tag:blogger.com,1999:blog-5541500.post8638725752710594922..comments2024-03-28T18:35:54.237+09:00Comments on BigHominid's Hairy Chasms: this week's Math Beast Challenge problemKevin Kimhttp://www.blogger.com/profile/01328790917314282058noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-5541500.post-88450257931282027982011-10-11T02:08:26.293+09:002011-10-11T02:08:26.293+09:00No one likes a fraction made out of fractions, so ...No one likes a fraction made out of fractions, so we've got to do something to make the fraction in Quantity B look a little more civilized. The denominators in that fraction are n, 3x, and x, so the least common denominator is 3nx.<br /><br />When I multiply the fraction by (3nx/3nx), I get a simpler-looking fraction:<br /><br />12x/(n + 15n) = (3/4)(x/n)<br /><br />At this point, it's just a matter of plugging in numbers. We know that x and n have to be nonzero quantities, but we're not told whether they might be positive or negative. So let's try some combinations of x and n that cover the major possibilities:<br /><br />x = 1, n = 1 (+/+)<br />x = -1, n = -1 (-/-)<br />x = -1, n = 1 (-/+)<br />x = 1, n = -1 (+/-)<br /><br />For the first pair:<br /><br />A = 1<br />B = 3/4<br /><br />A is greater than B.<br /><br />For the second pair:<br /><br />A = 1<br />B = 3/4<br /><br />A is greater than B.<br /><br />For the third pair:<br /><br />A = -1<br />B = -3/4<br /><br />B is greater than A.<br /><br />For the fourth pair:<br /><br />A = -1<br />B = -3/4<br /><br />B is greater than A.<br /><br />By plugging in simple numbers like 1 and -1, we quickly see that there are times when A is greater, and times when B is greater.<br /><br />The answer is D: The relationship cannot be determined from the information given.<br /><br />Or so I say, anyway.Kevin Kimhttps://www.blogger.com/profile/01328790917314282058noreply@blogger.com