Determining Values and Relationships

The video tutorial covers a series of math problems, focusing on integer properties, solving algebraic equations, evaluating fractional expressions, and analyzing triangle angles. Each problem is approached by examining given statements to determine sufficiency and solve for unknowns. The tutorial emphasizes logical reasoning and mathematical principles to arrive at solutions.

Which statement is sufficient to determine if x is an integer?

• Neither statement

• Both statements together

• Statement 2: 2x is an integer

• Statement 1: x/2 is an integer

Which of the following is true about the statement '2x is an integer'?

• It contradicts the first statement

• It is not sufficient to determine x is an integer

• It is sufficient to determine x is an integer

• It is irrelevant to the problem

What is the solution to the equation 2x + 1 = 0?

• x = 1

• x = 0

• x = -1/2

• x = 1/2

What is the value of x if (x + 1)^2 = x^2?

• x = 0

• x = -1/2

• x = -1

• x = 1

Which statement(s) are needed to find the value of 1/k + 1/r?

• Neither statement

• Statement 1: k + r = 20

• Statement 2: kr = 64

• Both statements together

If k + r = 20 and kr = 64, what is the value of 1/k + 1/r?

• 1/4

• 1/5

• Cannot be determined

• 1/3

If x is one of the numbers 1/4, 3/8, or 2/5, which statement(s) help determine its value?

• Both statements together

• Neither statement

• Statement 2 alone

• Statement 1 alone

If x is greater than 1/4 and less than 1/2, which value can x not be?

• 2/5

• 3/8

• 1/4

• 1/3

Which angle in triangle PQR has the greatest degree measure?

• Angle opposite side QR

• Angle opposite side PQ

• Cannot be determined

• Angle opposite side PR

In triangle PQR, if y = x + 3, which side is the longest?

• PQ

• QR

• Cannot be determined

• PR