The following article refers to the Problem Solving question #229 in the OG13, GMAT2015 and GMAT2016 books. You can view the question in its entirety here:<\/p>\n
https:\/\/gmatclub.com\/forum\/how-many-of-the-integers-that-satisfy-the-inequality-x-2-x-134194.html<\/p>\n
One of the interesting aspects of most GMAT questions is that they can be solved using more than one approach. In that way, you don\u2019t have to be a brilliant mathematician to get to the correct answer - strong critical thinkers, pattern-matchers and \u2018workers\u2019 can still get to the correct answer in a reasonable amount of time.<\/p>\n
From a pacing standpoint, sometimes the easiest\/fastest way to get to the correct answer is to use what\u2019s called \u2018brute force\u2019 \u2013 no fancy logic or math is required \u2013 just the willingness to do a bunch of simple calculations to PROVE what the correct answer actually is.<\/p>\n
In this prompt, we\u2019re told that (X+2)(X+3)\/(X-2) >= 0. We\u2019re asked for the number of INTEGERS that are LESS than 5 that satisfy this inequality.<\/p>\n
The \u2018key\u2019 to recognize that this question is susceptible to \u2018brute force\u2019 is that the answer choices are 1 through 5, inclusive. This emphasizes that there are not that many possible values for X - there is at least one solution, but no more than 5 solutions. How hard can it possibly be to find them all?<\/p>\n
To start, we should consider the largest integer that fits the given \u2018restrictions.\u2019 In this case, that would be X = 4.<\/p>\n
When X = 4, the fraction becomes\u2026.<\/p>\n
(6)(7)\/(2) = 21<\/p>\n
This is clearly greater than or equal to 0, so X = 4 is a solution to the prompt. Now we just have to \u2018brute force\u2019 as many additional integers as it takes to discover the number of additional solutions.<\/p>\n
Rather than \u2018cheat\u2019 you out of experiencing \u2018brute force\u2019 for yourself, I\u2019m going to \u2018nudge\u2019 you through the steps that have to come next.<\/p>\n
Is X = 3 a solution? How long would it actually take you to prove it (if it takes you more than about 10 seconds, then I would be surprised). X can\u2019t equal 2, since that would create a 0 in the denominator of the fraction, but could X = 1 or 0? How about negative integers? Could X = -1 or -2? At what point would you stop \u2018brute forcing\u2019 and conclude that you were done? (Hint: look at the \u2018sign\u2019 of each of your end calculations).<\/p>\n
All in, how long did it actually take you to \u2018brute force\u2019 this question? My guess is that it wouldn\u2019t take more than 2 minutes of basic calculations for you to get to the correct answer (AND the calculations were NOT difficult).<\/p>\n
This is all meant to show that a flexible thinker (and not one who\u2019s necessarily a \u2018genius\u2019) can solve lots of GMAT questions in a relatively short period of time. You too can train to think in these ways. To that end, we\u2019re here to help.<\/p>\n
GMAT assassins aren\u2019t born, they\u2019re made,
\nRich<\/p>\n","protected":false},"excerpt":{"rendered":"
The following article refers to the Problem Solving question #229 in the OG13, GMAT2015 and GMAT2016 books. You can view the question in its entirety here: https:\/\/gmatclub.com\/forum\/how-many-of-the-integers-that-satisfy-the-inequality-x-2-x-134194.html One of the…<\/p>\n","protected":false},"author":156,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,1,243,940],"tags":[],"class_list":["post-31119","post","type-post","status-publish","format-standard","hentry","category-gmat","category-uncategorized","category-blog","category-gmat-prep-gmat","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/31119","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\/156"}],"replies":[{"embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/comments?post=31119"}],"version-history":[{"count":2,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/31119\/revisions"}],"predecessor-version":[{"id":31161,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/31119\/revisions\/31161"}],"wp:attachment":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/media?parent=31119"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/categories?post=31119"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/tags?post=31119"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}