Angle Relationships and Inequalities

The video covers several problems from a data sufficiency sample, focusing on geometry, percentages, and inequalities. It begins with a geometry problem involving parallel lines and angles, followed by a percentage problem about red-haired women, and another percentage problem involving integers. The video concludes with an inequality problem, demonstrating how to manipulate inequalities. Each problem is explained with detailed solutions, emphasizing the importance of understanding the underlying concepts.

In a figure with parallel lines k and m, if angle y is 120 degrees, what is the value of angle x?

• 30 degrees

• 90 degrees

• 45 degrees

• 60 degrees

If angle z is 60 degrees in a figure with parallel lines, what can be inferred about angle y?

• y is 150 degrees

• y is 120 degrees

• y is 90 degrees

• y is 60 degrees

What percentage of a group are women with red hair if 5% of women and 10% of men have red hair?

• Cannot be determined

• 15%

• 10%

• 5%

If r is 3/4 of s, what percentage is r of s?

• 25%

• 50%

• 75%

• 100%

Given r/s = 75/100, what percentage is r of s?

• 100%

• 75%

• 50%

• 25%

If 2a is greater than 2b, what can be concluded about a and b?

• a is less than b

• Cannot be determined

• a is greater than b

• a is equal to b

If a + c is greater than b + c, what can be concluded about a and b?

• a is less than b

• Cannot be determined

• a is equal to b

• a is greater than b