Word Problems - Chapter 5 (Overlapping Sets)
10% of all aliens are capable of intelligent thought and have more than 3 arms, and 75% of aliens with 3 arms or less are capable of intelligent thought. If 40% of all aliens are capable of intelligent thought, what percent of aliens have more than 3 arms? (Problem Set #7)
*The 1st thing you should do is fill in 100 for the grand total* 3/4x = 30 x = 40 60% ←
*Setting up an extended double-set matrix chart can be helpful on certain Data Sufficiency problems. (pg. 89)
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The 38 movies in the video store fall into the following three categories: 10 action, 20 drama, and 18 comedy. However, some movies are classified under more than one category: 5 are both action and drama, 3 are both action and comedy, and 4 are both drama and comedy. How many action-drama-comedy movies are there? (Problem Set #8)
Assign the variable x to represent the number of action-drama-comedy movies. I solved this without considering x, but: 2 ← In the book, they added all of those equations together and got: 36 + x = 38, x = 2
Of 30 integers, 15 are in set A, 22 are in set B, and 8 are in both set A and B. How many of the integers are in NEITHER set A or set B? (pg. 86)
For GMAT problems involving only TWO categorizations or decisions, the most efficient tool is the Double-Set Matrix. When you construct a double-set matrix, the rows should correspond to the MUTUALLY EXCLUSIVE OPTIONS for one decision. Likewise, the columns should correspond to the mutually exclusive options for the other. The answer is 1 ←
Of 60 children, 30 are happy, 10 are sad, and 20 are neither happy nor sad. There are 20 boys and 40 girls. If there are 6 happy boys and 4 sad girls, how many boys are neither happy nor sad? (Problem Set #6)
Very rarely, you might need to consider more than two options for one or both of the dimensions of your chart. As long as each set of distinct options is complete and has NO OVERLAPS, you can simply extend the chart. = 8
70% of the guests at Company X's annual holiday party are employees of Company X. 10% of the guests are women who are not employees of Company X. If half the guests at the party are men, what percent of the guests are female employees of Company X?
Many overlapping-sets problems involve percents or fractions. The double-set matrix is still effective on these problems, especially if you pick a Smart Number for the GRAND TOTAL. *The 1st thing you should do is fill in 100 for the grand total* When you construct a double-set matrix, the rows should correspond to the MUTUALLY EXCLUSIVE OPTIONS for one decision. "You can't be a man and a women." Completing the matrix is an excellent way to check your computation, even if the problem does not require you to to. 40% of the guests at the party are female employees ←
Workers are grouped by their areas of expertise and are placed on at least one team. There are 20 workers on the Marketing team, 30 on the Sales team, and 40 on the Vision team. 5 workers are on both the Marketing and Sales teams, 6 workers are on both the Sales and Vision teams, 9 workers are on both the Marketing and Vision teams, and 4 workers are on all three teams. How many workers are there in total?
Problems that involve THREE OVERLAPPING SETS can be solved using a Venn Diagram. The sets are usually three teams or clubs. ** Venn Diagrams are easy to work with, if you remember one simple rule: WORK FROM THE INSIDE OUT ** Workers on 2 teams: You must remember to subtract those workers who are on all three teams. Workers on 1 team only: Subtract those workers who are one two teams and those workers who are on three teams. In order to determine the total, just add all seven number together: 74 ←
Santa estimates that 10% of the children in the world have been good this year but do not celebrate Christmas, and that 50% of the children who celebrate Christmas have been good this year. If 40% of the children in the world have been good, what percentage of children in the world are not good and do not celebrate Christmas?
When solving overlapping sets problems, you must PAY CLOSE ATTENTION TO THE WORDING of the problem. It is tempting to fill in the number 50 to represent the percent of good children who celebrate Christmas; however, this is incorrect. *The 1st thing you should do is fill in 100 for the grand total* You need to represent the unknown total number of children who celebrate Christmas with the variable x. 30% of the children are not good and do not celebrate ←
