![\"\"](\"https:\/\/magoosh.com\/gmat\/files\/2012\/03\/imb0590707.jpg\" "\\"percents\\"")
This is, among other things, a case study of one of the harder Data Sufficiency problems in the OG.<\/p>\nThis is, among other things, a case study of one of the harder Data Sufficiency problems in the OG.<\/p>\n
<\/p>\n
You can find several good tips on percent problems at\u00a0this post<\/a>.\u00a0 The most relevant here is the idea of a percent as multiplier.\u00a0 To change a percent into a multiplier:<\/p>\n (a) change it from a percent to a decimal<\/p>\n (b) for a percent increase, keep it positive; for a percent decrease, make it negative.<\/p>\n (c) add that to one.<\/p>\n For example, for a 12% decrease,<\/p>\n (a) 12% -> 0.12<\/p>\n (b) it's a decrease, so -0.12<\/p>\n (c) 1 + (-0.12) = 0.88<\/p>\n That final number, 0.88 is the multiplier for a 12% decrease.\u00a0 If we want to decrease any quantity by 12%, all we have to do is multiply by that multiplier.<\/p>\n <\/p>\n <\/strong>Here's the problem from the OG, practice DS #120.<\/p>\n 120) The annual rent collected by a corporation from a certain building was x percent more in 1998 than in 1997, and y percent less in 1999 than in 1998.\u00a0 Was the annual rent collected by the corporation from the building more in 1999 than in 1997?<\/p>\n (1)x > y<\/p>\n (2)xy\/100 < x - y<\/p>\n <\/p>\n <\/p>\n When a percent increase is combined with a percent decrease on the GMAT, the one archetypal mistake the testmakersare trying to educe is idea that you can find the net result by simply adding and subtracting percents.\u00a0 Increase of 20%, followed by a decrease of 15% \u2014 the huge mistake to say 20 \u2013 15 = 5%.\u00a0 That's like a huge booby trap the GMAT sets up every time, and test after test the unsuspecting masses predictably fall into it in swarms.\u00a0 Here, statement #1 is all about that huge mistake.\u00a0 Many people will mistakenly think (1) is sufficient, but it's not.<\/p>\n When a percent increase is combined with a percent decrease on the GMAT, you need to\u00a0multiply the multipliers<\/strong>.\u00a0 For example, 20% increase -> multiplier = 1.20; 15% decrease -> multiplier = 0.85.\u00a0 Combination = 1.20*0.85 = 1.02, a 2% increase.<\/p>\n In particular, increasing by a percent, then decreasing by that same percent, does\u00a0not<\/em> leave you in the same place.\u00a0 Consider an increase of 50% followed by a decrease of 50%.\u00a0 Start at $100.\u00a0 Increase by 50% to $150.\u00a0 Now, decrease by 50%, from $150 to 75%.\u00a0 The net result of a 50% increase, followed by a 50% decrease, is a 25% decrease.<\/p>\n <\/p>\n Call the initial 1997 amount of rent A.\u00a0 It increased x% from 1997 to 1998.\u00a0 Notice that x% as a multiplier is (1 + x\/100), so the amount of rent in 1998 is<\/p>\n A(1 + x\/100)<\/p>\n Then, it decreased y% from 1998 to 1999.\u00a0 The multiplier now is [pmath](1 - y\/100)[\/pmath], so the amount of rent in 1999 is:<\/p>\n A(1 + x\/100)*(1 - y\/100)<\/p>\n So, in order for the rent to be more in 1999 than in 1997, what multiplies A here, the composite factor multiplying A, must be greater than one.<\/p>\n (1 + x\/100)*(1 - y\/100) > 1<\/p>\n FOIL out the left side.<\/p>\n 1 + x\/100 - y\/100 - (x\/100)(y\/100) 1<\/p>\n Subtract 1 from both sides:<\/p>\n x\/100 - y\/100 - (xy\/10000) > 0<\/p>\n x\/100 - y\/100 > (xy\/10000)<\/p>\n Multiply both side by 100, to clear some of the fractions<\/p>\n x - y > xy\/100<\/p>\n This is the condition for the rent in 1999 being larger than the rent in 1997.\u00a0 Notice this equivalent to Statement #2.\u00a0 Since statement #2 is another form of the statement that the rent in 1999 is larger than the rent in 1997, it is sufficient, and the answer is B.<\/p>\n <\/p>\n Here's a practice PS question exploring some of the same ideas.<\/p>\n https:\/\/gmat.magoosh.com\/questions\/30<\/a><\/p>\n <\/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":" This is, among other things, a case study of one of the harder Data Sufficiency problems in the OG. Percents as Multipliers You can find several good tips on…<\/p>\n","protected":false},"author":133,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,243,718,717,736],"tags":[],"class_list":["post-10726","post","type-post","status-publish","format-standard","hentry","category-gmat","category-blog","category-data-sufficiency-gmat","category-problem-solving-gmat","category-quant-gmat","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/10726","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=10726"}],"version-history":[{"count":4,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/10726\/revisions"}],"predecessor-version":[{"id":10733,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/10726\/revisions\/10733"}],"wp:attachment":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/media?parent=10726"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/categories?post=10726"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/tags?post=10726"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}The DS Problem in the OG<\/h2>\n
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The Tempting Wrong Answer<\/h2>\n
Solution<\/h2>\n