### All ISEE Middle Level Quantitative Resources

## Example Questions

### Example Question #1 : How To Use A Venn Diagram

Define:

Universal set , the set of all natural numbers.

= { | is a multiple of 3}

= { | is a multiple of 5}

If all of the natural numbers were to be placed in their appropriate places in the above Venn diagram, which of the following would be placed in the gray region?

**Possible Answers:**

**Correct answer:**

The gray region is the region outside *both* and and is therefore the set of natural numbers that are multiples of *neither* 3 nor 5.

1,565 and 3,890 can be eliminated as choices as each is divisible by 5: the former ends in 5 and the latter ends in 0.

7,431 and 3,966 can be eliminated as each is divisible by 3: and .

7,916 is *not* divisible by 5 as it ends in 6; it is *not* divisible by 3 as . Therefore, it is the correct choice.

### Example Question #1 : Data Analysis

Define:

Universal set , the set of all natural numbers.

= { | is a multiple of 3}

= { | is a multiple of 5}

If all of the natural numbers were to be placed in their appropriate places in the above Venn diagram, which of the following would be placed in the gray region?

**Possible Answers:**

**Correct answer:**

The gray region is the region outside *both* and and is therefore the set of natural numbers that are multiples of *neither* 3 nor 5.

1,565 and 3,890 can be eliminated as choices as each is divisible by 5: the former ends in 5 and the latter ends in 0.

7,431 and 3,966 can be eliminated as each is divisible by 3: and .

7,916 is *not* divisible by 5 as it ends in 6; it is *not* divisible by 3 as . Therefore, it is the correct choice.

### Example Question #1 : Data Analysis

Which is the greater quantity?

(A) The midrange of the data set

(B) The midrange of the data set

**Possible Answers:**

(A) is greater

It is impossible to determine which is greater from the information given

(B) is greater

(A) and (B) are equal

**Correct answer:**

(A) is greater

The midrange of a data set is the mean of its least and greatest elements. The midrange of the first data set is ; that of the second data set is . (A) is greater.

### Example Question #1 : Data Analysis

Set is defined as:

Set is made by doubling the values in set .

What is the range of values in set ?

**Possible Answers:**

**Correct answer:**

To find the range of a set of numbers, you do not even have to put them in order. You merely need to subtract the smallest value from the largest. Given the way of constructing set by doubling set 's values, the largest and smallest values in will directly correlate to the same in set :

Smallest:

Largest:

Therefore, the range is:

### Example Question #1 : Data Analysis

The members of set are defined as the values for:

For values of between and .

What is the range of set ?

**Possible Answers:**

**Correct answer:**

To find the range of a set of numbers, you do not even have to put them in order. You merely need to subtract the smallest value from the largest. Given the way that we construct set from the function , we merely need to use that function to find the smallest and largest values. Luckily, that is pretty easy for this question. The smallest will be and the largest will be

Smallest:

Largest:

Therefore, the range is:

### Example Question #4 : Data Analysis

Set is defined as:

The members of set are defined by the function:

, where is a member of set .

So, for instance, set T contains because for , we get:

What is the range of set ?

**Possible Answers:**

**Correct answer:**

We first need to determine the members of set . Using our function, we will get:

Our largest value is , and our smallest value is ; therefore, the range is

### Example Question #5 : Data Analysis

Given the below set of numbers find the range:

**Possible Answers:**

**Correct answer:**

Range for a set of data is defined as the difference between the biggest and smallest number.

First we find the biggest number which is 15, we then subtract the smallest number in this set which is negative 2 as shown below:

Remember, when subtracting a negative number we must add the numbers.

### Example Question #6 : Data Analysis

Given the below set of numbers, find the range:

**Possible Answers:**

**Correct answer:**

In order to find the range, we must subtract the smallest number from the biggest number.

We must convert the fractions to have a common denominator which is 10.

Therefore, the range of this set is

.

### Example Question #7 : Data Analysis

Given the below set of numbers, find the range:

**Possible Answers:**

**Correct answer:**

In order to find the range, we must subtract the smallest number from the biggest number.

We must convert the fractions to have a common denominator which is 10.

Therefore, the range of this set is

.

### Example Question #8 : Data Analysis

Find the range of the data set provided:

**Possible Answers:**

**Correct answer:**

In order to answer this question correctly, we need to recall the definition of range:

**Range: **The range of a data set is the difference between the highest value and the lowest value in the set.

In order to find the range, we need to first organize the data from least to greatest to find the lowest and highest values:

Next, we can solve for the difference between the highest value and the lowest value:

The range for this data set is

Certified Tutor