Proportion / Ratio / Rate - GRE Quantitative Reasoning

Answer: 25
Explanation: For this type of problem, build an equation that represents the relationships between the quantities and solve for the quantitiy you need. The problem states that b=1/4c and a = 1/3b. Thus, a = 1/3(1/4)c, or 1/12 of c. Now put everything in terms of c, thus 1/12c + 1/4c +c = 400. Now comes the tricky step--combine like terms and create the improper fraction (1/12c + 3/12c + 12/12c = 16/12c). Reduce the fraction to 4/3. So 400 is 4/3 of c. Thus c is 3/4 of 400, or 300. a is 1/12 of 300, or 25.

Since she spent 1/4 on the ticket, 3/5 of the remaining 3/4 of the money was spent on popcorn: 3/5 x 3/4 = 9/20. This means 9/20 of the money was spent on popcorn so in total: 1/4 + 9/20 = 14/20 = 7/10 of her money was spent. This leaves 3/10 of her money behind: 3/10x 10 = 3.00.

Set up a proportion: 18.50/5 = x/2. Cross multiply and solve for x: 37 = 5x.... x = 7.40.

It's tempting to pick 1 hour, but that is a trick answer! Picture 3 men each painting 1 room. All 3 of the rooms are done after 3 hours, so each man actually spends 3 hours painting his room, not 1 hour.

The easiest way to solve this is with a rate formula: 1 / combined time = 1 / Bob's time + 1 / Ron's time. We know the combined time and Bob's time, so we can solve for Ron's time:

1/2 = 1/3 + 1/Ron's time

1/Ron's time = 1/2 – 1/3 = 1/6

Ron's time = 6 hours

Although it seems as though "Quantity B is greater" is the correct answer at first glance, a further analysis indicates that this answer is a trap. If and are negative numbers, such as and , then would be the larger number. Similarly, is larger if both and are positive numbers. Thus, it cannot be determined which variable is larger simply based on the information given.

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.

One remote is defective for every 199 non-defective remotes.

First, compute the new number of philosophy books. This will be .

The ratio of philosophy books to history books is thus:

This can be reduced by dividing the numerator and the denominator by :

Therefore, the ratio is .

27 of the 72 cars are 4-wheel drive, we can write this as a proportion.

The proportion of the 4-wheel drive cars to the total number of vehicles.

Therefore, to find the proportion of 2-wheel drive cars is,

Therefore the ratio of 2-wheel drive:4-wheel drive vehicles is 5:3.

Begin by making your life easier: presume that there are papers on the desk. Immediately, we know that there are paper clips. Now, if there are papers, you know that there also must be greeting cards. Technically you figure this out by using the ratio:

By cross-multiplying you get:

Solving for , you clearly get .

(Many students will likely see this fact without doing the algebra, however. The numbers are rather simple.)

Now, this means that our desk has on it:

papers

paper clips

greeting cards

Therefore, you have total items. Based on this, your ratio of paper clips to total items is:

, which is the same as .

To begin, you need to do a simple addition to find the total number of flowers in the garden:

Now, the ratio of petunias to the total number of flowers in the garden can be represented by a simple division of the number of petunias by . This is:

Next, reduce the fraction by dividing out the common from the numerator and the denominator:

This is the same as .

To begin, you need to calculate how many students are taking Old Norse. This is:

Now, the ratio of students taking Old Norse to students taking Greek is the same thing as the fraction of students taking Old Norse to students taking Greek, or:

Next, just reduce this fraction to its lowest terms by dividing the numerator and denominator by their common factor of :

This is the same as .

A ratio is two numbers separated by a colon. When expressing fractions as a ratio, the numerator is the number to the left of the colon while the denominator is to the right of the colon. The answer is

To find an integer ratio, let's find the fractions with a common denominator. This will be . Then, we multiply the left by and the right by to get fractions of and . With the same denominators, we just have numerators to compare. Ratio is then .

Let's convert the words into numbers. Since there are girls and boys, we need ratio of boys to girls. The ratio should be .

If there are girls and boys, that means we have students in the class. To continue to have this ratio, we need an answer than is a multiple of .

is a multiple of which is the right answer.

In the problem, the drink is espresso since the overall weight of the drink is ounces. If we are reducing the concentration of espresso to , then we can create an equation to figure out the addition of water.

represents the addition of water.

Cross-multiply.

Subtract on both sides.

Let's list a bunch of square numbers from noninclusive.

doesn,t count since it's not included HOWEVER: count.

Let's list a bunch of cubic numbers from noninclusive.

doesn,t count since it's not included HOWEVER: count.

There are four square numbers to two cubic numbers. The ratio becomes or .