{"id":1857,"date":"2019-08-24T15:54:11","date_gmt":"2019-08-24T20:54:11","guid":{"rendered":"http:\/\/www.kaptest.com\/blog\/prep\/?p=1857"},"modified":"2023-08-29T19:36:25","modified_gmt":"2023-08-29T19:36:25","slug":"psat-math-percentages","status":"publish","type":"post","link":"https:\/\/wpapp.kaptest.com\/study\/psat\/psat-math-percentages\/","title":{"rendered":"PSAT Math: Percentages"},"content":{"rendered":"<p>Percentages aren\u2019t just for test grades; you\u2019ll find them frequently throughout life\u2014discount pricing in stores, income tax brackets, and stock price trackers all use percents in some form. It\u2019s critical that you know how to use them correctly, especially on Test Day.<\/p>\n<p>Suppose you have a bag containing <span class=\"no-break\">10 blue<\/span> marbles and <span class=\"no-break\">15 pink<\/span> marbles, and you\u2019re asked what percent of the marbles are pink. You can determine this easily by using the formula Percent = part\/whole \u00d7 100 % . Plug 15 in for the part and <span class=\"equation\">10 + 15 (= 25)<\/span> for the whole to get 15\/25 \u00d7 100 % = 60 % pink marbles.<\/p>\n<p>Another easy way to solve many percent problems is to use the following statement: (blank) percent of (blank) is (blank). Translating from English into math, you obtain <span class=\"equation\">(blank)% \u00d7 (blank) = (blank).<\/span><\/p>\n\t<div  style='background:#ffffff;color:#545454;border-color:#545454;' class='av_promobox  avia-button-no   avia-builder-el-0  el_before_av_promobox  avia-builder-el-first '>\t\t<div class='avia-promocontent'><\/p>\n<aside class=\"sidenote sidenote-note\">\n<h5 class=\"sidenote-title\">Note<\/h5>\n<p>The percent formula requires the percent component to be in decimal form. Remember to move the decimal point appropriately before using this formula.<\/p>\n<\/aside>\n<p>\n<\/div><\/div>\n<p>You might also be asked to determine the <b>percent change<\/b> in a given situation. Fortunately, you can find this easily using a variant of the percent formula:<\/p>\n<div class=\"s9-scrollable\">Percent\u00a0increase\u00a0or\u00a0decrease = amount\u00a0of\u00a0increase\u00a0or\u00a0decrease\/original\u00a0amount \u00d7 100%<\/div>\n<p>Sometimes more than one change will occur. Be especially careful here, as it can be tempting to take a \u201cshortcut\u201d by just adding two percent changes together (which will almost always lead to an incorrect answer). Instead you\u2019ll need to find the total amount of the increase or decrease and calculate accordingly.<\/p>\n<p>An example of a question that tests your percentage expertise follows.\t<div  style='background:#ffffff;color:#545454;border-color:#545454;' class='av_promobox  avia-button-no   avia-builder-el-1  el_after_av_promobox  el_before_av_promobox '>\t\t<div class='avia-promocontent'><\/p>\n<p>1. A bank normally offers a compound annual interest rate of 0.25% on any savings account with a minimum balance of $5,000. The bank is currently offering college students a higher rate, 0.42%, with a $1,000 minimum balance. Assume the average balances are kept constant at the required minima (e.g., all interest is withdrawn) for the following.<\/p>\n<p>How much more interest does the regular account earn after three years than the student account?<\/p>\n<\/div><\/div><\/p>\n<p>Work through the Kaplan Method for Math Questions step-by-step to solve this question. The following table shows Kaplan\u2019s strategic thinking on the left, along with suggested math scratchwork on the right.<\/p>\n<table cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td valign=\"middle\"><b>Strategic Thinking<\/b><\/td>\n<td valign=\"middle\"><b>Math Scratchwork<\/b><\/td>\n<\/tr>\n<tr>\n<td valign=\"middle\"><b>Step 1: Read the first question in the set, looking for clues<\/b><br \/>\nThe intro provides information on two account types.<\/td>\n<td valign=\"middle\">regular acct: 0.25%, $5,000 min<br \/>\nstudent acct: 0.42%, $1,000 min<\/td>\n<\/tr>\n<tr>\n<td valign=\"middle\"><b>Step 2: Identify and organize the information you need<\/b><br \/>\nYou need to find how much more interest the $5,000 account will have after three years.<\/td>\n<td valign=\"middle\">difference in interest: ?<\/td>\n<\/tr>\n<tr>\n<td valign=\"middle\"><b>Step 3: Based on what you know, plan your steps to navigate the first question<\/b><br \/>\n<i>What pieces needed to find the answer are missing? How do you find the difference in interest?<\/i>You\u2019ll need the amount of interest that each account accrues after three years. Use the three-part percent formula to find annual interest, then find the interest after three years, then take the difference.<\/td>\n<td valign=\"middle\">reg. int. = ?<br \/>\nstu. int. = ?<\/p>\n<p>reg. int. x 3 = ?<\/p>\n<p>stu. int. x 3 = ?<br \/>\nreg. \u2013 stu. = ?<br \/>\n(blank)% of (blank) is (blank)<\/td>\n<\/tr>\n<tr>\n<td valign=\"middle\"><b>Step 4: Solve, step-by-step, checking units as you go<\/b><br \/>\n<i>How much interest does each account earn after one year? After three years?<\/i>Plug in appropriate values. Remember to adjust the decimal point on the percents appropriately. Triple the interest amounts to get the total accrued interest after three years.<i>What\u2019s the difference in interest earned?<\/i><br \/>\nSubtract.<\/td>\n<td valign=\"middle\">0.0025 x $5,000 = $12.50<br \/>\n0.0042 x $1,000 = $4.20<\/p>\n<p>$12.50 x 3 = $37.50<\/p>\n<p>$4.20 x 3 = $12.60<br \/>\n$37.50 \u2013 $12.60 = $24.90<\/td>\n<\/tr>\n<tr>\n<td valign=\"middle\"><b>Step 5: Did I answer the<\/b> <b><i>right<\/i><\/b> <b>question?<\/b><br \/>\nYou\u2019ve found how much more interest the regular account makes after three years, so you\u2019re done with the first question.<\/td>\n<td valign=\"middle\">24.9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\t<div  style='background:#ffffff;color:#545454;border-color:#545454;' class='av_promobox  avia-button-no   avia-builder-el-2  el_after_av_promobox  avia-builder-el-last '>\t\t<div class='avia-promocontent'><\/p>\n<h5 class=\"sidenote-title\">Note<\/h5>\n<p>Disregard the 0 in the hundredths place when gridding in your answer.<\/p>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Percentages aren\u2019t just for test grades; you\u2019ll find them frequently throughout life\u2014discount pricing in stores, income tax brackets, and stock price trackers all use percents in some form. It\u2019s critical that you know how to use them correctly, especially on Test Day. Suppose you have a bag containing 10 blue marbles and 15 pink marbles, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":28740,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[240],"tags":[],"_links":{"self":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/1857"}],"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=1857"}],"version-history":[{"count":10,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/1857\/revisions"}],"predecessor-version":[{"id":44147,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/1857\/revisions\/44147"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media\/28740"}],"wp:attachment":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media?parent=1857"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/categories?post=1857"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/tags?post=1857"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}