Geometry - GMAT Quantitative

The sum of the measures of the six interior angles of any hexagon is , so if Statement 1 is true, then the sum of the six numbers is 720, regardless of the individual values.

Statement 2 is not enough, however, for us to deduce this sum; this only tells us the mean of the third- and fourth-highest values.

The sum of the measures of the six interior angles of any hexagon is , so if Statement 1 is true, then the sum of the six numbers is 720, regardless of the individual values.

Statement 2 is not enough, however, for us to deduce this sum; this only tells us the mean of the third- and fourth-highest values.

The sum of the measures of the five interior angles of any pentagon is , so if Statement 1 is true, then the sum of the five numbers is 540, regardless of the individual values.

The mean of five data values multiplied by 5 is the sum of the values, so if Statement 2 is true, then their sum is .

The sum of the measures of the six interior angles of any hexagon is , so if Statement 1 is true, then the sum of the six numbers is 720, regardless of the individual values.

Statement 2 is not enough, however, for us to deduce this sum; this only tells us the mean of the third- and fourth-highest values.

The sum of the measures of the five interior angles of any pentagon is , so if Statement 1 is true, then the sum of the five numbers is 540, regardless of the individual values.

The mean of five data values multiplied by 5 is the sum of the values, so if Statement 2 is true, then their sum is .

The sum of the measures of the six interior angles of any hexagon is , so if Statement 1 is true, then the sum of the six numbers is 720, regardless of the individual values.

Statement 2 is not enough, however, for us to deduce this sum; this only tells us the mean of the third- and fourth-highest values.

The sum of the measures of the five interior angles of any pentagon is , so if Statement 1 is true, then the sum of the five numbers is 540, regardless of the individual values.

The mean of five data values multiplied by 5 is the sum of the values, so if Statement 2 is true, then their sum is .

The sum of the measures of the six interior angles of any hexagon is , so if Statement 1 is true, then the sum of the six numbers is 720, regardless of the individual values.

Statement 2 is not enough, however, for us to deduce this sum; this only tells us the mean of the third- and fourth-highest values.

The sum of the measures of the five interior angles of any pentagon is , so if Statement 1 is true, then the sum of the five numbers is 540, regardless of the individual values.

The mean of five data values multiplied by 5 is the sum of the values, so if Statement 2 is true, then their sum is .

The sum of the measures of the six interior angles of any hexagon is , so if Statement 1 is true, then the sum of the six numbers is 720, regardless of the individual values.

Statement 2 is not enough, however, for us to deduce this sum; this only tells us the mean of the third- and fourth-highest values.

The sum of the measures of the five interior angles of any pentagon is , so if Statement 1 is true, then the sum of the five numbers is 540, regardless of the individual values.

The mean of five data values multiplied by 5 is the sum of the values, so if Statement 2 is true, then their sum is .

The sum of the measures of the six interior angles of any hexagon is , so if Statement 1 is true, then the sum of the six numbers is 720, regardless of the individual values.

Statement 2 is not enough, however, for us to deduce this sum; this only tells us the mean of the third- and fourth-highest values.

The sum of the measures of the five interior angles of any pentagon is , so if Statement 1 is true, then the sum of the five numbers is 540, regardless of the individual values.

The mean of five data values multiplied by 5 is the sum of the values, so if Statement 2 is true, then their sum is .

The sum of the measures of the six interior angles of any hexagon is , so if Statement 1 is true, then the sum of the six numbers is 720, regardless of the individual values.

Statement 2 is not enough, however, for us to deduce this sum; this only tells us the mean of the third- and fourth-highest values.

The sum of the measures of the five interior angles of any pentagon is , so if Statement 1 is true, then the sum of the five numbers is 540, regardless of the individual values.

The mean of five data values multiplied by 5 is the sum of the values, so if Statement 2 is true, then their sum is .

If , then

.

This makes an equiangular triangle.

If , and is equiangular, then, since corresponding angles of similar triangles are congruent, has the same angle measures, and is itself equiangular.

From either statement, since all equiangular triangles are equilateral, we can draw this conclusion about .

The lines of the two equations must have slopes that are the opposites of each others reciprocals.

Write each equation in slope-intercept form:

As can be seen, knowing the value of is necessary and sufficient to answer the question. The value of is irrelevant.

The answer is that Statement 1 alone is sufficient to answer the question, but Statement 2 alone is not sufficient to answer the question.

The sum of the measures of the angles of a hexagon is

Therefore,

Suppose we only know that , , and are the first three terms of an arithmetic sequence, in order. Then for some common difference ,

Suppose we only know that . Then

With no further information, we cannot determine .

The relationship between the number of sides of a regular polygon and the measure of a single angle is

If we are given that , then we can substitute and solve for :

making the figure a nine-sided polygon.

Knowing only the measure of each side is neither necessary nor helpful; for example, it is possible to construct an equilateral triangle with sidelength 8 or a square with sidelength 8.

The correct answer is that Statement 1 alone is sufficient to answer the question, but not Statement 2 alone.