{"id":117,"date":"2015-12-02T03:20:50","date_gmt":"2015-12-02T11:20:50","guid":{"rendered":"https:\/\/magoosh.com\/praxis\/?p=117"},"modified":"2019-01-30T20:30:16","modified_gmt":"2019-01-31T04:30:16","slug":"difficult-math-questions-on-the-praxis-core","status":"publish","type":"post","link":"https:\/\/magoosh.com\/praxis\/difficult-math-questions-on-the-praxis-core\/","title":{"rendered":"Difficult Math Questions on the Praxis Core"},"content":{"rendered":"

Here are six Praxis Math challenge problems.\u00a0 If you can handle these, you are in good shape for the Praxis Core Math Test!<\/p>\n

\"dmqotpcmt_img1\"<\/a>
\n 
\n1) The number line shows seven points, each of them labeled with a letter of the alphabet.\u00a0\u00a0 Consider the quotient<\/p>\n

\"dmqotpcmt_img2\"<\/a><\/p>\n

The coordinate of which of the following points is closest to this quotient?<\/p>\n

(A) A<\/p>\n

(B) B<\/p>\n

(C) C<\/p>\n

(D) D<\/p>\n

(E) E
\n 
\n 
\n2) The Triangulum Galaxy is a distance from Earth of approximately D = \"1.8.\u00a0 If light travels at a speed of c = \"c and if 1 \u00a0year =\"2, then approximately how many years does it take the light from the Triangulum Galaxy to reach Earth?<\/p>\n

\"dmqotpcmt_img3\"<\/a>
\n 
\n 
\n3) A certain municipal pump was able to pump five and five sixths cubic meters of water in one and three quarters of an hour.\u00a0 What is the hourly rate of this pump, in cubic meters per hour?<\/p>\n

\"dmqotpcmt_img4\"<\/a><\/p>\n

\"dmqotpcmt_img5\"<\/a>
\n 
\n 
\n4) An L-shape is constructed by attaching three identical cubes, each with an edge length of 1 unit.\u00a0 The three cubes are permanently attached so that no seam is visible.\u00a0 When the exterior of this shape was painted, it took 28 ounces of paint.\u00a0 This first shape is just a scaled model.\u00a0 The final shape will be created in the same manner by joining three cubes with edge length 5.\u00a0 How many ounces of paint will be required to paint the exterior of this final shape?<\/p>\n

(A) 140<\/p>\n

(B) 280<\/p>\n

(C) 700
\n(D) 1050<\/p>\n

(E) 3500
\n 
\n 
\n5) Set J is a set of 150 numbers.\u00a0 The average of Set J is 62 and the range is 250.\u00a0 Set Q is a new set: each element in Set Q equals twice the corresponding number in Set J.\u00a0 What can we say about the average and range of Set Q?<\/p>\n

(A) average of Set Q = 62; range of Set Q = 250<\/p>\n

(B) average of Set Q > 62; range of Set Q = 250<\/p>\n

(C) average of Set Q = 62; range of Set Q > 250
\n(D) average of Set Q > 62; range of Set Q < 250<\/p>\n

(E) average of Set Q > 62; range of Set Q > 250
\n 
\n 
\n6) For a single evening’s performance, a certain theater company sold N orchestra tickets and M balcony tickets.\u00a0 A single orchestra ticket costs A dollars, and a single balcony ticket costs B dollars. These ticket sales were the company’s only source of revenue.\u00a0 The company had to pay a fee of R dollars to rent the space.\u00a0 In addition, there were T actors, and each actor had to be paid the same pay.\u00a0 Suppose after paying the rent and the actors’ pay, there was D dollars leftover from the ticket sales.\u00a0 Which of the following would represent the pay of a single actor?<\/p>\n

\"dmqotpcmt_img6\"<\/a><\/p>\n

 
\n <\/p>\n

Praxis Core Math<\/h2>\n

If you are a math pro, someone who studied something quantitative in college, then you should find the Praxis Core Mathematics Test quite manageable.\u00a0 You won\u2019t find much on the Praxis that is more challenging than these problems.<\/p>\n

What if math is not your very favorite thing in the world?\u00a0 What if you found these problems no fun at all? \u00a0\u00a0Suppose you bid a less-than-fond farewell to math sometime in high school, hoping that this ogre would never arise again, but now, because you want to be a teacher, you have to face the Praxis Core Mathematics Test and you have no confidence in your ability to do math: what should you do then?\u00a0 Well, in that case, I would passionately recommend the Magoosh Praxis product<\/a>, because we have a full library of math lessons: even if you are starting from Square One, we can teach you everything you need and make you feel comfortable with math again.\u00a0 So, math-phobes who want to be teachers, take heart!\u00a0 Magoosh has your back!<\/p>\n

\"dmqotpcmt_img7\"<\/a><\/p>\n

Practice problem explanations<\/h2>\n

1) The coordinate of R appears to be about +1.2, and the coordinate of S appears to be about \u20132.5, so the desired quotient = (1.2)\/(\u20132.5).\u00a0 We do not need to reach for a calculator or do a detailed calculation.\u00a0 First of all, we know positive divided by negative is negative, so the quotient will be negative.\u00a0 We also notice that the absolute value of the numerator is smaller than the absolute value of the denominator, so the quotient will have an absolute value of less than one.\u00a0 Thus, we need a quotient between \u20131 and 0.\u00a0 The only possible value is (C)<\/strong>.
\n 
\n 
\n2) Since D = RT, it\u2019s true that T = D\/R.\u00a0 We will begin by dividing the distance by the rate to give us a time.<\/p>\n

\"dmqotpcmt_img8\"<\/a><\/p>\n

That\u2019s the time in seconds.\u00a0 We need to multiply that by a conversion factor to change to years.<\/p>\n

\"dmqotpcmt_img9\"<\/a>
\n 
\n 
\n3) To get the rate, we need to dive the cubic meters of water divided by the number of hours.\u00a0 Both of these are given as mixed numerals.\u00a0 For the purposes of calculations such as division, mixed numerals are worse than useless<\/strong>.\u00a0 We have to convert the given mixed numerals to improper fractions, do the calculation with fractions, and change back to mixed numerals to select the answer.<\/p>\n

\"dmqotpcmt_img10\"<\/a><\/p>\n

That\u2019s the rate in cubic meters per hour.\u00a0 Answer = (D)<\/strong>
\n 
\n 
\n4) For this, we use scale factor.\u00a0 Each length has been increased by 5, so k = 5.\u00a0 The surface of any shape is two-dimensional, and its area increases proportional to the square of k.\u00a0 The area, and the amount of paint, should be 25 times more.<\/p>\n

new amount of paint = 25*(28 oz) = 50 * 14 oz = 100 * 7 oz = 700 oz<\/p>\n

Notice that we used the doubling & halving trick to complete the calculation.<\/p>\n

Answer = (C)<\/strong>
\n 
\n 
\n5) When we multiply all the numbers by two, the average gets multiplied by two, so the average increases.\u00a0 Also, the spacing between the numbers increases, so the range would be doubled as well: it also increase.<\/p>\n

Answer = (E)<\/strong>
\n 
\n 
\n6) Let X be each actor\u2019s salaries: that\u2019s the number we have to find.\u00a0 The ticket sales provide the money in.<\/p>\n

Money in = AN + BM<\/p>\n

The expenses are the rent and the money paid to the actors for their salaries.<\/p>\n

Money out = R + TX<\/p>\n

The first minus the second leaves D, the leftover amount.<\/p>\n

(AN + BM) \u2013 (R + TX) = D<\/p>\n

We have to solve this for X.<\/p>\n

AN + BM \u2013 R \u2013 TX = D<\/p>\n

AN + BM \u2013 R = D + TX<\/p>\n

AN + BM \u2013 R \u2013 D = TX<\/p>\n

(AN + BM \u2013 R \u2013 D)\/T = X<\/p>\n

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

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

Here are six Praxis Math challenge problems.\u00a0 If you can handle these, you are in good shape for the Praxis Core Math Test!   1) The number line shows seven points, each of them labeled with a letter of the alphabet.\u00a0\u00a0 Consider the quotient The coordinate of which of the following points is closest to […]<\/p>\n","protected":false},"author":26,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"footnotes":""},"categories":[2435],"tags":[],"ppma_author":[4911],"class_list":["post-117","post","type-post","status-publish","format-standard","hentry","category-praxis-math-practice"],"acf":[],"yoast_head":"\nDifficult Math Questions on the Praxis Core - Magoosh Blog \u2013 Praxis\u00ae\ufe0f Test<\/title>\n<meta name=\"description\" content=\"Here are six Praxis Math challenge problems.\u00a0 If you can handle these, you are in good shape for the Praxis Core Math Test!\" \/>\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\/praxis\/difficult-math-questions-on-the-praxis-core\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Difficult Math Questions on the Praxis Core\" \/>\n<meta property=\"og:description\" content=\"Here are six Praxis Math challenge problems.\u00a0 If you can handle these, you are in good shape for the Praxis Core Math Test!\" \/>\n<meta property=\"og:url\" content=\"https:\/\/magoosh.com\/praxis\/difficult-math-questions-on-the-praxis-core\/\" \/>\n<meta property=\"og:site_name\" content=\"Magoosh Blog \u2013 Praxis\u00ae\ufe0f Test\" \/>\n<meta property=\"article:published_time\" content=\"2015-12-02T11:20:50+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2019-01-31T04:30:16+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/magoosh.com\/praxis\/wp-content\/blogs.dir\/14\/files\/2015\/12\/dmqotpcmt_img1.png\" \/>\n<meta name=\"author\" content=\"Mike M\u1d9cGarry\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\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=\"5 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/magoosh.com\/praxis\/difficult-math-questions-on-the-praxis-core\/\",\"url\":\"https:\/\/magoosh.com\/praxis\/difficult-math-questions-on-the-praxis-core\/\",\"name\":\"Difficult Math Questions on the Praxis Core - Magoosh Blog \u2013 Praxis\u00ae\ufe0f Test\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/praxis\/#website\"},\"datePublished\":\"2015-12-02T11:20:50+00:00\",\"author\":{\"@id\":\"https:\/\/magoosh.com\/praxis\/#\/schema\/person\/320346c205075513344435baf9b0521b\"},\"description\":\"Here are six Praxis Math challenge problems.\u00a0 If you can handle these, you are in good shape for the Praxis Core Math Test!\",\"breadcrumb\":{\"@id\":\"https:\/\/magoosh.com\/praxis\/difficult-math-questions-on-the-praxis-core\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/magoosh.com\/praxis\/difficult-math-questions-on-the-praxis-core\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/magoosh.com\/praxis\/difficult-math-questions-on-the-praxis-core\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/magoosh.com\/praxis\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Difficult Math Questions on the Praxis Core\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/magoosh.com\/praxis\/#website\",\"url\":\"https:\/\/magoosh.com\/praxis\/\",\"name\":\"Magoosh Blog \u2013 Praxis\u00ae\ufe0f Test\",\"description\":\"Everything you need to know about the Praxis\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/magoosh.com\/praxis\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/magoosh.com\/praxis\/#\/schema\/person\/320346c205075513344435baf9b0521b\",\"name\":\"Mike M\u1d9cGarry\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/magoosh.com\/praxis\/#\/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. 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\/praxis\/author\/mikemcgarry\/\"}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Difficult Math Questions on the Praxis Core - Magoosh Blog \u2013 Praxis\u00ae\ufe0f Test","description":"Here are six Praxis Math challenge problems.\u00a0 If you can handle these, you are in good shape for the Praxis Core Math Test!","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/magoosh.com\/praxis\/difficult-math-questions-on-the-praxis-core\/","og_locale":"en_US","og_type":"article","og_title":"Difficult Math Questions on the Praxis Core","og_description":"Here are six Praxis Math challenge problems.\u00a0 If you can handle these, you are in good shape for the Praxis Core Math Test!","og_url":"https:\/\/magoosh.com\/praxis\/difficult-math-questions-on-the-praxis-core\/","og_site_name":"Magoosh Blog \u2013 Praxis\u00ae\ufe0f Test","article_published_time":"2015-12-02T11:20:50+00:00","article_modified_time":"2019-01-31T04:30:16+00:00","og_image":[{"url":"https:\/\/magoosh.com\/praxis\/wp-content\/blogs.dir\/14\/files\/2015\/12\/dmqotpcmt_img1.png"}],"author":"Mike M\u1d9cGarry","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Mike M\u1d9cGarry","Est. reading time":"5 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/magoosh.com\/praxis\/difficult-math-questions-on-the-praxis-core\/","url":"https:\/\/magoosh.com\/praxis\/difficult-math-questions-on-the-praxis-core\/","name":"Difficult Math Questions on the Praxis Core - Magoosh Blog \u2013 Praxis\u00ae\ufe0f Test","isPartOf":{"@id":"https:\/\/magoosh.com\/praxis\/#website"},"datePublished":"2015-12-02T11:20:50+00:00","author":{"@id":"https:\/\/magoosh.com\/praxis\/#\/schema\/person\/320346c205075513344435baf9b0521b"},"description":"Here are six Praxis Math challenge problems.\u00a0 If you can handle these, you are in good shape for the Praxis Core Math Test!","breadcrumb":{"@id":"https:\/\/magoosh.com\/praxis\/difficult-math-questions-on-the-praxis-core\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/magoosh.com\/praxis\/difficult-math-questions-on-the-praxis-core\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/magoosh.com\/praxis\/difficult-math-questions-on-the-praxis-core\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/magoosh.com\/praxis\/"},{"@type":"ListItem","position":2,"name":"Difficult Math Questions on the Praxis Core"}]},{"@type":"WebSite","@id":"https:\/\/magoosh.com\/praxis\/#website","url":"https:\/\/magoosh.com\/praxis\/","name":"Magoosh Blog \u2013 Praxis\u00ae\ufe0f Test","description":"Everything you need to know about the Praxis","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/magoosh.com\/praxis\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/magoosh.com\/praxis\/#\/schema\/person\/320346c205075513344435baf9b0521b","name":"Mike M\u1d9cGarry","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/magoosh.com\/praxis\/#\/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. 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\/praxis\/author\/mikemcgarry\/"}]}},"authors":[{"term_id":4911,"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>."}],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/magoosh.com\/praxis\/wp-json\/wp\/v2\/posts\/117","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/magoosh.com\/praxis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/magoosh.com\/praxis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/magoosh.com\/praxis\/wp-json\/wp\/v2\/users\/26"}],"replies":[{"embeddable":true,"href":"https:\/\/magoosh.com\/praxis\/wp-json\/wp\/v2\/comments?post=117"}],"version-history":[{"count":0,"href":"https:\/\/magoosh.com\/praxis\/wp-json\/wp\/v2\/posts\/117\/revisions"}],"wp:attachment":[{"href":"https:\/\/magoosh.com\/praxis\/wp-json\/wp\/v2\/media?parent=117"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magoosh.com\/praxis\/wp-json\/wp\/v2\/categories?post=117"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magoosh.com\/praxis\/wp-json\/wp\/v2\/tags?post=117"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/magoosh.com\/praxis\/wp-json\/wp\/v2\/ppma_author?post=117"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}