GMAT Quant Chapter 12: Overlapping Sets

Question 1

In a 2 x 2 set matrix that contains Number of A, Number of B, Number of both, Number of neither, how do we calculate the total number of elements in a set?

Answer 1

Number of A
+
Number of B
+
Number of Both
+
Number of Neither
=
Total Number of Unique Elements

Question 2

When we don’t know the total value of the two subsets, how can we calculate subset values?

Answer 2

Attribute the total number of items to 100 or an unknown variable such as x.

Question 3

When we are given an overlapping set problem in terms of fractions but no total number of ideas, how should we proceed?

Answer 3

Calculate the LCM of all the given fractions and make that the total number.

Question 4

The outside cell values in a 2 x 2 matrix sum to 1 (the total number of values in a set), but which other group of cells in the matrix also sums to 1?

Answer 4

The central 4 cells.

Question 5

How do we find the total number of elements in either set? (words & algebra)

Answer 5

(A or B) = #(A) + #(B) – #(A and B)

Total Number in A + Total Number in B – Total in Both A and B

Question 6

How should we answer maximization / minimization problems within sets?

Answer 6

Test out extreme values.

Question 7

In a group of 3 overlapping sets, how do we calculate the number in only 1 set?

Answer 7

Total Number in Exactly only 1 group = # in A only + # in B only + # in C only

Question 8

In a group of 3 overlapping sets, how do we calculate the number in exactly 3 groups?

Answer 8

Total number in A, B, and C only.

Question 9

How do we calculate the number of members that belong to only 2 groups?

Answer 9

Total number in A & B only, + Total Number in b & c only, + Total number in a & c only.

Question 10

How do we calculate the total number of elements in 2 out of 3 overlapping sets?

Answer 10

Number of elements that are in both sets – the number of elements that are in all 3 sets.

Question 11

How do we calculate the number in a particular subset when we know the total number of elements in all 3 sets?

Answer 11

Group A Only + # Group B Only + # Group C Only + # Double Overlaps Only + # Triple Overlaps + # Neither

Question 12

How do we calculate the number in a particular subset of three overlapping sets when we don’t know the total amount of elements in all 3 sets?

Answer 12

Group A + # Group B + # Group C - # Groups of Exactly 2 – 2x Group of Exactly 3 + # Neither

Question 13

There are two formulas for calculating the amount of individuals in subsets when we have 3 overlapping sets, what are they and why do we need 2 distinct formulas?

Answer 13

Individual Onlys + Overlaps when we know the total number of elements in the 3 sets.

Total Individual groups – number of doubles – 2x number of triples + neither. When we don’t know the total amount in all 3 sets.