{"id":4184,"date":"2013-12-25T09:00:36","date_gmt":"2013-12-25T17:00:36","guid":{"rendered":"https:\/\/magoosh.com\/gmat\/?p=4184"},"modified":"2020-01-15T10:48:49","modified_gmt":"2020-01-15T18:48:49","slug":"backsolving-on-gmat-math","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gmat\/backsolving-on-gmat-math\/","title":{"rendered":"Backsolving on GMAT Math"},"content":{"rendered":"

First of all, try these challenging GMAT Problem Solving practice problems without a calculator<\/i><\/a>.<\/p>\n

\"bogm_img1\"<\/a><\/p>\n

    \n\t(A) 2
    \n\t(B) 3
    \n\t(C) 4
    \n\t(D) 5
    \n\t(E) 6\n<\/ol>\n

    2) In the month of August, Pentheus Corporation made $200,000 in profit.\u00a0 Pentheus made 6% of that profit on the second Wednesday of August.\u00a0\u00a0 If the profits that day were approximately 14.5% of the revenue for that day, then what was Pentheus’s revenue on the second Wednesday of August?<\/p>\n

      \n\t(A) $65,536
      \n\t(B) $75,025
      \n\t(C) $77,922
      \n\t(D) $80,000
      \n\t(E) $82,756\n<\/ol>\n

      3) Harold needs to buy a ticket to attend a conference for work.\u00a0 His own department contributes $4 less than half the price of the ticket.\u00a0 The HR department will contributes $1 more than a third of the price of the ticket.\u00a0 With these two contributions, Harold has to pay only $10 out of his own pocket to cover the cost of the ticket.\u00a0\u00a0 What was the price of the ticket?<\/p>\n

        \n\t(A) $36
        \n\t(B) $42
        \n\t(C) $48
        \n\t(D) $54
        \n\t(E) $60\n<\/ol>\n

        4) Jackson invested $300,000, dividing it all unequally between Account P and Account Q.\u00a0 At the end of the year, it turned out that Account P had earned 12% interest and Account Q had earned 25% interest.\u00a0\u00a0 If Jackson earned a total of $60,000 in interest between the two accounts, which of the following is approximately the amount he put in account P?<\/p>\n

          \n\t(A) $115,384
          \n\t(B) $120,000
          \n\t(C) $121,072
          \n\t(D) $124,129
          \n\t(E) $130,000\n<\/ol>\n

          Solutions will come at the end of this article.<\/p>\n

           <\/p>\n

          Backsolving basics<\/h2>\n

          When all five answers are numerical, that puts us in an excellent position to use backsolving.\u00a0 Backsolving is an alternative to the algebraic method of solution that your wizened Algebra Two teacher would have deemed the only correct way.\u00a0\u00a0 Backsolving means starting with a numerical answer, and working through with that number to see if it fits the requirements of the scenario.<\/p>\n

          In a previous post, I recommended the #1 backsolving strategy: start with answer (C)<\/a>.\u00a0 You see, if all five answer are integers, the GMAT always lists them from smallest to largest.\u00a0\u00a0 Answer choice (C)<\/b> will always be in the middle.\u00a0 If we plug in (C)<\/b> and it comes out to the correct value, then we are done.\u00a0 If it is too big, then we can eliminate (C)<\/b> & (D)<\/b> & (E)<\/b>; if it is too small, then we can eliminate (A)<\/b> & (B)<\/b> & (C)<\/b>.\u00a0 Choice (C)<\/b> is often the best place to start, because whether it turns out to be too high or too low, there’s more than one answer to eliminate.<\/p>\n

          Make it easy!<\/p>\n

          Of course, backsolving is a strategy that should be used to make things easier.\u00a0 Suppose a problem presents a scenario, and then has these answer choices:<\/p>\n

          (A) 14,641<\/p>\n

          (B) 15,000<\/p>\n

          (C) 16,384<\/p>\n

          (D) 17,711<\/p>\n

          (E) 19,683<\/p>\n

          Well, hmmm.\u00a0 Whatever the calculations in the problem may be, starting with (C)<\/b> doesn’t seem like it would be a whole lot of fun without a calculator.\u00a0 Also, notice the answers are too close together to estimate<\/a>.\u00a0 BUT, notice that of the five answer choices, here answer choice (B)<\/b> is a nice neat round number.\u00a0 In a way, the design of the answer choices presents (B)<\/b> on a silver platter as the best possible choice for backsolving.\u00a0\u00a0 If you decide to backsolve, don’t simply go on automatic pilot and choose (C)<\/b>.\u00a0 Scope out the answers, and see if one stands out as a much easier choice for backsolving calculations: if there is such answer choice available, chances are very good that the question-writer placed it for just that purpose.<\/p>\n

           <\/p>\n

          Summary<\/h2>\n

          The GMAT math section demands flexibility, and backsolving is an excellent alternative approach to have up your sleeve.\u00a0 If you had any insights reading this post, you may want to give the problems at the top another look before reading the explanations below.\u00a0\u00a0 Here’s another practice problem that lends itself to backsolving.<\/p>\n

          5) http:\/\/gmat.magoosh.com\/questions\/29<\/a><\/p>\n

          If you have any questions about what I have said here, or if you would like to add anything, please use our comments section below.<\/p>\n

          \"bogm_img2\"<\/a><\/p>\n

           <\/p>\n

          Practice problem explanations<\/h2>\n

          1) We’ll use backsolving.\u00a0 Start with choice (C)<\/a>.\u00a0 If x = 4, then<\/p>\n

          \"bogm_img3\"<\/a><\/p>\n

          That’s just larger than 80, so this may well be the answer.\u00a0 We have to verify that x = 3 is below 80:<\/p>\n

          \"bogm_img4\"<\/a><\/p>\n

          That’s well below 80, so x = 4 is the lowest integer for which the expression is greater than 80.\u00a0 Answer = (C)<\/b>.<\/p>\n

          2) First of all, 1% of $200,000 is $2000, and six times this\u00a0 means 6% is $12,000.\u00a0 That’s the easy part of the problem.\u00a0 Now we know 14.5% of revenue is $12,000.<\/p>\n

          As we discussed in this post, starting with (C)<\/b> in this problem would not be fun.\u00a0 Instead, we’ll backsolving starting with the round number, choice (D)<\/b>.\u00a0 Suppose revenue = $80,000.<\/p>\n

          (a)<\/b> 1% of $80,000 = $800<\/p>\n

          (b)<\/b> 10% of $80,000 = $8,000<\/p>\n

          (c)<\/b> Multiply (a) by 4: 4% of $80,000 = $3,200<\/p>\n

          (d)<\/b> Divide (a) by half: 0.5% of $80,000 = $400<\/p>\n

          (e)<\/b> add (b) & (c) & (d): 14.5% of $80,000 = $11,600<\/p>\n

          That’s a bit shy of the required $12,000, so revenue must be larger than $80,000.\u00a0 That leads up immediately to the last choice.\u00a0 Answer = (E)<\/b><\/p>\n

          3) We’ll use backsolving.\u00a0 Start with choice (C)<\/a>.\u00a0 If price = 48, then<\/p>\n

          department pays $4 less than half = $24 – $4 = $20<\/p>\n

          HR pays $1 more than a third = $16 + $1 = $17<\/p>\n

          Together, they pay $37, leaving Harold to pay the remaining $11.\u00a0 Harold pays a bit too much, so the price must be a bit less.\u00a0 We strongly suspect that (B) will work, but we have to verify that assumption.<\/p>\n

          Try (B).\u00a0 If price = $42, then<\/p>\n

          department pays $4 less than half = $21 – $4 = $17<\/p>\n

          HR pays $1 more than a third = $14 + $1 = $15<\/p>\n

          Together, they pay $32, leaving Harold to pay the remaining $10.\u00a0 This works.<\/p>\n

          Answer = (B)<\/b>.<\/p>\n

          4) As we discussed in this post, starting with (C)<\/b> in this problem would not be fun.\u00a0 We’ll backsolving starting with a round number.\u00a0 The answers give us two round numbers, choice (B)<\/b> and choice (E)<\/b>.\u00a0 Let’s think strategically about this.\u00a0 If we try (E)<\/b> and it works, then we have the answer, but if it doesn’t work, we would know the amount would have to be less, but we can already see that.\u00a0 Backsolving with (E)<\/b> does not necessarily give us a lot of information.<\/p>\n

          Instead, backsolving with (B)<\/b>.\u00a0 Let’s say Jackson puts $120,000 in P and $180,000 in Q.<\/p>\n

          In P, Jackson earns 12% of $120,000<\/p>\n

          10% of $120,000 = $12,000<\/p>\n

          1% of $120,000 = $1,200<\/p>\n

          2% of $120,000 = $2,400<\/p>\n

          12% of $120,000 = $14,400<\/p>\n

          In Q, Jackson earns 25% of $180,000<\/p>\n

          50% of $180,000 = $90,000<\/p>\n

          half of that: 25% of $180,000 = $45,000<\/p>\n

          Total interest earned = $14,400 + $45,000 = $59,400<\/p>\n

          Not quite enough interest.\u00a0 To earn that extra $600 of interest that would bring the total interest up to $60,000, Jackson would have to have taken money out of P, which earns less interest, and have put it in Q, which earns more interest.\u00a0 That means, the amount in Account P must be less than $120,000.\u00a0 That leaves only one answer.<\/p>\n

          Answer = (A)<\/b><\/p>\n

           <\/p>\n","protected":false},"excerpt":{"rendered":"

          First of all, try these challenging GMAT Problem Solving practice problems without a calculator. (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 2) In the month of August, Pentheus Corporation made $200,000 in profit.\u00a0 Pentheus made 6% of that profit on the second Wednesday of August.\u00a0\u00a0 If the profits that day were approximately […]<\/p>\n","protected":false},"author":26,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[150],"tags":[],"ppma_author":[13209],"class_list":["post-4184","post","type-post","status-publish","format-standard","hentry","category-basics"],"acf":[],"yoast_head":"\nBacksolving on GMAT Math - Magoosh Blog \u2014 GMAT\u00ae Exam<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/magoosh.com\/gmat\/backsolving-on-gmat-math\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Backsolving on GMAT Math\" \/>\n<meta property=\"og:description\" content=\"First of all, try these challenging GMAT Problem Solving practice problems without a calculator. (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 2) In the month of August, Pentheus Corporation made $200,000 in profit.\u00a0 Pentheus made 6% of that profit on the second Wednesday of August.\u00a0\u00a0 If the profits that day were approximately […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/magoosh.com\/gmat\/backsolving-on-gmat-math\/\" \/>\n<meta property=\"og:site_name\" content=\"Magoosh Blog \u2014 GMAT\u00ae Exam\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/MagooshGMAT\/\" \/>\n<meta property=\"article:published_time\" content=\"2013-12-25T17:00:36+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2020-01-15T18:48:49+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/magoosh.com\/gmat\/files\/2013\/11\/bogm_img1.png\" \/>\n<meta name=\"author\" content=\"Mike M\u1d9cGarry\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@MagooshGMAT\" \/>\n<meta name=\"twitter:site\" content=\"@MagooshGMAT\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Mike M\u1d9cGarry\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"7 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/magoosh.com\/gmat\/backsolving-on-gmat-math\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/backsolving-on-gmat-math\/\"},\"author\":{\"name\":\"Mike M\u1d9cGarry\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/320346c205075513344435baf9b0521b\"},\"headline\":\"Backsolving on GMAT Math\",\"datePublished\":\"2013-12-25T17:00:36+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/backsolving-on-gmat-math\/\"},\"wordCount\":1076,\"commentCount\":3,\"publisher\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/#organization\"},\"articleSection\":[\"GMAT Math Basics\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/magoosh.com\/gmat\/backsolving-on-gmat-math\/\",\"url\":\"https:\/\/magoosh.com\/gmat\/backsolving-on-gmat-math\/\",\"name\":\"Backsolving on GMAT Math - Magoosh Blog \u2014 GMAT\u00ae Exam\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/#website\"},\"datePublished\":\"2013-12-25T17:00:36+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/backsolving-on-gmat-math\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/magoosh.com\/gmat\/backsolving-on-gmat-math\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/magoosh.com\/gmat\/backsolving-on-gmat-math\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/magoosh.com\/gmat\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Backsolving on GMAT Math\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#website\",\"url\":\"https:\/\/magoosh.com\/gmat\/\",\"name\":\"Magoosh Blog \u2014 GMAT\u00ae Exam\",\"description\":\"Everything you need to know about the GMAT\",\"publisher\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/magoosh.com\/gmat\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#organization\",\"name\":\"Magoosh\",\"url\":\"https:\/\/magoosh.com\/gmat\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/magoosh.com\/gmat\/files\/2019\/04\/Magoosh-logo-purple-60h.png\",\"contentUrl\":\"https:\/\/magoosh.com\/gmat\/files\/2019\/04\/Magoosh-logo-purple-60h.png\",\"width\":265,\"height\":60,\"caption\":\"Magoosh\"},\"image\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/MagooshGMAT\/\",\"https:\/\/twitter.com\/MagooshGMAT\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/320346c205075513344435baf9b0521b\",\"name\":\"Mike M\u1d9cGarry\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/image\/15a1e36ef1c2c3940179212433de141a\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/6b06de81592cd77bb46aa560cc59aee179cba4d042835c3529221ea1b344cce0?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/6b06de81592cd77bb46aa560cc59aee179cba4d042835c3529221ea1b344cce0?s=96&d=mm&r=g\",\"caption\":\"Mike M\u1d9cGarry\"},\"description\":\"Mike holds an A.B. in Physics (graduating magna cum laude) and an M.T.S. in Religions of the World, both from Harvard. 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Beyond standardized testing, Mike has over 20 years of both private and public high school teaching experience specializing in math and physics. In his free time, Mike likes smashing foosballs into orbit, and despite having no obvious cranial deficiency, he insists on rooting for the NY Mets. Learn more about the GMAT through Mike's Youtube video explanations.","sameAs":["https:\/\/www.youtube.com\/c\/MagooshGMATChannel\/featured"],"award":["Magna cum laude from Harvard"],"knowsAbout":["GMAT"],"knowsLanguage":["English"],"jobTitle":"Content Creator","worksFor":"Magoosh","url":"https:\/\/magoosh.com\/gmat\/author\/mikemcgarry\/"}]}},"authors":[{"term_id":13209,"user_id":26,"is_guest":0,"slug":"mikemcgarry","display_name":"Mike M\u1d9cGarry","avatar_url":"https:\/\/secure.gravatar.com\/avatar\/6b06de81592cd77bb46aa560cc59aee179cba4d042835c3529221ea1b344cce0?s=96&d=mm&r=g","user_url":"","last_name":"M\u1d9cGarry","first_name":"Mike","description":"Mike served as a GMAT Expert at Magoosh, helping create hundreds of lesson videos and practice questions to help guide GMAT students to success. He was also featured as \"member of the month\" for over two years at <a href=\"https:\/\/gmatclub.com\/blog\/2012\/09\/mike-mcgarrys-gmat-experience\/\" rel=\"noopener noreferrer\">GMAT Club<\/a>. Mike holds an A.B. in Physics (graduating <em>magna cum laude<\/em>) and an M.T.S. in Religions of the World, both from Harvard. Beyond standardized testing, Mike has over 20 years of both private and public high school teaching experience specializing in math and physics. In his free time, Mike likes smashing foosballs into orbit, and despite having no obvious cranial deficiency, he insists on rooting for the NY Mets. Learn more about the GMAT through Mike's <a href=\"https:\/\/www.youtube.com\/c\/MagooshGMATChannel\/featured\" rel=\"noopener noreferrer\">Youtube <\/a>video explanations and resources like <a href=\"https:\/\/magoosh.com\/gmat\/whats-a-good-gmat-score\/\" rel=\"noopener noreferrer\">What is a Good GMAT Score?<\/a> and the <a href=\"https:\/\/magoosh.com\/gmat\/gmat-diagnostic-test\/\" rel=\"noopener noreferrer\">GMAT Diagnostic Test<\/a>."}],"_links":{"self":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/4184","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/users\/26"}],"replies":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/comments?post=4184"}],"version-history":[{"count":0,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/4184\/revisions"}],"wp:attachment":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/media?parent=4184"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/categories?post=4184"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/tags?post=4184"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/ppma_author?post=4184"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}