Tiêu đề Venn Diagrams .pdf ✅

Venn Diagrams
Index 1. Pre-Session Quant Review 2. In-Session Quant Handout 3. In-Session Quant Handout - Answer Key 4. Post-Session Quant Questions 5. Post-Session Quant Questions - Answer Key 6. Post-Session Quant Questions – Answer Explanations 7. Official Guide 2022/2021 Problem Solving Questions 8. Official Guide 2022/2021 Problem Solving - Answer Key 9. Official Guide 2022/2021 Data Sufficiency Questions 10.Official Guide 2022/2021 Data Sufficiency -Answer Key 11.Official Guide 2022/2021 Problem Solving - Answer Explanations 12.Official Guide 2022/2021 Data Sufficiency - Answer Explanations
Pre-Session Quant Review
Chapter 3 Venn Diagrams Venn Diagram is an important concept that can be combined with Probability, Permutation and Combination, Numbers, and many more. While solving Venn Diagram questions, observe the language of questions carefully. 1. VENN DIAGRAM FOR 2 CATEGORIES Let’s say, of total people in a group, some play cricket and some play football. So, some people might play both of these sports and some might play neither of these. Let above rectangle represents Total Strength of group, and two circles represent people in 2 categories A and B (in the above example, A and B represent cricket players and football players, respectively). Then, area outside the 2 circles represents people who belong to neither of these 2 categories, and common area represents people who belong to both of these categories (in the above example, those who play neither of these 2 sports and who play both of these sports, respectively). T = Total strength; A = Number of people in category A; B = Number of people in category B; k = Number of people in both categories; N = Number of people in neither of these 2 categories. T Pre-Session Quant Review 26
• Number of people in only category A = A − k (Area inside A but not in B) • Number of people in only category B = B − k (Area inside B but not in A) • Number of people in exactly 1 category = (A − k) + (B − k) (Area within 2 circles but not common area) • Number of people in atleast 1 category = (A −k) + (B− k) + k However, above quantity can also be calculated as T − N. (Number of people in at least 1 category = Area within 2 circles = Total area of rectangle − area outside 2 circles). Hence, T − N = A + B − k. This gives an important relation for Venn diagram of 2 categories. Example 1: In an office, 20 employees drink Coffee, 40 employees drink Tea and 15 employees drink both of these. If 5 employees drink neither of the two drinks,then: a) How many employees drink at least one of the two drinks? b) How many employees drink only one of the two drinks? c) How many total employees are there in the office? Solution: a) Number of employees who drink at least one of these = 20 + 40 − 15 = 45 b) Number of employees who drink only one of the two drinks = (20 − 15) + (40 − 15) = 30 c) Total − Neither = Tea + Coffee − Both ⇒ Total = 20 + 40 − 15 + 5 = 50 Formula 1: Total − Neither = A + B − Both 27 Pre-Session Quant Review