{"id":15346,"date":"2012-11-21T09:00:28","date_gmt":"2012-11-21T16:00:28","guid":{"rendered":"https:\/\/gmatclub.com\/blog\/?p=15346"},"modified":"2012-11-08T14:38:57","modified_gmt":"2012-11-08T21:38:57","slug":"gmat-math-the-many-meaning-of-minus","status":"publish","type":"post","link":"https:\/\/gmatclub.com\/blog\/gmat-math-the-many-meaning-of-minus\/","title":{"rendered":"GMAT Math: The Many Meaning of Minus"},"content":{"rendered":"

\"\"First of all, for warm-up, a practice Data Sufficiency question.<\/p>\n

\"\"<\/a><\/p>\n

The symbol<\/h2>\n

What does this symbol mean in math?<\/p>\n

\"\"<\/a><\/p>\n

Technically, this symbol, typographically a dash, has three different meanings in mathematics, viz.:<\/p>\n

a) a subtraction sign<\/p>\n

b) a negative sign<\/p>\n

c) an\u00a0opposite<\/em>\u00a0sign<\/p>\n

 <\/p>\n

The subtraction sign<\/h2>\n

When the dash appears between two terms\u00a0 --- between two numbers (5 \u2013 3), between two variables (x \u2013 y), between a number and a variable (x \u2013 2), etc. --- then it indicates\u00a0the operation of subtraction.\u00a0 This is, undoubtedly, the very first meaning folks associate with the dash, because folks learned this way back in grammar school math.\u00a0 Furthermore, as soon as kids understand money and spending money, essentially they understand something about subtraction, so rare is the kid who doesn't get subtraction early on.<\/p>\n

 <\/p>\n

The negative sign<\/h2>\n

When the dash appears in front of a stand-alone number (\u20135, \u20132.7, <m>-pi<\/m>, etc.), then it is a negative sign, denoting that the number in question is less than zero and to the left of zero on a standard number line.\u00a0 Folks tend to learn this idea relatively early on as well.\u00a0 Moreover, it's easy to see how this meaning \"blurs\" into the subtraction-sign meaning, because after all, 8 + (\u20132) is just another way of saying 8 \u2013 2.\u00a0 Both have a kind of \"minus-making\" meaning to them.<\/p>\n

 <\/p>\n

The opposite sign<\/h2>\n

This is the one that can through folks into a tizzy.\u00a0 When you put the dash not in front of a stand-alone number but rather a stand-alone variable, then it is NOT a negative sign anymore.\u00a0 Rather, it is an opposite sign, which changes the sign of the variable to the opposite of whatever it was originally.\u00a0 If y is a positive, then \u2013y is negative.\u00a0 BUT, if we know y is negative, then we know \u2013y is positive.<\/p>\n

Right there, that is precisely what wigs people out!\u00a0 Since before puberty, they were accustomed the dash having a universal \"negatizing\" effect, and yet, in this strange instance, when y is already negative, the dash in front of \u2013y actually makes it positive.\u00a0 To some folks, this seems an unholy violation of everything they have ever learned about the sign!\u00a0 Technically, folks learn about the opposite sign somewhere in algebra, but it is seldom explained well there, setting folks up for this massive confusion when they encounter the opposite sign on, for example, the GMAT Quantitative section.<\/p>\n

For example, the algebraic statement:<\/p>\n

|y| = \u2013y<\/p>\n

is a sophisticated way of indicating that y \u2264 0.\u00a0 Conceivably, the GMAT could give you the former and expect you to deduce the latter.<\/p>\n

 <\/p>\n

Practice<\/h2>\n

It may be that the foregoing discussion gave you some insight into the practice question at the top of this pages.\u00a0 Take another look at that before reading the solution below.\u00a0 Also, here's a free practice question with some positive\/negative variable issues.<\/p>\n

2)\u00a0https:\/\/gmat.magoosh.com\/questions\/301<\/a><\/p>\n

 <\/p>\n

Practice Problem Solution<\/h2>\n

1) This is a difficult DS question.\u00a0 First of all, some folks might mistakenly think the prompt is already decided as it is written.\u00a0 After all, we know that the right side of the inequality,[pmath]y^2[\/pmath], is always positive.\u00a0 Some folks may mistakenly think that the left side of the inequality is always negative, but that would entail reading the dash incorrectly as a negative sign, rather than correctly as an opposite sign.<\/p>\n

Statement #1 implies that y = \u00b11\/5.\u00a0 (How do you know you have to take both the positive and negative square roots?\u00a0 See\u00a0this GRE post<\/a>.)\u00a0 Those two values imply different conclusions to the prompt.\u00a0 If y = +1\/5, then \u2013y\/2 = \u20131\/10, which is clearly\u00a0less than<\/em>\u00a0[pmath]y^2 = 1\/25 [\/pmath]\u00a0.\u00a0 But, if y = \u20131\/5, then \u2013y\/2 = +1\/10, which happens to be\u00a0greater than<\/em>\u00a0[pmath]y^2= 1\/25[\/pmath].\u00a0 The two different possible values imply different conclusions, which means no definitive answer to the prompt is possible.\u00a0 This statement, by itself, is\u00a0insufficient<\/strong>.<\/p>\n

Statement #2 is a fancy way of saying that y \u2264 0.\u00a0 If y = \u20135, then the inequality is false, but if y = \u20131\/100, then \u2013y\/2 = +1\/200, which is\u00a0greater than<\/em>\u00a0[pmath]y^2 = 1\/10000 [\/pmath], and the inequality is true.\u00a0 Two different possible values imply different conclusions, which means no definitive answer to the prompt is possible.\u00a0 This statement, by itself, is\u00a0insufficient<\/strong>.<\/p>\n

Statement combined: when we combine the restraints of both statements, we know that y can only have one value: y must equal \u20131\/5, and this, by itself leads to a definite answer to the prompt.\u00a0 Thus, the combined statements are\u00a0sufficient<\/strong>.<\/p>\n

Answer =\u00a0C<\/strong>.<\/p>\n

This post was written by Mike McGarry, GMAT expert at Magoosh<\/a>, and originally posted here<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

First of all, for warm-up, a practice Data Sufficiency question. The symbol What does this symbol mean in math? Technically, this symbol, typographically a dash, has three different meanings in…<\/p>\n","protected":false},"author":133,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,783,243,718,736],"tags":[],"class_list":["post-15346","post","type-post","status-publish","format-standard","hentry","category-gmat","category-magoosh-blog","category-blog","category-data-sufficiency-gmat","category-quant-gmat","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/15346","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/users\/133"}],"replies":[{"embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/comments?post=15346"}],"version-history":[{"count":1,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/15346\/revisions"}],"predecessor-version":[{"id":15348,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/15346\/revisions\/15348"}],"wp:attachment":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/media?parent=15346"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/categories?post=15346"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/tags?post=15346"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}