{"id":13799,"date":"2026-10-01T17:03:50","date_gmt":"2026-10-01T17:03:50","guid":{"rendered":"http:\/\/grockit.com\/blog\/gre\/?p=679"},"modified":"2026-10-01T17:03:50","modified_gmt":"2026-10-01T17:03:50","slug":"gre-quantitative-percents","status":"publish","type":"post","link":"https:\/\/wpapp.kaptest.com\/study\/gre\/gre-quantitative-percents\/","title":{"rendered":"GRE Quantitative: Percents"},"content":{"rendered":"<p>Because of their broad applicability to real life, percent problems are common in standardized tests. We calculate percents every day, from leaving fair tips at restaurants to figuring out which sale will save the most money. While the percent problems on the <a title=\"GRE Score Predictor: What is your GRE Math Score?\" href=\"https:\/\/www.kaptest.com\/blog\/prep\/gre\/gre-score-predictor-what-is-your-gre-math-score\/\">GRE quantitative<\/a> may be a little more complicated than those everyday calculations, they all follow the same basic rules.<\/p>\n<p><div  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h3    avia-builder-el-0  el_before_av_heading  avia-builder-el-first  '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Converting Decimals to Percents<\/h3><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div><br \/>\nThe word \u201cpercent\u201d means \u201cper hundred,\u201d so 19% can be written as either 0.19 or 19\/100. To convert a decimal to a percent, multiply by 100, moving the decimal point two places to the right. For example, 0.19 becomes 19%, and 0.00031 becomes 0.031%. To convert a percent to a decimal, divide by 100, moving the decimal point two places to the left.<br \/>\n<div  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h3    avia-builder-el-1  el_after_av_heading  el_before_av_table  '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Converting Percents to Fractions<\/h3><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div><br \/>\nTo convert a percent to a fraction, drop the percent symbol, write the number over 100, and then reduce. Here are a few familiar examples and some not so familiar ones.<br \/>\n<div class='avia-data-table-wrap avia_responsive_table'><table  class='avia-table avia-data-table avia-table-1  avia-builder-el-2  el_after_av_heading  el_before_av_heading  avia_pricing_default '  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Table\" ><tbody><tr class=''><td class=''>25%<\/td><td class=''>25\/100<\/td><td class=''>1\/4<\/td><\/tr><tr class=''><td class=''>12.5%<\/td><td class=''>12.5\/100<\/td><td class=''>1\/8<\/td><\/tr><tr class=''><td class=''>5%<\/td><td class=''>5\/100<\/td><td class=''>1\/20<\/td><\/tr><tr class=''><td class=''>1%<\/td><td class=''>1\/100<\/td><td class=''>1\/100<\/td><\/tr><tr class=''><td class=''>250%<\/td><td class=''>250\/100<\/td><td class=''>5\/2<\/td><\/tr><\/tbody><\/table><\/div><style type='text\/css'><\/style><br \/>\n<a title=\"Converting Fractions to Decimals: Tips and Tricks\" href=\"https:\/\/www.kaptest.com\/blog\/prep\/gre\/converting-fractions-to-decimals-tips-and-tricks\/\">See a full chart of conversions here &gt;\u00a0<\/a><\/p>\n<p><div  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h3    avia-builder-el-3  el_after_av_table  el_before_av_promobox  '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Finding Percents of Numbers<\/h3><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div><br \/>\nCommon percent problems involve finding the percent of number and its many variations. Check out these simple examples below:<br \/>\n\t<div   class='av_promobox  avia-button-no   avia-builder-el-4  el_after_av_heading  el_before_av_toggle_container '>\t\t<div class='avia-promocontent'><p>\nWhat is 45% of 200?<br \/>\n90 is 45% of what number?<br \/>\n90 is what percent of 200?<\/p>\n<\/div><\/div><br \/>\nThese kinds of questions should look familiar. The arithmetic involved is rather simple, but if you\u2019re unfamiliar with the technique for solving them, they could pose a challenge. Let\u2019s go over how to solve each one.<br \/>\nIn each case, we want to translate each sentence by replacing \u201cwhat\u201d with x (since \u2018what\u2019 means the unknown variable), \u2018is\u2019 with \u2018=\u2019, \u2018of\u2019 with * (multiplication symbol), and also convert any percents to decimals.<br \/>\n<div  class=\"togglecontainer   toggle_close_all  avia-builder-el-5  el_after_av_promobox  el_before_av_hr \" >\n<section class=\"av_toggle_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\"  >    <div role=\"tablist\" class=\"single_toggle\" data-tags=\"{All} \"  >        <p data-fake-id=\"#toggle-id-1\" class=\"toggler \"  itemprop=\"headline\"    role=\"tab\" tabindex=\"0\" aria-controls=\"toggle-id-1\">Explanations<span class=\"toggle_icon\" >        <span class=\"vert_icon\"><\/span><span class=\"hor_icon\"><\/span><\/span><\/p>        <div id=\"toggle-id-1\" class=\"toggle_wrap \"  >            <div class=\"toggle_content invers-color \"  itemprop=\"text\"   ><p><em>x<\/em> = 45% of 200\u00a0 \u2192 <em>x<\/em> = .45*200 \u2192 90<br \/>\n90 = 45% of <em>x<\/em> \u2192 90 = .45<em>x<\/em> \u2192 90\/.45 = <em>x <\/em>\u2192 200<br \/>\n90 = <em>x<\/em>% of 200 \u2192 90 = (<em>x<\/em>\/100) * 200 \u2192 90 = 2<em>x<\/em> \u2192 45<\/p>\n            <\/div>        <\/div>    <\/div><\/section>\n<\/div><br \/>\n<div  style='height:20px' class='hr hr-invisible   avia-builder-el-6  el_after_av_toggle_container  el_before_av_heading '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<div  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h3    avia-builder-el-7  el_after_av_hr  el_before_av_tab_container  '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Percentage Increase and Decrease<\/h3><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div><\/p>\n<p>GRE percent change questions compare the amount of an increase or decrease with the original value. The key is to divide the change by the original amount, then multiply by 100:<\/p>\n<p><strong>Percent increase = [(new value \u2212 original value) \u00f7 original value] \u00d7 100%<\/strong><\/p>\n<p><strong>Percent decrease = [(original value \u2212 new value) \u00f7 original value] \u00d7 100%<\/strong><\/p>\n<p>For questions asking how much greater or smaller one quantity is than another, the comparison value is the denominator. For example, \u201cWhat percent more than 6 is 8?\u201d uses 6 as the base. \u201cWhat percent less than 8 is 6?\u201d uses 8.<\/p>\n<div  class=\"tabcontainer   top_tab   avia-builder-el-8  el_after_av_heading  el_before_av_heading \" role=\"tablist\">\n\n<section class=\"av_tab_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div aria-controls=\"tab-id-1\" role=\"tab\" tabindex=\"0\" data-fake-id=\"#tab-id-1\" class=\"tab active_tab\"  itemprop=\"headline\" >Question #1<\/div>\n<div id=\"tab-id-1\" class=\"tab_content active_tab_content\" aria-hidden=\"false\">\n<div class=\"tab_inner_content invers-color\"  itemprop=\"text\" >\n<p>1. A pair of pants was selling for $20 last week, but now is selling for $27 this week. By what percent did the price of the pants increase?<\/p>\n\n<\/div>\n<\/div>\n<\/section>\n\n<section class=\"av_tab_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div aria-controls=\"tab-id-2\" role=\"tab\" tabindex=\"0\" data-fake-id=\"#tab-id-2\" class=\"tab \"  itemprop=\"headline\" >Explanation<\/div>\n<div id=\"tab-id-2\" class=\"tab_content \" aria-hidden=\"true\">\n<div class=\"tab_inner_content invers-color\"  itemprop=\"text\" >\n<p>27 &#8211; 20 = 7<br \/>\n7 \/ 20 = 35 \/ 100 = 35 percent<\/p>\n\n<\/div>\n<\/div>\n<\/section>\n\n<\/div>\n\n<h4>\u201cPercent Of\u201d vs. \u201cPercent Change\u201d on the GRE<\/h4>\n<p>Small changes in wording can produce different answers, even when the numbers stay the same. \u201cPercent of\u201d compares one amount with another. \u201cPercent more\u201d or \u201cpercent less\u201d compares the difference between the amounts with the stated base.<\/p>\n<table>\n<tbody>\n<tr>\n<th>Question<\/th>\n<th>Calculation<\/th>\n<th>Answer<\/th>\n<\/tr>\n<tr>\n<td>6 is what percent of 8?<\/td>\n<td>(6 \u00f7 8) \u00d7 100%<\/td>\n<td>75%<\/td>\n<\/tr>\n<tr>\n<td>8 is what percent of 6?<\/td>\n<td>(8 \u00f7 6) \u00d7 100%<\/td>\n<td>133\u2153%<\/td>\n<\/tr>\n<tr>\n<td>8 is what percent more than 6?<\/td>\n<td>[(8 \u2212 6) \u00f7 6] \u00d7 100%<\/td>\n<td>33\u2153%<\/td>\n<\/tr>\n<tr>\n<td>6 is what percent less than 8?<\/td>\n<td>[(8 \u2212 6) \u00f7 8] \u00d7 100%<\/td>\n<td>25%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The difference between 6 and 8 is always 2, but the base changes. That is why increasing from 6 to 8 is a 33\u2153% increase, while decreasing from 8 to 6 is a 25% decrease. Equal numerical changes do not necessarily produce equal percentage changes.<\/p>\n<p><div  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h3    avia-builder-el-9  el_after_av_tab_container  el_before_av_tab_container  '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >A Percent Word Problem<\/h3><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div><br \/>\nFor the most part, if you are not dealing with quantitative comparisons, you\u2019ll have to solve percent problems in the word problem form. Here\u2019s a common type that you might encounter.<br \/>\n<div  class=\"tabcontainer   top_tab   avia-builder-el-10  el_after_av_heading  el_before_av_heading \" role=\"tablist\">\n\n<section class=\"av_tab_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div aria-controls=\"tab-id-3\" role=\"tab\" tabindex=\"0\" data-fake-id=\"#tab-id-3\" class=\"tab active_tab\"  itemprop=\"headline\" >Question #2<\/div>\n<div id=\"tab-id-3\" class=\"tab_content active_tab_content\" aria-hidden=\"false\">\n<div class=\"tab_inner_content invers-color\"  itemprop=\"text\" >\n<p>1. After John gave 110 baseball cards to Steve and 75 to Bill, he still had 315 left. What percent of his cards did John give away?<br \/>\nA .25%<br \/>\nB. 33 1\/3 %<br \/>\nC. 37%<br \/>\nD. 40%<br \/>\nE. 50%<\/p>\n\n<\/div>\n<\/div>\n<\/section>\n\n<section class=\"av_tab_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div aria-controls=\"tab-id-4\" role=\"tab\" tabindex=\"0\" data-fake-id=\"#tab-id-4\" class=\"tab \"  itemprop=\"headline\" >Explanation<\/div>\n<div id=\"tab-id-4\" class=\"tab_content \" aria-hidden=\"true\">\n<div class=\"tab_inner_content invers-color\"  itemprop=\"text\" >\n<p>The key here is that John gave away a total of 185 cards and had 315 left. That means he must have started with 185+315 = 500 cards. The question, then, is really asking \u201c185 is what percent of 500?\u201d<br \/>\n185 = (x\/100)*500 \u2192 5x=185 \u2192 x=185\/5\u2192 37<br \/>\nOur answer is C.<\/p>\n\n<\/div>\n<\/div>\n<\/section>\n\n<\/div>\n<\/p>\n<div  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h3    avia-builder-el-11  el_after_av_tab_container  el_before_av_tab_container  '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >GRE Percent Change Practice: Profit on Cost<\/h3><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div>\n<p><div  class=\"tabcontainer   top_tab   avia-builder-el-12  el_after_av_heading  el_before_av_sidebar \" role=\"tablist\">\n\n<section class=\"av_tab_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div aria-controls=\"tab-id-5\" role=\"tab\" tabindex=\"0\" data-fake-id=\"#tab-id-5\" class=\"tab active_tab\"  itemprop=\"headline\" >Question #3<\/div>\n<div id=\"tab-id-5\" class=\"tab_content active_tab_content\" aria-hidden=\"false\">\n<div class=\"tab_inner_content invers-color\"  itemprop=\"text\" >\n<p data-pm-slice=\"1 1 &#091;&#093;\">A clothing store purchased a dress wholesale for $80 and sold it for $200. What was the store\u2019s percent profit on the wholesale price of the dress?<\/p>\n<p>A. 40%<br \/>\nB. 66\u2154%<br \/>\nC. 60%<br \/>\nD. 150%<br \/>\nE. 250%<\/p>\n\n<\/div>\n<\/div>\n<\/section>\n\n<section class=\"av_tab_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div aria-controls=\"tab-id-6\" role=\"tab\" tabindex=\"0\" data-fake-id=\"#tab-id-6\" class=\"tab \"  itemprop=\"headline\" >Explanation<\/div>\n<div id=\"tab-id-6\" class=\"tab_content \" aria-hidden=\"true\">\n<div class=\"tab_inner_content invers-color\"  itemprop=\"text\" >\n<p data-pm-slice=\"1 1 &#091;&#093;\">The profit is the difference between the selling price and the wholesale cost:<\/p>\n<p>$200 \u2212 $80 = $120<\/p>\n<p>Because the question asks for percent profit <strong>on the wholesale price<\/strong>, the original $80 cost is the denominator:<\/p>\n<p>Percent profit = ($120 \u00f7 $80) \u00d7 100% = <strong>150%<\/strong><\/p>\n<p>The correct answer is <strong>D<\/strong>.<\/p>\n<p>Dividing $200 by $80 gives 250%, but that answers a different question: the selling price is what percent of the wholesale cost? Dividing $120 by $200 gives 60%, which measures profit as a percentage of the selling price. Neither calculation answers the question asked.<\/p>\n<p>For GRE percent change questions, identify both the change and the base before calculating. This habit also helps with Data Interpretation questions involving charts and graphs.<\/p>\n\n<\/div>\n<\/div>\n<\/section>\n\n<\/div>\n<br \/>\n<div  class='avia-builder-widget-area clearfix  avia-builder-el-13  el_after_av_tab_container  avia-builder-el-last '><div id=\"text-70\" class=\"widget clearfix widget_text\">\t\t\t<div class=\"textwidget\"><p><span data-sumome-listbuilder-embed-id=\"a78fe19e226d385662749ccaadcdccd7ecdcab651c77e3b874bfcb76a80605a7\"><\/span><\/p>\n<\/div>\n\t\t<\/div><div id=\"text-71\" class=\"widget clearfix widget_text\">\t\t\t<div class=\"textwidget\"><p><span data-sumome-listbuilder-embed-id=\"185e834399a9fdd414ded52f3f51a4735f464b8c612f006f44ffba835a649b4f\"><\/span><\/p>\n<\/div>\n\t\t<\/div><\/div><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Because of their broad applicability to real life, percent problems are common in standardized tests. We calculate percents every day, from leaving fair tips at restaurants to figuring out which sale will save the most money. While the percent problems on the GRE quantitative may be a little more complicated than those everyday calculations, they [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":28957,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[68],"tags":[357],"_links":{"self":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/13799"}],"collection":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/comments?post=13799"}],"version-history":[{"count":2,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/13799\/revisions"}],"predecessor-version":[{"id":50604,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/13799\/revisions\/50604"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media\/28957"}],"wp:attachment":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media?parent=13799"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/categories?post=13799"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/tags?post=13799"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}