Proportion / Ratio / Rate - GRE Quantitative Reasoning

One teaspoon of salt requires 2 teaspoons of baking powder, which requires 16 teaspoons of milk and 32 teaspoons of sugar. 32 teaspoons of sugar requires 96 teaspoons of flour, which equals two cups of flour.

If 2/3 is cut off and thrown away, that means 1/3 of the original length remains. Of this, 1/4 gets cut off and thrown away, meaning 3/4 of 1/3 still remains. Multiplying 3/4 * 1/3, we get 1/4.

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 is really an easy fraction division. You should first divide the lemon juice amount by the water amount:

Remember, to divide fractions, you multiply by the reciprocal:

This is the same as saying:

If 2/3 is cut off and thrown away, that means 1/3 of the original length remains. Of this, 1/4 gets cut off and thrown away, meaning 3/4 of 1/3 still remains. Multiplying 3/4 * 1/3, we get 1/4.

This problem is really an easy fraction division. You should first divide the lemon juice amount by the water amount:

Remember, to divide fractions, you multiply by the reciprocal:

This is the same as saying:

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 .

To get the apple to carrot ratio, we need to equal out the bananas. The least common denominator of and is . So if apples equal bananas, then bananas equal apples. Also, if bananas equal carrots, then bananas equal carrots. Since now the total bananas are equal, we can find the ratio of apples to carrots. We have as the final answer.

If Jill, Jack and John get , that means there are parts.

Because they found , each part gets or .

Jack gets or .

John gets or .

Since the question is asking how much more did Jack get than John, we subtract and to get .