### All GRE Math Resources

## Example Questions

### Example Question #1 : How To Express A Fraction As A Ratio

There are philosophy books and history books on a shelf. The number of philosophy books is doubled. What is the ratio of philosophy books to history books after this?

**Possible Answers:**

**Correct answer:**

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 .

### Example Question #2 : How To Express A Fraction As A Ratio

A used car lot has total vehicles to be sold. of the vehicles are 4-wheel drive and the rest are 2-wheel drive. What is the ratio of 2-wheel drive to 4-wheel drive vehicles on the lot?

**Possible Answers:**

**Correct answer:**

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.

### Example Question #3 : How To Express A Fraction As A Ratio

When television remotes are shipped from a certain factory, 1 out of every 200 is defective. What is the ratio of defective to nondefective remotes?

**Possible Answers:**

1:200

199:1

200:1

1:199

**Correct answer:**

1:199

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

### Example Question #2 : How To Express A Fraction As A Ratio

On a desk, there are papers for every paper clips and papers for every greeting card. What is the ratio of paper clips to total items on the desk?

**Possible Answers:**

**Correct answer:**

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 .

### Example Question #35 : Proportion / Ratio / Rate

In a classroom of students, each student takes a language class (and only one—nobody studies two languages). take Latin, take Greek, take Anglo-Saxon, and the rest take Old Norse. What is the ratio of students taking Old Norse to students taking Greek?

**Possible Answers:**

**Correct answer:**

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 .

### Example Question #3 : How To Express A Fraction As A Ratio

In a garden, there are pansies, lilies, roses, and petunias. What is the ratio of petunias to the total number of flowers in the garden?

**Possible Answers:**

**Correct answer:**

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 .

### Example Question #3 : How To Express A Fraction As A Ratio

Express as a ratio.

**Possible Answers:**

**Correct answer:**

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

### Example Question #4 : How To Express A Fraction As A Ratio

If there are fifteen girls and six boys in a class, what is the ratio of boys to girls?

**Possible Answers:**

**Correct answer:**

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

### Example Question #5 : How To Express A Fraction As A Ratio

What is the ratio of square numbers to cubic numbers from noninclusive?

**Possible Answers:**

**Correct answer:**

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 .

### Example Question #6 : How To Express A Fraction As A Ratio

If apples equal bananas and bananas equal carrots, what is the ratio of an apple to a carrot?

**Possible Answers:**

**Correct answer:**

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.