Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "1960 AHSME Problems/Problem 10"

(→‎Solution)
(→‎Solution)
 
(7 intermediate revisions by 2 users not shown)
Line 21: Line 21:
  
 
==Solution==
 
==Solution==
−
We can obviously see that statement <math>3</math> contradicts statement <math>6</math> since it says that all men are not good drivers while statement <math>6</math> says they are. So the answer is <math>\boxed{C}</math>
+
<math>\fbox{(C)3}</math>
 +
Because No men are good negates All men are good.

Latest revision as of 13:47, 5 February 2019

Problem 10

Given the following six statements: \[\text{(1) All women are good drivers}\] \[\text{(2) Some women are good drivers}\] \[\text{(3) No men are good drivers}\] \[\text{(4) All men are bad drivers}\] \[\text{(5) At least one man is a bad driver}\] \[\text{(6) All men are good drivers.}\]


The statement that negates statement $(6)$ is:


$\textbf{(A) }(1)\qquad \textbf{(B) }(2)\qquad \textbf{(C) }(3)\qquad \textbf{(D) }(4)\qquad \textbf{(E) }(5)$


Solution

$\fbox{(C)3}$ Because No men are good negates All men are good.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1960_AHSME_Problems/Problem_10&oldid=101281"