Proportion / Ratio / Rate - GRE Quantitative Reasoning

To begin, notice that there is a ratio between the water in your container and the water specified by the mix of the components. Given that there are total parts in your solution, this means that you can set up this equation:

Multiplying both sides by 8, you get:

There are total gallons of solution.

To begin, you know that the basic form of the solution has a total of , or parts. Now, we know that we are going to have to add parts of orange juice. This means that the new solution will have parts orange juice and total parts (since we are adding to the original). Since we want this to be % orange juice, we really want the following equation to be true:

Solve the following equation, therefore:

Multipy by :

Now, isolate :

First we set up two equations, one for Mary and one for Todd. Mary’s money growth is represented by y = 2x + 17 (she starts with $17 so this is our y-intercept and she gains $2 weekly so this is our slope).

Todd’s money growth is represented by y = 3x + 4 (he starts with $4 so this is our y-intercept and he gains $3 weekly so this is our slope). Set these two equal and solve for x. We find that after 13 weeks they have the same amount of money. But this is not what the question asked for. They want to know how many weeks it will take before Todd has MORE than Mary. Thus the answer must be 14 weeks.

It's tempting to take the two rates and average them. This is wrong but the GRE will always give you this as a trap answer choice. In this problem, looking at the two rates separately would give us 40 mi/hr and 20 mi/hr, making the trap answer here 30 mi/hr.

The key is that Kathy goes 40 mi/hr for 1 hour and then 20 mi/hr for 3 hours, so the speed should be less than the middle number of 30. 18 mi/hr is lower than her lowest speed so that doesn't make sense, and 20 mi/hr is too low because the 1 hour at 40 mi/hr should bring the average up a little bit. Therefore the answer must be 25 mi/hr.

We can also do the computations to find the answer. The correct formula is average miles per hour = total miles / total hours. Plugging in our values, average speed = (40 + 60) miles / (1 + 3) hours = 25 mi/hr.

You know that the distance between these cars is defined by the following equation: Answer "250" = 500 – 90t. This is because the cars get 90 miles closer every t hours. You want to solve for t when the distance is 150: 150 = 500 – 90t; –350 = –90t; t = 35/9. Recall, however, that the question asked for the rounded-down number of minutes; therefore, multiply your answer by 60: 35 * 60/9 = 2331/3

Rounding down, you get 233.

In this rate word problem, we need to find the rates at which Mary and Bejamin frost their respective cupcakes, and then sum their respective rates per hour. In one hour Mary frosts 133 cupcakes. (Note: the question specifies COMPLETELY frosted cupcakes only, so the fractional results here will need to be rounded down to the nearest integer.) Benjamin frosts 82 cupcakes.

82 + 133=215

This is a plug and chug sort of problem, where choosing values is arbitrary. Suppose the generators consume 5 cubic meters of fuel per day and there are 10 generators. Then the number of days that 100 cubic meters of fuel will last is expressed as 100/5*10. Switching back to variables, that comes out to t/fg.

Answer: 27 days
Explanation: Recall that the rate of gas consumption is INVERSELY related to the time it takes to consume the gas. Thus, if the rate of gas consumption increases to 5/3 of it's original rate (a 66.6% increase), then the time it will take to consume all of the gas decreases to the inverse, or 3/5 of the original. The answer is thus 27 (3/5 of 45).

It is probably easiest just to write out the eating schedule:

Roll 1: 8:00 AM - 8:10 AM

Roll 2: 10:10 AM - 10:20 AM

Roll 3: 12:20 PM - 12:30 PM

Roll 4: 2:40 PM - 2:50 PM

Therefore, he eats 4 rolls, or 1450 * 4 = 5800 calories. To get the rate, this must be divided across the whole day's minutes: 9 work hours * 60 = 540 minutes. The average calories per minute = 10.74.

The cold-water faucet fills the bucket in 30 minutes, so in 1 minute it fills 1/30 of the bucket. The hot-water faucet fills the bucket in 60 minutes, so in 1 minute it fills 1/60 of the bucket. Then, when they're both running together they fill 1/30 + 1/60 of the bucket in 1 minute.

1/30 + 1/60 = 2/60 + 1/60 = 3/60 = 1/20, so they fill the whole bucket in 20 minutes.

The puppy starts at 4 pounds and gains 1 pound per month for 8 months, so he weighs 4 + 8 = 12 pounds at the end of 8 months. The kitten starts at 2 pounds and gains 2 pounds per month for 7 months, so he weighs 2 + 14 = 16 pounds at the end of 7 months. Therefore Quantity B is greater.

This problem gives the rate of Hose A instead of the time it takes to fill the shark tank. Let's convert the rest of the problem information into rates as well. The tank is 10,000 gallons, and it takes the two hoses together 4 hours to fill the tank. Therefore, the combined rate is 10,000/4 = 2,500 gallons per hour.

Now we know that Hose A can deliver 1,000 gallons in an hour, and together Hose A and Hose B can deliver 2,500 gallons in an hour. So 1,000 gallons + Hose B gallons = 2,500 gallons. Then Hose B fills the tank at 2500 – 1000 = 1500 gallons/hour.

The change in temperature is 100 – 65 = 35 degrees. The change in time is 9 AM to 2 PM, or 5 hours. So the rate of change is 35 degrees / 5 hours = 7 degrees / hour.

Ben mows 1 lawn in 1 hour, or 1/60 of the lawn in 1 minute. Ken mows 1 lawn in 2 hours, or 1/120 of the lawn in 1 minute. Then each minute they mow 1/60 + 1/120 = 3/120 = 1/40 of the lawn. That means the entire lawn takes 40 minutes to mow.

First, we must determine how many feet per hour the train travels.

50 feet per second * 60 seconds in a minute * 60 minutes in an hour.

50 * 60 * 60 = 180,000

Then, it's just a matter of converting 180,000 feet to miles. Because there are 5280 feet in a mile, just divide.

180,000 / 5280 = 34.091

First find what fraction of the job is completed per hour. If John can paint the room in 4 hours, then he completes $\frac{1}{4}$ of it per hour. Similarly, Susan paints $\frac{1}{6}$ of it per hour. So together they paint $\frac{1}{4}$+\frac{1}{6}$ of the room per hour.

Add $\frac{1}{4}$+\frac{1}{6}$ by rewriting them with the same common denominator (least common multiple of 4 and 6 is 12, so 12 is the least common denominator):

$\frac{1}{4}$ + $\frac{1}{6}$ = $\frac{1times 3}{4times 3}$ + $\frac{1times 2}{6times 2}$ = $\frac{3}{12}$ + $\frac{2}{12}$ = $\frac{5}{12}$

This means $\frac{5}{12}$ of the job is completed per hour. To find the number of hours for the whole job (1 room), divide the whole by the fraction completed per hour:

1 div $\frac{5}{12}$ = 1times $\frac{12}{5}$ = $\frac{12}{5}$ hours

Convert hours to minutes:

$\frac{12}{5}$ hours times $\frac{60 minutes}{1 hour}$ = $\frac{720}{5}$ = 144 minutes

If Carol ate 3 pancakes in 5 minutes, she can eat $\frac{3}{5}$ of a pancake every minute. $\frac{3}{5}$ pancakestimes 24 minutes=14.4 pancakes.

That means she ate 14 whole pancakes (and an additional 2/5 of another pancake).

Approach this problem with the following reasoning.

Unit of work done = number of workers * rate * time

In our case, we are given 24 "workers," able to make 5 "units of work," in 0.5 "time." The rate is not given, but can be solved for with our given information.

Units of work = 5

Number of workers = 24

Time = 0.5 hours (30 minutes)

Now, since we know the rate, which does not chage, we can solve for the new time when the number of machines is decreased and the number of devices is increased.

Unit of work done = number of workers * rate * time

The rate is given by amount of probems over time.

To find the amount of problems done in a given amount of time, mulitply the rate by the given amount of time.

We can combine our y terms and cancel our n terms to simplify.