Math Goodies is a free math help portal for students, teachers, and parents.
|
Interactive Math Goodies Software

testing left nav
Math Forums @ Math Goodies
Home | Profile | Register | Active Topics | Members | Search | FAQ
 All Forums  Homework Help Forums  Miscellaneous Math Topics  true or false New Topic  Reply to Topic  Printer Friendly
Author  Topic

westworld
Average Member

USA
19 Posts

 Posted - 02/01/2012 :  13:18:46 Consider the following ten statements. 1. Exactly one of these statements is false. 2. Exactly two of these statements are false. 3. Exactly three of these statements are false. 4. Exactly four of these statements are false. 5. Exactly five of these statements are false. 6. Exactly six of these statements are false. 7. Exactly seven of these statements are false. 8. Exactly eight of these statements are false. 9. Exactly nine of these statements are false. 10. Exactly ten of these statements are false. How many of the statements are true?

the_hill1962

USA
1468 Posts

 Posted - 02/01/2012 :  16:42:09 Take statements 1 and 2. They both can't be true at the same time because you can't have EXACTLY one and EXACTLY two at the same time. If ONE statement is false, then that says it, ONE statement is false (it isn't two). It is the same situation for any combination of the statements. Only one could be true at a time. That would eliminate #1 itself from being true because #1 being true would state that 9 of the statements are true, which can't happen because of what I already stated above. It also eliminates #2 from being true because that would say 8 of the statements are true.And so on up to statement #8 (that would say two of them are true and that is impossible).So, if one of them is true, which one? Look at #9. If it is true, that makes all the all the others false (because there are only 9 other statements and it says 9 statements are false). Does that cause a problem? No. Statement 10 would be false because NOT exactly ten would be false (9 of the would be).
Topic
 New Topic  Reply to Topic  Printer Friendly Jump To: Select Forum New Visitor Forum       Testing Forum Homework Help Forums       Basic Math and Pre-Algebra       Algebra       Geometry and Trigonometry       Pre-Calculus and Calculus       Probability and Statistics       Standardized Test Preparation Help       Miscellaneous Math Topics Educator Forum       Teacher Talk Parent Forum       Parent's Place  -------------------- Home Active Topics Frequently Asked Questions Member Information Search Page
 Math Forums @ Math Goodies © 2000-2004 Snitz Communications
testing footer