{"id":4584,"date":"2024-06-05T09:00:52","date_gmt":"2024-06-05T16:00:52","guid":{"rendered":"https:\/\/magoosh.com\/gmat\/?p=4584"},"modified":"2020-01-15T10:48:38","modified_gmt":"2020-01-15T18:48:38","slug":"gmat-practice-questions-with-fractions-and-decimals","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gmat\/gmat-practice-questions-with-fractions-and-decimals\/","title":{"rendered":"GMAT Practice Questions with Fractions and Decimals"},"content":{"rendered":"

Here are ten problems on fractions and decimals, some of which are quite challenging.\u00a0 Remember, no calculator!<\/p>\n

\"gpqwfad_img1\"<\/p>\n

\"gpqwfad_img2\"<\/p>\n

    \n\t(A) 0.1
    \n\t(B) 1
    \n\t(C) 10
    \n\t(D) 100
    \n\t(E) 1000\n<\/ol>\n

    \"gpqwfad_img3\"<\/p>\n

    \"gpqwfad_img4\"<\/p>\n

    \"gpqwfad_img5\"<\/p>\n

    6)\u00a0 Suppose you have access to a large vat of distilled water, several gallons large.\u00a0 You have two precise measuring pipettes, one to measure exactly 1\/3 of an ounce and one to measure exactly 1\/4 of an ounce.\u00a0 You can pour precisely measured amounts into a beaker, which initially is empty.\u00a0 You can use either pipette to remove distilled water from the vat or from the beaker and use either pipette to dispense water into either of those receptacles, but you cannot use either pipette to take any quantity of distilled water other than the amount for which it is designed.\u00a0 Which of the following represents, in ounces,\u00a0 a precise amount of distilled water you can transfer from the vat to the beaker?<\/p>\n

    \"gpqwfad_img6\"<\/p>\n

      \n\t(A) I only
      \n\t(B) III only
      \n\t(C) I and III only
      \n\t(D) II and III only
      \n\t(E) I, II, and III\n<\/ol>\n

      \"gpqwfad_img7\"<\/p>\n

      \"gpqwfad_img8\"<\/p>\n

        \n\t(A) 440
        \n\t(B) 6,600
        \n\t(C) 13,200
        \n\t(D) 44,000
        \n\t(C) 132,000\n<\/ol>\n

        \"gpqwfad_img9\"<\/p>\n

        \"gpqwfad_img10\"<\/p>\n

          \n\t(A) 2
          \n\t(B) 4
          \n\t(C) 6
          \n\t(D) 8
          \n\t(E) 12\n<\/ol>\n

           <\/p>\n

          Fractions and Decimals<\/h2>\n

          I have already written a few blogs that would be germane to these topics.<\/p>\n

          1) Fractions<\/a>: some of the basic ideas of fractions<\/p>\n

          2) Terminating and Repeating Decimals<\/a>: an assortment of decimal ideas<\/p>\n

          3) Advanced Factoring<\/a>: some sophisticated techniques for factoring ungainly looking decimals<\/p>\n

          More advanced ideas will be discussed the explanations to these problems, below.<\/p>\n

          \"gpqwfad_img11\"<\/p>\n

           <\/p>\n

          Solutions to Practice Problems<\/h2>\n

          1) First, let’s separate out the denominators and simplify them.<\/p>\n

          \"gpqwfad_img12\"<\/p>\n

          and<\/p>\n

          \"gpqwfad_img13\"<\/p>\n

          We are adding the reciprocals of these two fractions:<\/p>\n

          \"gpqwfad_img14\"<\/p>\n

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

          2) Let’s handle the numerator and denominator separately to begin.\u00a0 The number is the cube root of a decimal.\u00a0 The first thing we have to recognize is that 4 cubed is 64, so the cube root of 64 is 4.\u00a0 There are six total decimal places, so when we take a cube root, that will get divided by 3, down to only two decimal places.\u00a0 Thus,<\/p>\n

          \"gpqwfad_img15\"<\/p>\n

          The denominator is a little easier.<\/p>\n

          \"gpqwfad_img16\"<\/p>\n

          Those are the two numbers we have to divide.\u00a0 When divide decimals, we move both decimals an equal number of places to the right until the denominator is a whole number.\u00a0\u00a0 Here, after we set up the fraction, we will have to move both decimals four places to the right, because the denominator starts with four decimal point.<\/p>\n

          \"gpqwfad_img17\"<\/p>\n

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

          3) There are a few different ways to think about this.\u00a0 First, I will multiply the entire inequality by positive 6.\u00a0 This will leave the direction of the inequality unchanged, and I can multiply right through the absolute value signs.\u00a0 This will eliminate any fractions.<\/p>\n

          |3y \u2013 1| < 4<\/p>\n

          Well, the only way a thing can have an absolute value less than 4 is if it’s true value is between \u20134 and +4.\u00a0 Thus<\/p>\n

          \u20134 < 3y \u2013 1 < 4<\/p>\n

          Add one to each term.<\/p>\n

          \u20133 < 3y < 5<\/p>\n

          Now, divide by +3.\u00a0 Because we are dividing by a positive, the direction of the inequalities stay the same.<\/p>\n

          \"gpqwfad_img18\"<\/p>\n

          So, y could be any positive or negative fraction between \u20131 and +1, so (B)<\/b> & (C)<\/b> & (D)<\/b> are all allowed, and choice (E)<\/b> is less than 5\/3, so that’s also allowed.\u00a0 The only one that is not allowed is (A)<\/b>, and that’s the answer.<\/p>\n

          4) Notice that all the denominators are multiples of 30, so factor out a factor of 1\/30:<\/p>\n

          \"gpqwfad_img19\"<\/p>\n

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

          5) It’s actually better to change the decimals into fractions:<\/p>\n

          \"gpqwfad_img20\"<\/p>\n

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

          6) If you fill the 1\/3 oz pipette and put this into the beaker.\u00a0 Then use the other pipette to remove 1\/4 oz from the beaker.\u00a0 This 1\/4 oz can be put back in the vat.<\/p>\n

          \"gpqwfad_img21\"<\/p>\n

          Thus, there would be 1\/12 oz left in the beaker: that’s the amount that would have been transferred from the vat to the beaker.<\/p>\n

          If we repeat this same procedure, we will transfer another 1\/12 oz from the vat to the beaker, and 2\/12 = 1\/6.\u00a0 Therefore, we could transfer either 1\/12 or 1\/6 from the vat to the beaker.<\/p>\n

          There is no way to transfer 1\/7 to the beaker.\u00a0 No combination of arithmetic involving 1\/3 and 1\/4 will produce 1\/7.<\/p>\n

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

          7) Let’s think about this is in stages.\u00a0 First, call the entire denominator D; then (0.2)\/D = 4.\u00a0 From this, we must recognize that D must be 1\/4 of 0.2, or D = 0.05.<\/p>\n

          Now, set that denominator equal to 0.05.<\/p>\n

          0.3 \u2013 x = 0.05<\/p>\n

          x = 0.3 \u2013 0.05 = 0.25 = 1\/4<\/p>\n

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

          8) Let’s make things easier by breaking this into two fraction.\u00a0 First, let’s work with 3.3 divided by 0.015.\u00a0 We will begin by sliding the decimals to the right a couple spaces:<\/p>\n

          \"gpqwfad_img22\"<\/p>\n

          Now, notice that the denominator is 3\/2, so we will replace that decimal with the fraction:<\/p>\n

          \"gpqwfad_img23\"<\/p>\n

          That’s the first piece of the fraction.\u00a0 Now, consider the rest:<\/p>\n

          \"gpqwfad_img24\"<\/p>\n

          Multiply the pieces<\/p>\n

          (220)*(200) = 44,000<\/p>\n

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

          9) For this one, we need to use some advanced factoring<\/a>.\u00a0 Notice that<\/p>\n

          0.9996 = 1 \u2013 0.0004<\/p>\n

          Thus, we can express this as a difference of two squares<\/a>, and use that to factor it<\/p>\n

          \"gpqwfad_img25\"<\/p>\n

          Now, consider that 0.98 = 1 \u2013 0.02; then<\/p>\n

          \"gpqwfad_img26\"<\/p>\n

          When we subtract 1, we get 0.02, which equals 1\/50.<\/p>\n

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

          10) Think of this in stages. Call the denominator D.\u00a0 If 3\/D = 12, then D must equal 1\/4.<\/p>\n

          Now, look at the denominator. One minus thing equals 1\/4, so that thing must equal 3\/4.<\/p>\n

          Well, 6\/c = 3\/4, so c = 8.<\/p>\n

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

           
          \nIf you’re looking to strengthen your Quant skills, Magoosh is here to help!           Magoosh GMAT<\/a> offers high-quality, affordable test prep to help you reach your score goals. Get access for a year with premium, or try us for free with a 1-week trial!<\/p>\n","protected":false},"excerpt":{"rendered":"

          Here are ten problems on fractions and decimals, some of which are quite challenging.\u00a0 Remember, no calculator! (A) 0.1 (B) 1 (C) 10 (D) 100 (E) 1000 6)\u00a0 Suppose you have access to a large vat of distilled water, several gallons large.\u00a0 You have two precise measuring pipettes, one to measure exactly 1\/3 of an […]<\/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-4584","post","type-post","status-publish","format-standard","hentry","category-basics"],"acf":[],"yoast_head":"\nGMAT Practice Questions with Fractions and Decimals - 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\/gmat-practice-questions-with-fractions-and-decimals\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"GMAT Practice Questions with Fractions and Decimals\" \/>\n<meta property=\"og:description\" content=\"Here are ten problems on fractions and decimals, some of which are quite challenging.\u00a0 Remember, no calculator! (A) 0.1 (B) 1 (C) 10 (D) 100 (E) 1000 6)\u00a0 Suppose you have access to a large vat of distilled water, several gallons large.\u00a0 You have two precise measuring pipettes, one to measure exactly 1\/3 of an […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/magoosh.com\/gmat\/gmat-practice-questions-with-fractions-and-decimals\/\" \/>\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=\"2024-06-05T16:00:52+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2020-01-15T18:48:38+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/magoosh.com\/gmat\/files\/2014\/04\/gpqwfad_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=\"10 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/magoosh.com\/gmat\/gmat-practice-questions-with-fractions-and-decimals\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/gmat-practice-questions-with-fractions-and-decimals\/\"},\"author\":{\"name\":\"Mike M\u1d9cGarry\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/320346c205075513344435baf9b0521b\"},\"headline\":\"GMAT Practice Questions with Fractions and Decimals\",\"datePublished\":\"2024-06-05T16:00:52+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/gmat-practice-questions-with-fractions-and-decimals\/\"},\"wordCount\":889,\"commentCount\":17,\"publisher\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/#organization\"},\"articleSection\":[\"GMAT Math Basics\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/magoosh.com\/gmat\/gmat-practice-questions-with-fractions-and-decimals\/\",\"url\":\"https:\/\/magoosh.com\/gmat\/gmat-practice-questions-with-fractions-and-decimals\/\",\"name\":\"GMAT Practice Questions with Fractions and Decimals - 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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\/4584","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=4584"}],"version-history":[{"count":0,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/4584\/revisions"}],"wp:attachment":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/media?parent=4584"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/categories?post=4584"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/tags?post=4584"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/ppma_author?post=4584"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}