# GMAT Math : Algebra

## Example Questions

### Example Question #81 : Algebra

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

Explanation:

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.

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

Write 64 in the square and 512 in the circle

Explanation:

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.

Explanation:

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:

Unable to simplify

Explanation:

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).

and

Therefore:

### Example Question #61 : Exponents

Which of the following is true if  ?

The equation has no solution.

Explanation:

To answer this question, note that

and

.

Therefore, since

it follows that

and

.

### Example Question #62 : Exponents

Solve for :

The equation has no solution.

Explanation:

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 :

The equation has no solution.

Explanation:

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 :

The equation has no solution.

Explanation:

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 :

The equation has no solution.

Explanation:

Rewrite the first expression to get:

### Example Question #65 : Exponents

Solve for :

The equation has no solution.