### All ISEE Upper Level Quantitative Resources

## Example Questions

### Example Question #1 : How To Find The Common Part Of A Venn Diagram

What is the greatest common factor of and ?

**Possible Answers:**

**Correct answer:**

To solve for the greatest common factor, it is necessary to get your numbers into prime factor form. For each of your numbers, this is:

Next, for each of your sets of prime factors, you need to choose the exponent for which you have the smallest value; therefore, for your values, you choose:

:

:

:

Taking these together, you get:

### Example Question #1 : How To Find The Common Part Of A Venn Diagram

For the Venn Diagram pictured above, what is the value for the overlap of the two sets drawn as circles?

**Possible Answers:**

**Correct answer:**

Solving for the overlap of two sets is easy when you have all of your data. You know that the two circles added up will have to equal or . This is the total amount in the "universe" () *minus* the amount that is found outside of the two circles ().

Because the overlap happens once in each circle, you know that:

Given your data, you know:

Solving, this means:

### Example Question #3 : How To Find The Common Part Of A Venn Diagram

For the Venn Diagram pictured above, what is the value for the overlap of the two sets drawn as circles?

**Possible Answers:**

No answer possible.

**Correct answer:**

Solving for the overlap of two sets is easy when you have all of your data. You know that the two circles added up will have to equal or . This is the total amount in the "universe" () *minus* the amount that is found outside of the two circles ().

Because the overlap happens once in each circle, you know that:

Given your data, you know:

Solving, this means: . The overlap is the whole of circle !

### Example Question #4 : How To Find The Common Part Of A Venn Diagram

For the Venn Diagram pictured above, what is the value for the overlap of the two sets drawn as circles?

**Possible Answers:**

**Correct answer:**

Solving for the overlap of two sets is easy when you have all of your data. You know that the two circles added up will have to equal or . This is the total amount in the "universe" () *minus* the amount that is found outside of the two circles ().

Because the overlap happens once in each circle, you know that:

Given your data, you know:

Solving, this means:

### Example Question #5 : How To Find The Common Part Of A Venn Diagram

**Possible Answers:**

No answer is possible.

**Correct answer:**

No answer is possible.

Do not be tricked by this question! In order to solve for the overlap, you need to know the amount that is in the area *outside* of the circles *but still inside the universal box area!* You cannot figure out the answer without knowing this fact; therefore, you must select "No answer is possible." We *know* that the two circles do not exhaust the universe because . This is not large enough to fill the complete . If it were, you would know that the overlap is .

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