$70.20 (current purchase price) + $3.51 (5% sales tax = 0.05 × $70.20) = $73.71 (total cost) The difference in total cost, subtracting the Store B cost from the Store A cost, is thus $75.60 - $73.71 = $1.89. The correct answer is D.
Store A:
$60 (MSRP) + $12 (+ 20% mark-up = 0.20 × $60) = $72.00 (purchase price)
$72.00 (purchase price) + $3.60 (+ 5% sales tax = 0.05 × $72) = $75.60 (total cost)
Store B:
$60 (MSRP) + $18 (+ 30% mark-up = 0.30 × $60)= $78.00 (regular price)
$78.00 (regular price)– $7.80 (–10% sale = –0.10 × $78) = $70.20 (current purchase price)
$70.20 (current purchase price) + $3.51 (5% sales tax = 0.05 × $70.20) = $73.71 (total cost) The difference in total cost, subtracting the Store B cost from the Store A cost, is thus $75.60 - $73.71 = $1.89. The correct answer is D.
Given an initial deposit of $1,000, we must figure out the ending balance to calculate the total percent change.
After the first year, Sam's account has increased by $100 to $1,100.
After the second year, Sam's account again increased by 10%, but we must take 10% of $1,100, or $110. Thus the ending balance is $1,210 ($1,100 + $110).
To calculate the percent change, we first calculate the difference between the ending balance and the initial balance: $1,210 – $1,000 = $210. We divide this difference by the initial balance of $1,000 and we get $210/$1,000 = .21 = 21%.
The correct answer is C.
After the first year, Sam's account has increased by $100 to $1,100.
After the second year, Sam's account again increased by 10%, but we must take 10% of $1,100, or $110. Thus the ending balance is $1,210 ($1,100 + $110).
To calculate the percent change, we first calculate the difference between the ending balance and the initial balance: $1,210 – $1,000 = $210. We divide this difference by the initial balance of $1,000 and we get $210/$1,000 = .21 = 21%.
The correct answer is C.
Problems that involve successive price changes are best approached by selecting a smart number. When the problem deals with percentages, the most convenient smart number to select is 100. Let’s assign the value of 100 to the initial price of the painting and perform the computations:
Original price of the painting = 100.
Price increase during the first year = 20% of 100 = 20.
Price after the first year = 100 + 20 = 120.
Price decrease during the second year = 15% of 120 = 18.
Price after the second year = 120 – 18 = 102.
Final price as a percent of the initial price = (102/100) = 1.02 = 102%.
The correct answer is A.
Original price of the painting = 100.
Price increase during the first year = 20% of 100 = 20.
Price after the first year = 100 + 20 = 120.
Price decrease during the second year = 15% of 120 = 18.
Price after the second year = 120 – 18 = 102.
Final price as a percent of the initial price = (102/100) = 1.02 = 102%.
The correct answer is A.
Varify the options by substituting x=10,y=20,z=100.
The correct answer is A.
The correct answer is A.
If p is the price that the shop originally paid for the clock, then the price that the collector paid was 1.2p (to yield a profit of 20%). When the shop bought back the clock, it paid 50% of the sale price, or (.5)(1.2)p = .6p. When the shop sold the clock again, it made a profit of 80% on .6p or (1.8)(.6)p = 1.08p.
The difference between the original cost to the shop (p) and the buy-back price (.6p) is $100.
Therefore, p – .6p = $100. So, .4p = $100 and p = $250.
If the second sale price is 1.08p, then 1.08($250) = $270. (Note: at this point, if you recognize that 1.08p is greater than $250 and only one answer choice is greater than $250, you may choose not to complete the final calculation if you are pressed for time.)
The correct answer is A.
The difference between the original cost to the shop (p) and the buy-back price (.6p) is $100.
Therefore, p – .6p = $100. So, .4p = $100 and p = $250.
If the second sale price is 1.08p, then 1.08($250) = $270. (Note: at this point, if you recognize that 1.08p is greater than $250 and only one answer choice is greater than $250, you may choose not to complete the final calculation if you are pressed for time.)
The correct answer is A.
We are told that the boys of Jones Elementary make up 40% of the total of x students.
Therefore: # of boys = .4x
We are also told that x% of the # of boys is 90.
Thus, using x/100 as x%:
(x/100) × (# of boys) = 90
Substituting for # of boys from the first equation, we get:
(x/100) × .4x = 90
(.4x2) / 100 = 90
.4x2 = 9,000
x2 = 22,500
x = 150
Therefore: # of boys = .4x
We are also told that x% of the # of boys is 90.
Thus, using x/100 as x%:
(x/100) × (# of boys) = 90
Substituting for # of boys from the first equation, we get:
(x/100) × .4x = 90
(.4x2) / 100 = 90
.4x2 = 9,000
x2 = 22,500
x = 150
The dress has three different prices throughout the course of the problem: the original price (which we will call x), the initial sales price ($68) and the final selling price (which we will call y). In order to answer the question, we must find the other two prices x and y.
According to the problem, (the original price) × 85% = initial sales price = $68, therefore x = 68 / 0.85. How can we do this arithmetic efficiently? 0.85 is the same as 85/100 and this simplifies to 17/20. 68 / (17/20) = 68 × (20/17). 17 goes into 68 four times, so the equation further simplifies to 4 × 20 = 80. The original price was therefore $80.
According to the problem, the initial sales price × 125% = final selling price, therefore 68 × 125% = y. Multiplying by 125% is the same thing as finding 25% of 68 and adding this figure to 68. 25% of 68 is 17, so the final selling price was $68 + $17 = $85.
The difference between the original and final prices is $85 – $80 = $5.
The correct answer is D.
According to the problem, (the original price) × 85% = initial sales price = $68, therefore x = 68 / 0.85. How can we do this arithmetic efficiently? 0.85 is the same as 85/100 and this simplifies to 17/20. 68 / (17/20) = 68 × (20/17). 17 goes into 68 four times, so the equation further simplifies to 4 × 20 = 80. The original price was therefore $80.
According to the problem, the initial sales price × 125% = final selling price, therefore 68 × 125% = y. Multiplying by 125% is the same thing as finding 25% of 68 and adding this figure to 68. 25% of 68 is 17, so the final selling price was $68 + $17 = $85.
The difference between the original and final prices is $85 – $80 = $5.
The correct answer is D.