World Problems Flashcards by James Nguyen

How do you translate this statement: “If Kelly received 1/3 times more votes than Mike”

K = M + 1/3 M

How well did you know this?

Not at all

Perfectly

A passenger train leaves the train depot 2 hours after a freight train left the same depot. If it overtakes the freight train in three hours, what is the same value in this problem?

Distance - both trains traveled from the same spot and catch up at the same spot in the future.

How well did you know this?

Not at all

Perfectly

If two objects travel towards each other, what is their rate of travel?

The rate is the addition of object’s rates

Note: The objects reduce the distance themselves at this ADDITION rate

How well did you know this?

Not at all

Perfectly

If two objects travel away from each other, what is their rate of travel?

The rate is the addition of object’s rates

Note: The objects increase the distance themselves at this ADDITION rate

How well did you know this?

Not at all

Perfectly

Translate this into equation: If french fries cost twice as much as coleslaw.

F = 2C

How well did you know this?

Not at all

Perfectly

How do you translate this statement: Twice as many paperpack fiction as paperpack nonfiction

PF = 2x PN
Tip: middle out, number in, last stay

How well did you know this?

Not at all

Perfectly

Considering the same travel distance

T or F: IF the speed increase by 20%, the time will reduced by 20%

False - For % increase/decrease, be careful even though the speed and time have reciprocal relationship:
- speed increases by 20% = 1+ 1/5 = 6 /5 of the actual speed
- hypothetical time will be 5/ 6 of the actual time or 1/6 time will be reduced (16.67%)

How well did you know this?

Not at all

Perfectly

Translate 25% Profit into the Cost: Rev Ratio?
Translate 20% Loss into the Cost: Rev Ratio?

25% Profit R- C 1.25 of the cost = 1+ 1/4 =5/4 —> flip C:R = 4/5
20% Loss = 0.8 of the cost = 1- 1/5 = 4/5 —-> flip C:R = 5/4

How well did you know this?

Not at all

Perfectly

Translate/ Draw the inference:
- The difference between Mary’s & Jim’s salaries was twice the difference between Mary’s & Kate’s. If Mary has the highest salaries of the three.

Mary, Jim & Kate’s salaries belong to a group of consecutive space integer with Kate’s salaries in the middle:
- J, K, M (i.e: 2,4,6 -> 6-2 = 2 (6-4)

How well did you know this?

Not at all

Perfectly

What does “each was paid in proportion to the number of hours he or she worked” given the total amount of wages mean?

Each person = total amount of wages x (the # of hours/ total hours)

How well did you know this?

Not at all

Perfectly

How does the increase (or decrease) in constant rate differ from a fix amount?

Increase/decrease in constant rate = increases (or decreases) by a fixed percentage in a given time interval.
- a(2) = k a (1)….a(3) = k a(2)….a(n) = a(1) x k^(n-1)
- its the compounding interest graph

Increase/Decrease by a fix amount = Consecutive Sequence: a(n) = a(1) + k (n-1)
- its the linear equation

How well did you know this?

Not at all

Perfectly

How do we know if the 9 times hard copies include its original number?

There were 36.000 hardback copies of a certain novel sold before the paperback version was issued. From the time 1st paperback copy was sold until the last copy of the novel was sold, 9 times as many paperpack copies has hardback copies were sold.

The problem quite explitcitly indicates that during the specific period (2nd sentence), paperback is 9 times of the only number of hardback copies for the period that paperback copies were sold.

How well did you know this?

Not at all

Perfectly

What is the hidden theme in this DS problem?

A certain dealership has a number of cars to be sold by its salespeople. How many cars are to be sold?
(1) If each of the salespeople sells 4 of the cars, 23 cars will remain unsold.
(2) If each of the salespeople sells 6 of the cars, 5 cars will remain unsold.

Divisibility & Unit conversion:
- 4x + 23 = 6x + 5 -> number of salesperson
- Note the assumption: same # of hired salespeople & same # of cars sold.

How well did you know this?

Not at all

Perfectly

Of the 230 single-family homes built in City X last year, how many were occupied at the end of the year?
(1) Of all single-family homes in City X, 90 percent were occupied at the end of last year.
(2) A total of 7,200 single-family homes in City X were occupied at the end of last year.

1) Practice Quant reading just as how you do on Verbal section
2) No information relating to single-family homes built in either statements. Therefore, anwer is E

How well did you know this?

Not at all

Perfectly

Intuitively draw the conclusion about the rate relationship

It takes Machine X twice as long to produce the lot of cans as it takes Machines X and Y running simultaneously to produce the lot.

-taking twice as long then rate of Machine X is 1/2 the rate of both machine X & Y working together
- machine Y has the same constant rate as X: two identical machines cut down the time by half

How well did you know this?

Not at all

Perfectly

If a tank is leaking water at a constant rate of 3gal/hr, and became empty less than 12hrs. Does the tank contain more than 30 gallons of water?

Yes & No:
1) No: if the tank emptied at one hour, w/ constant rate of 3gal/hr, the tank contain 3 gal, which is less than 30
2) Yes: If the tank emptied at 11 hours, the tank would contain 33 gal, which is more than 30

Tim and Élan are 90 miles away from one another. They are starting to move towards each other simultaneously, Tim at a speed of 10 Mph and Élan at a speed of 5 Mph. If every hour they double their speeds, what is the distance that Tim will pass until he meets Élan?

The fact that Tim & Elan both double their speeds every hours doesn’t change the original ratio of speed 2:1. Therefore, their distance must follow the ratio of 2:1 (as their travel time is the same)

when you see double matrix…

In a certain group of 50 people, how many are doctors who have a law degree?

(1) In the group, 36 people are doctors.
(2) In the group, 18 people have a law degree.

1) Be wary of the assumption that neither categories is ZERO
2) Only If the statement indicate that a member must be either or, you can make the assumption for 1)

A clothing manufacturer makes jackets that are wool or cotton or a combination of wool and cotton. The manufacturer has 3,000 pounds of wool and 2,000 pounds of cotton on hand. Is this enough wool and cotton to make at least 1,000 jackets?

(1) Each wool jacket requires 4 pounds of wool, and no cotton
(2) Each cotton jacket requires 6 pounds of cotton, and no wool

Notice the language asking: how many jackets in general, and not a specific type
Always think why the information in the stimulus is there. DON’T TAKE IT for granted.

For data sufficiency

What technique can we use to test whether two linear equations of X & Y (rev, units, costs..) has a unique solution or they are just the same equation in disguise?

Calculate the slopes of two equation - if they are equal then they are parallel, and hence they are just the same equation

How come there are more than one possible solutions for A &C?

the regular admission fees were ¥5,500 for each adult and ¥4,800 for each child. Because there were at least 10 people in the group, each paid an admission fee that was 10% less that the regular admission fee. How many children were in the group?
(1) The total of the admission fees paid for the children in the group was ¥4,860 more than the total of the admission fees paid for the adults in the group.

Because there is no upper limit of total A +C, which is given by the problem that is greater than 10

Under what condition that this following paradox can occur?

At a certain clothing store, customers who buy 2 shirts pay the regular price for the first shirt and a discounted price for the second shirt. The store makes the same profit from the sale of 2 shirts that it makes from the sale of 1 shirt at the regular price. For a customer who buys 2 shirts, what is the discounted price of the second shirt?

Since the store makes the same profit selling 2 shirts as 1 shirt, the shirt at a discounted price must bring zero profit to the store. In result, the discounted price must be equal to the cost of the shirt to store (sale price - cost = 0)

Express the discounted price in term of original price & saving

If Mel saved more than $10 by purchasing a sweater at a 15 percent discount, what is the smallest amount the original price of the sweater could be, to the nearest dollar?

Percentage discount (15%) of the Original Price >= the amount of Saving ($10)
- 0.15 X > 10 -> X = 1000/15

Why this statement is sufficient?

For a certain city’s library, the average cost of purchasing each new book is $28. The library receives $15,000 from the city each year; the library also receives a bonus of $2,000 if the total number of items checked out over the course of the year exceeds 5,000. Did the library receive the bonus last year?
1. The library purchased an average of 50 new books each month last year and received enough money from the city to cover this cost.

1) Extract all the given info: 50 books/month x 12 x28 = $16,800.
2) Since it is said that the library received enough money to cover this cost, it must have received the bonus

# Use the efficient conversion unit to find distance difference/ minute While on a straight road, Car X and Car Y are traveling at different constant rates. If Car X is now 1 mile ahead of Car Y, how many minutes from now will Car X be 2 miles ahead of Car Y ? (1) Car X is traveling at 50 miles per hour and Car Y is traveling at 40 miles per hour.

Car X is traveling at 5 miles/6 mins. (50/60) Car Y is traveling at 4 miles/6 mins. (40/60) Every 6 mins, Car X moves away from car Y at a rate 1miles. Therefore, it would take 12 mins for 2 miles away between car X and Y

# What is the key lesson from this? At Perry High School, the ratio of students who participate in either the band program or the choral program to students who participate in neither program is 3 to 8. If 220 students attend Perry High School, how many of them participate in neither program?

It is not double matrix problem - Not every question with either/neither requires double matrix solution

# Use limited algebra & test case If a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster, he would have covered 70 more miles than he actually did. How many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day?

1) S (speed) x T (time) = D (distance) (S+5)(T+1) = D + 70 -> ST +5T+S+5 = 70+D, then 5T + S = 65 2) Test case w/ T=1, S = 60 then D= 60 & the extra will have 2x65 = 130 (exactly 70 extra miles), this means: 3 (2hrs longer) x70 (10mph faster) = 210 or 150 more miles than the original S & T

# Translate all possible relationships & Find assumption If an organization were to sell n tickets for a theater production, the total revenue from ticket sales would be 20 percent greater than the total costs of the production. If the organization actually sold all but 5 percent of the n tickets, the total revenue from ticket sales was what percent greater than the total costs of the production?

1) Sell n tickets will have 20% profit, so 5% unsold ticket n will have less than 20% profit 2) The sale price for each ticket is 20% greater than the cost production of each ticket 3) The sale price for each ticket is implied constant - Actual revenue = 0.95 Projected Rev - Projec Rev = 1.2 Cost

# Can you see the analogy w/ other question? In 1980 John’s salary was $15,000 a year and Don’s salary was $20,000 a year. If every year thereafter. John receives a raise of $2,450 and Don receives a raise of $2,000, the first year in which John’s salary will be more than Don’s salary is

This question is a variation on the "Chase Down" prompts (e.g. A car chasing another car or a runner chasing another runner) that are in the same rare category of questions as Combined Rates. The method for solving is also the same: - $5000 (Distance Difference)/ Relative Speed (2450-2000) = 12 years

# Translate the bold part into algebraic expression Regulators are likely to end what are, in effect, long-standing exemptions permitting pilots of small turboprop aircraft at small carriers to fly **as many as 20 percent more hours per month than pilots at larger airlines do**, and consequently some carriers could be forced to hire additional pilots.

Pilots at small carriers are allowed to fly more hours than those at larger airlines (X). How much more? - 1%....20% -> If X is the # of hours then: X < Y < 1.2X

# Why is this statement alone is sufficient? MachinesXandYproducedidenticalbottlesat different constant rates. Machine X, operating alone for 4 hours, filled part of a production lot; then Machine Y, operating alone for 3 hours, filled the rest of this lot. How many hours would it have taken Machine X operating alone to fill the entire production lot? **(1) Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours.**

Machine Y produce **A** bottles in 3 hrs then Machine X will produce **2A** in 4hrs. Therefore, the total number of bottles for THE JOB is **3A** bottles. - Using proportional technique, we have (3A x 4)/ 2A = 6 hours Key word: fill part & fill the rest - Y didn’t join X at the same time

# What is the key lesson in this problem? On a certain road, 10 percent of the motorists exceed the posted speed limit and receive speeding tickets, but 20 percent of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on that road exceed the posted speed limit ?

Careful reading of the key words/modifiers & Double Matrix map outline: - 10% of the motorists exceed the posted speed limit & receiving speeding tickets = 0.1 of the total motorists on that road (X) or 0.1X - 20% of the motorists who exceeded the posted speed limits (Y) do not receive ticket or 0.2Y - Find Y/X relation via: 0.1 X + 0.2Y = Y -> 0.1 X = 0.8Y so Y/X = 12.5%

# Why this statement is not sufficient? A jewelry dealer initially offered a bracelet for sale at an asking price that would give a profit to the dealer of 40 percent of the original cost. What was the original cost of the bracelet? (2) The jewelry dealer sold the bracelet for $1,953.

Its the trap - the key word is "initially offered". Hence, we can’t infer the sale price of $1,953 relationship to original cost (it could be lower or greater than 40% profit)

# Express the constant rate relationship here The net value of a certain stock increased at a constant rate during the ten-year period between 1990 and 2000. What was the value of the stock in the year 1998? (1)In 1991, the value of the stock was 130 U.S dollars. (2)In 1992, the value of the stock was 149.5 U.S dollars.

Constant rate = a(3)/ a(2) = 149.5/130 = 1.15 - or 15% increase by each year - a(1998) = 9th term of sequence - a (1990) = 1st term of sequence hence : a (1998) = a (1990) x 1.15^(9-1)

# What do you need to pay attention to? The cost of deluxe hamburger and a shake is $7.00. If prices do not vary with quantity purchased, how much does one shake cost? (1) If the price of the shake were 1/2 of its present price, a shake would cost 1/5 of what the deluxe hamburger costs.

The wording of hypothetical scenario: - Price of hypothetical (H) = 1/2 P - P (H) = 1/5 Price of hamburger (H) -> 1/2 P = 1/5H -> H + P = $7 so this statement is sufficient

# T or F You can use weighted average for the average speed, time, or rate

F- There are reciprocals in Work, Rate & Distance relationship

# Interprete this passage A certain clock marks every hour by striking a number of times equal to the hour, and the time required for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stroke and the end of the last stroke is 22 seconds.

At 6:00, 22 seconds include = time of 6 strikes + time of the 5 intevals (between each strike) - each strike time = interval time --> 22 seconds/ 11parts or 2sec/ part

# T or F: Distance Ratio X: Y = Ratio of Rate X:Y when t(x)=t(y) Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y ?

True - Since they travel the same mount of time when they meet, the distance is only dependent on the ratio of rate - Train X will travel in ratio 5:3 to train y: 5x 100/ (3+5) = 62.5 miles

# What is this question in disguise? A bicyclist begins a race at a constant rate of 10 miles per hour, slowing down by 1 mile per hour every half-hour. How many miles has the bicyclist traveled after exactly 2.5 hours?

Sequence: 10, 9, 8,... Given that each half hour, we have the total distance for each decreasing interval as: 0.5x 10 + 0.5x9 +. ..+ 0.5x6 = 0.5 (10+9+..+6) = 0.5x8x5 = 20 miles