Double-set Matrix

Official Guide practice (find these in your Official Guide or at www.gmatclub.com)

PS24210.02 According to a survey of 200 people

PS21260.02 In a certain high school

DS07949 How many people in a group of 50

DS06905 George has a total of B books in his library,

PS51950.02 Results of a Poll

DS13122 In a certain group of 50 people

DS04536 Every object in a box

PS04089 A certain high school has 5,000 students

PS06133 Each person who attended a company meeting

DS61602.01 A company produces a certain toy

DS01544 Of a group of 50 households

DS06096 In a product test of a common cold remedy

DS12008 Is the number of members of Club X

Reflective practice (scroll down for suggested answers)

1.      Look at the PS problems above. What challenges and traps do they include in addition to being set problems?

2.      Look at the DS problems above. What patterns can you see for sufficiency when using the double-set matrix?

A note on 3-set problems

As the name suggests, the double-set matrix works for 2-set problems, but it doesn’t work for 3-set problems (that would require a 3-dimensional matrix!). In any case, 3-set problems are rare in the GMAT and are only worth studying if your Quant score is already high (perhaps 46+). For most GMAT students, your time will be better invested in other areas. Here’s an example of how I approach 3-set problems: https://www.manhattanprep.com/gmat/forums/post130354.html#p130354

Reflective practice suggested answers

1.     The GMAT often combines double-set problems with other topics, especially for more difficult problems. You’re likely to see fractions, ratios, percentages (especially the trap of ‘percentage of a sub-group’ rather than ‘percentage of the total’), probability, and max / min. However, be ready for just about any combination of topics with doublt-set problems.

2.    Information about percentages or proportions won’t give you a value for the actual size of a sub-set. If you can fill in the “total” row and column, then you just need on of the central 4 boxes in order to complete the double-set matrix