{"id":1572,"date":"2024-06-05T15:07:50","date_gmt":"2024-06-05T22:07:50","guid":{"rendered":"https:\/\/magoosh.com\/gmat\/?p=1572"},"modified":"2020-01-15T10:50:46","modified_gmt":"2020-01-15T18:50:46","slug":"variables-in-gmat-answer-choices-algebraic-approach-vs-numerical-approach","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gmat\/variables-in-gmat-answer-choices-algebraic-approach-vs-numerical-approach\/","title":{"rendered":"Variables in GMAT Answer Choices: Algebraic Approach vs. Numerical Approach"},"content":{"rendered":"<p><strong>Fact<\/strong>: On GMAT Problem Solving, some of the prompts will state quantities in terms of variables, and then expect you to answer in terms of those variables.\u00a0 Such questions are known as &#8220;variable in the answer choice&#8221; questions (or VICs in some circles).<\/p>\n<p><strong>Fact<\/strong>: There are two basic strategies you can use to solve these: (a) a full-on algebraic approach; or (b) plugging in numbers for the variables.<\/p>\n<p>&nbsp;<\/p>\n<p>Which of these two approaches is better?\u00a0 Well, we all know your Algebra Two teacher back in high school would have wanted you to pick the algebraic approach &#8212; perhaps that teacher even would have considered plugging in numbers a form of &#8220;cheating.&#8221;\u00a0 BUT &#8212; this ain&#8217;t high school no more!\u00a0 This is about GMAT, and as in the business world, the guiding principle for getting through the GMAT is: whatever works.<\/p>\n<p>Which of the two approaches is better?\u00a0 It depends entirely on you.\u00a0 This is where you need to practice, trying each approach on questions like this, getting a feel for both approaches, so you develop a sense of which one works better with your style.<\/p>\n<p>&nbsp;<\/p>\n<h2>An Example Question<\/h2>\n<p>As an example, I&#8217;ll solve a new question from the OG 13 in both ways.\u00a0 The question is Problem Solving #177 in the 13th edition:<\/p>\n<p>&nbsp;<\/p>\n<p>177) Last year the price per share of Stock X increased by k percent and the earning per share increased by m percent, where k is greater than m.\u00a0 By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?<\/p>\n<p>(A) <img decoding=\"async\" src=\"https:\/\/magoosh.com\/gmat\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_984_59be1212b5140c0138341eb4a785a29f.png\" style=\"vertical-align:-16px; display: inline-block ;\" alt=\"k\/m %\" title=\"k\/m %\"\/><\/p>\n<p>(B) <img decoding=\"async\" src=\"https:\/\/magoosh.com\/gmat\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_990.5_454bd9f104f977d28cc4032b82718392.png\" style=\"vertical-align:-9.5px; display: inline-block ;\" alt=\"(k - m)%\" title=\"(k - m)%\"\/><\/p>\n<p>(C) <img decoding=\"async\" src=\"https:\/\/magoosh.com\/gmat\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_979_bfbdef14c53cf6dac62fd0d33e4bfafc.png\" style=\"vertical-align:-21px; display: inline-block ;\" alt=\"100*(k - m)\/(100 + k) %\" title=\"100*(k - m)\/(100 + k) %\"\/><\/p>\n<p>(D)\u00a0<img decoding=\"async\" src=\"https:\/\/magoosh.com\/gmat\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_979_4f047c6446162e1126e9420848f4f05d.png\" style=\"vertical-align:-21px; display: inline-block ;\" alt=\"100*(k - m)\/(100 + m) %\" title=\"100*(k - m)\/(100 + m) %\"\/><\/p>\n<p>(E) <img decoding=\"async\" src=\"https:\/\/magoosh.com\/gmat\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_979_591f7f18e4ba3a37e97c75eede6aaadf.png\" style=\"vertical-align:-21px; display: inline-block ;\" alt=\"100*(k - m)\/(100 + k+ m) %\" title=\"100*(k - m)\/(100 + k+ m) %\"\/><\/p>\n<p>&nbsp;<\/p>\n<p>This is a doozy of a question, because there are two variables in the question, and both play a role in the answer.\u00a0 This question is only #177 of 230 PS questions, but it&#8217;s one of the hardest questions in that whole section.<\/p>\n<p>&nbsp;<\/p>\n<h2>Algebraic Approach<\/h2>\n<p>First, the approach that would have made your Algebra II teacher happy.\u00a0 This will be hairy.\u00a0 Let price per share be P, and earnings per share be E.\u00a0 Then<\/p>\n<p align=\"center\">original ratio = <img decoding=\"async\" src=\"https:\/\/magoosh.com\/gmat\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_984_1083af431748f4643d69fb88dd87558c.png\" style=\"vertical-align:-16px; display: inline-block ;\" alt=\"P\/E\" title=\"P\/E\"\/><\/p>\n<p align=\"center\">new price per share = <img decoding=\"async\" src=\"https:\/\/magoosh.com\/gmat\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_982_8e49d6a616ebc5b611bb6ac4ffb09a32.png\" style=\"vertical-align:-18px; display: inline-block ;\" alt=\"P*(1 + k\/100)\" title=\"P*(1 + k\/100)\"\/><\/p>\n<p align=\"center\">new earnings per share = <img decoding=\"async\" src=\"https:\/\/magoosh.com\/gmat\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_982_ce712a7dfd07f6b8a6803eebc6e80794.png\" style=\"vertical-align:-18px; display: inline-block ;\" alt=\"E*(1 + m\/100)\" title=\"E*(1 + m\/100)\"\/><\/p>\n<p align=\"center\">new ratio = (new P)\/(new E) =<img decoding=\"async\" src=\"https:\/\/magoosh.com\/gmat\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_962_e01219a5a87bb7cf4ae59bc2e33aa8b2.png\" style=\"vertical-align:-38px; display: inline-block ;\" alt=\"{P*(1 + k\/100)}\/{E*(1 + m\/100)}\u00a0 = {P*(100 + k)}\/{E*(100 + m)}\" title=\"{P*(1 + k\/100)}\/{E*(1 + m\/100)}\u00a0 = {P*(100 + k)}\/{E*(100 + m)}\"\/><\/p>\n<p>&nbsp;<\/p>\n<p>Some comments.\u00a0 Notice that to create the percent increases, I used multipliers.\u00a0 If that&#8217;s unfamiliar, it&#8217;s a hugely important idea with which you need to acquaint yourself: see this post [<a href=\"https:\/\/magoosh.com\/gmat\/understanding-percents-on-the-gmat\/\">https:\/\/magoosh.com\/gmat\/math\/understanding-percents-on-the-gmat\/<\/a>].\u00a0\u00a0 Now, we need a percent increase from the original ratio to the new ratio.\u00a0 This will be<\/p>\n<p>&nbsp;<\/p>\n<p>Percent increase =\u00a0<img decoding=\"async\" src=\"https:\/\/magoosh.com\/gmat\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_979_fab745912d029c8a3598de8d5c1163f0.png\" style=\"vertical-align:-21px; display: inline-block ;\" alt=\"{{(new ratio) - (original ratio)}\/(original ratio)}*100\" title=\"{{(new ratio) - (original ratio)}\/(original ratio)}*100\"\/><\/p>\n<p>=\u00a0<img decoding=\"async\" src=\"https:\/\/magoosh.com\/gmat\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_962_fc0c050826f84463da169535af724dca.png\" style=\"vertical-align:-38px; display: inline-block ;\" alt=\"{{{P(100 + k)}\/{E(100 + k)} - (P\/E)}\/(P\/E)}*100\" title=\"{{{P(100 + k)}\/{E(100 + k)} - (P\/E)}\/(P\/E)}*100\"\/><\/p>\n<p>&nbsp;<\/p>\n<p>Cancel the factor of P\/E everywhere in the fraction<\/p>\n<p>&nbsp;<\/p>\n<p>=\u00a0<img decoding=\"async\" src=\"https:\/\/magoosh.com\/gmat\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_976_2b839352be35f5b80e438d0dccded2f0.png\" style=\"vertical-align:-24px; display: inline-block ;\" alt=\"((100 + k)\/(100 + m) - 1)*100\" title=\"((100 + k)\/(100 + m) - 1)*100\"\/><\/p>\n<p>&nbsp;<\/p>\n<p>Find a common denominator inside the parentheses.<\/p>\n<p>&nbsp;<\/p>\n<p>=\u00a0<img decoding=\"async\" src=\"https:\/\/magoosh.com\/gmat\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_976_0d581d450df1db38eee753b9b522e4d2.png\" style=\"vertical-align:-24px; display: inline-block ;\" alt=\"((100 + k)\/(100 + m) - (100 + m)\/(100 + m))*100\" title=\"((100 + k)\/(100 + m) - (100 + m)\/(100 + m))*100\"\/><\/p>\n<p>&nbsp;<\/p>\n<p>=\u00a0<img decoding=\"async\" src=\"https:\/\/magoosh.com\/gmat\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_976_5f6cd410bde923c89dff87a9824aa23c.png\" style=\"vertical-align:-24px; display: inline-block ;\" alt=\"((k - m)\/(100 + m))*100\" title=\"((k - m)\/(100 + m))*100\"\/><\/p>\n<p>&nbsp;<\/p>\n<p>=\u00a0<img decoding=\"async\" src=\"https:\/\/magoosh.com\/gmat\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_979_3c02281cd10ba6495ddd2541b3c4678a.png\" style=\"vertical-align:-21px; display: inline-block ;\" alt=\"100*(k - m)\/(100 + m)\" title=\"100*(k - m)\/(100 + m)\"\/><\/p>\n<p>&nbsp;<\/p>\n<p>This matches exactly answer <strong>D<\/strong>, the correct answer.<\/p>\n<p>&nbsp;<\/p>\n<h2>Numerical Approach<\/h2>\n<p>We need several numbers, which we will pick for ease of calculation rather than for realism.\u00a0 First, say price per share P = 100 (many common stocks are in the ballpark of $100\/share) and say that earnings per share is also E = 100 (that&#8217;s the part that is unrealistic, but it makes for an easy calculation).\u00a0 The original ratio, P\/E = 100\/100 = 1.<\/p>\n<p>We need k &gt; m, so let&#8217;s say k = 50 and m = 20.\u00a0 Then the new P is 150, the new E is 120, and the new ratio is 150\/120 = 15\/12 = 5\/4.<\/p>\n<p>The change from 1 to 5\/4 involves adding a quarter, and a quarter is 25%, so it&#8217;s a 25% increase in the ratio.\u00a0 Now, the question is: with values of k = 50 and m = 20, which answer choice gives the correct answer of 25?\u00a0 Before we plug in, we don&#8217;t know &#8212; it&#8217;s possible the values we pick work for two answers: in that case, we would eliminate the cases which didn&#8217;t work, then pick new values, and repeat, but only checking the cases that worked the first time.<\/p>\n<p>So, the answers:<\/p>\n<p>&nbsp;<\/p>\n<p>(A) k\/m % = 50\/20% does not equal 25%!\u00a0 <strong>Out<\/strong>.<\/p>\n<p>&nbsp;<\/p>\n<p>(B) (k \u2013 m)% = (50 \u2013 20)% = 30% <strong>Out<\/strong>.<\/p>\n<p>&nbsp;<\/p>\n<p>(C) 100*(k \u2013 m)\/(100 + k) % = (100*30)\/150 = 3000\/150 = 20% <strong>Out<\/strong>.<\/p>\n<p>&nbsp;<\/p>\n<p>(D) 100*(k \u2013 m)\/(100 + m) % = (100*30)\/120 = 3000\/120 = 25% <strong>Works<\/strong>.<\/p>\n<p>&nbsp;<\/p>\n<p>(E) 100*(k \u2013 m)\/(100 + k + m) % = (100*30)\/170 = 3000\/170 = 300\/17 = not a whole number, so it certainly doesn&#8217;t equal 25.\u00a0<strong>Out<\/strong>.<\/p>\n<p>&nbsp;<\/p>\n<p>We got lucky!\u00a0 One choice for the variables was enough to eliminate four of the five, leaving only the correct answer <strong>D<\/strong>.\u00a0 In general, if you don&#8217;t pick the most obvious choices (k = 200 &amp; m = 100, or k = 100 &amp; m = 50), then you are likely to eliminate four answer choices on your first pick of numbers.\u00a0 That&#8217;s one of many reasons it&#8217;s an excellent idea to pick less-than-perfectly-obvious numbers when you are taking a numerical approach to a problem like this.<\/p>\n<p>Here&#8217;s another question with variables in the answer choices on which you can practice: <a href=\"http:\/\/gmat.magoosh.com\/questions\/325\">http:\/\/gmat.magoosh.com\/questions\/325<\/a><\/p>\n<p>If you sign up for the Magoosh product, you will get access to this important lesson on problems with variables in the answer choices: <a href=\"http:\/\/gmat.magoosh.com\/lessons\/283-variables-in-answer-choices\">http:\/\/gmat.magoosh.com\/lessons\/283-variables-in-answer-choices<\/a><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Fact: On GMAT Problem Solving, some of the prompts will state quantities in terms of variables, and then expect you to answer in terms of those variables.\u00a0 Such questions are known as &#8220;variable in the answer choice&#8221; questions (or VICs in some circles). Fact: There are two basic strategies you can use to solve these: [&hellip;]<\/p>\n","protected":false},"author":26,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[193],"tags":[],"ppma_author":[13209],"class_list":["post-1572","post","type-post","status-publish","format-standard","hentry","category-word-problems"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Variables in GMAT Answer Choices: Algebraic Approach vs. Numerical Approach - 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\/variables-in-gmat-answer-choices-algebraic-approach-vs-numerical-approach\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Variables in GMAT Answer Choices: Algebraic Approach vs. Numerical Approach\" \/>\n<meta property=\"og:description\" content=\"Fact: On GMAT Problem Solving, some of the prompts will state quantities in terms of variables, and then expect you to answer in terms of those variables.\u00a0 Such questions are known as &#8220;variable in the answer choice&#8221; questions (or VICs in some circles). 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Fact: There are two basic strategies you can use to solve these: [&hellip;]","og_url":"https:\/\/magoosh.com\/gmat\/variables-in-gmat-answer-choices-algebraic-approach-vs-numerical-approach\/","og_site_name":"Magoosh Blog \u2014 GMAT\u00ae Exam","article_publisher":"https:\/\/www.facebook.com\/MagooshGMAT\/","article_published_time":"2024-06-05T22:07:50+00:00","article_modified_time":"2020-01-15T18:50:46+00:00","author":"Mike M\u1d9cGarry","twitter_card":"summary_large_image","twitter_creator":"@MagooshGMAT","twitter_site":"@MagooshGMAT","twitter_misc":{"Written by":"Mike M\u1d9cGarry","Est. reading time":"4 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/magoosh.com\/gmat\/variables-in-gmat-answer-choices-algebraic-approach-vs-numerical-approach\/#article","isPartOf":{"@id":"https:\/\/magoosh.com\/gmat\/variables-in-gmat-answer-choices-algebraic-approach-vs-numerical-approach\/"},"author":{"name":"Mike M\u1d9cGarry","@id":"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/320346c205075513344435baf9b0521b"},"headline":"Variables in GMAT Answer Choices: Algebraic Approach vs. Numerical Approach","datePublished":"2024-06-05T22:07:50+00:00","mainEntityOfPage":{"@id":"https:\/\/magoosh.com\/gmat\/variables-in-gmat-answer-choices-algebraic-approach-vs-numerical-approach\/"},"wordCount":909,"commentCount":4,"publisher":{"@id":"https:\/\/magoosh.com\/gmat\/#organization"},"articleSection":["GMAT Word Problems"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/magoosh.com\/gmat\/variables-in-gmat-answer-choices-algebraic-approach-vs-numerical-approach\/","url":"https:\/\/magoosh.com\/gmat\/variables-in-gmat-answer-choices-algebraic-approach-vs-numerical-approach\/","name":"Variables in GMAT Answer Choices: Algebraic Approach vs. Numerical Approach - Magoosh Blog \u2014 GMAT\u00ae Exam","isPartOf":{"@id":"https:\/\/magoosh.com\/gmat\/#website"},"datePublished":"2024-06-05T22:07:50+00:00","breadcrumb":{"@id":"https:\/\/magoosh.com\/gmat\/variables-in-gmat-answer-choices-algebraic-approach-vs-numerical-approach\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/magoosh.com\/gmat\/variables-in-gmat-answer-choices-algebraic-approach-vs-numerical-approach\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/magoosh.com\/gmat\/variables-in-gmat-answer-choices-algebraic-approach-vs-numerical-approach\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/magoosh.com\/gmat\/"},{"@type":"ListItem","position":2,"name":"Variables in GMAT Answer Choices: Algebraic Approach vs. Numerical Approach"}]},{"@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. 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. 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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\/1572","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=1572"}],"version-history":[{"count":0,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/1572\/revisions"}],"wp:attachment":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/media?parent=1572"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/categories?post=1572"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/tags?post=1572"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/ppma_author?post=1572"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}