### All GMAT Math Resources

## Example Questions

### Example Question #81 : Algebra

Fill in the circle with a number so that this polynomial is prime:

**Possible Answers:**

**Correct answer:**

If is not prime, then, as a quadratic trinomial of the form it is factorable as

where and .

Therefore, we are looking for a whole number that is *not* the difference of two factors of 60. The integers that *are* such a difference are

Of the choices, only 23 is not on the list, so it is the correct choice.

### Example Question #51 : Exponents

Examine these two polynomials, each of which is missing a number:

Write a whole number inside each shape so that the first polynomial is a factor of the second.

**Possible Answers:**

Write 64 in the square and 4.096 in the circle

Write 64 in the square and 64 in the circle

Write 8 in the square and 64 in the circle

Write 64 in the square and 512 in the circle

Write 8 in the square and 512 in the circle

**Correct answer:**

Write 64 in the square and 512 in the circle

The factoring pattern to look for in the second polynomial is the sum of cubes, so the number in the circle must be a perfect cube of a whole number . We can write this polynomial as

which can be factored as

By the condition of the problem, , so the number that replaces the square is , and the number that replaces the circle is .

### Example Question #81 : Algebra

Simplify.

**Possible Answers:**

**Correct answer:**

There are different ways to approach this problem. We just need to remember three things:

Keeping those in mind, we can simplify the numerator and coefficients:

I'm going to move the negative exponents (number **2** in the list above) in order to make them positive:

We can now simplify the numerator again with the exponents (number **3**) and the exponents (number **1**):

### Example Question #84 : Algebra

Simplify:

**Possible Answers:**

Unable to simplify

**Correct answer:**

The first thing we must do is distribute the exponents outside of the parentheses across each expression (remembering of course that exponents set to another exponent are multiplied).

The last step is to follow the rules of exponent addition/subtraction:

and

Therefore:

### Example Question #61 : Exponents

Which of the following is true if ?

**Possible Answers:**

The equation has no solution.

**Correct answer:**

To answer this question, note that

and

.

Therefore, since

it follows that

and

.

### Example Question #62 : Exponents

Solve for :

**Possible Answers:**

The equation has no solution.

**Correct answer:**

Rewrite both sides as powers of 2 using the exponent rules as follows:

Since powers of the same base are equal, set the exponents equal to each other:

### Example Question #1161 : Problem Solving Questions

Solve for :

**Possible Answers:**

The equation has no solution.

**Correct answer:**

Rewrite both sides as powers of 3 using the exponent rules as follows:

Since powers of the same base are equal, set the exponents equal to each other:

### Example Question #83 : Algebra

Solve for :

**Possible Answers:**

The equation has no solution.

**Correct answer:**

Rewrite all expressions as powers of 2, and use the exponent rules as follows:

Since powers of the same base are equal, set the exponents equal to each other:

### Example Question #82 : Algebra

Solve for :

**Possible Answers:**

The equation has no solution.

**Correct answer:**

Rewrite the first expression to get:

### Example Question #65 : Exponents

Solve for :

**Possible Answers:**

The equation has no solution.

**Correct answer:**

The equation has no solution.

Rewrite both sides as powers of 2 using the exponent rules as follows:

Since powers of the same base are equal, set the exponents equal to each other:

This is identically false, so the equation has no solution.