[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-266399-105":59,"doc-detail-266399-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","hard-percentages-key","HARD percentages KEY","","A set of SAT Math practice questions focused on percentages and quantitative reasoning. Items cover expressing a daily allowance percentage in terms of cereal servings, comparing percentage-based committee composition counts, predicting a two-stage percent change in subscriptions across multiple years, calculating percent decrease from line-graph snowfall values, and solving multi-step inequalities involving unknown quantities. Each question includes answer options, a correct choice, and a rationale emphasizing correct percentage-to-multiplicative relationships and linear versus incorrect exponential interpretation.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/hard-percentages-key/266399/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/hard-percentages-key/266399.png","ImageObject",300,407,{"name":92,"@type":93},"Ben ","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-23","2026-09-14",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",15,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you express an adult potassium allowance percentage (p) in terms of cereal servings (x)?","Question",{"text":113,"@type":114},"Use the given per-serving allowance percentage: x servings provide x times that percentage, so p scales linearly with x.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Why do percent-change prediction problems typically use multiplication by (1 + rate) for each step?",{"text":118,"@type":114},"The percent increase from one year to the next is applied as a multiplicative factor to the previous year’s amount; combining stages uses the expected rates for each interval.",{"name":120,"@type":111,"acceptedAnswer":121},"How is a percent decrease computed from two values on a graph?",{"text":122,"@type":114},"Compute the difference (original minus new), divide by the original value, then multiply by 100 to convert to a percentage.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},266399,1789407079,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":130,"read_time":145},2336478951081,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Question ID 954943a4  \n\n| Assessment\u003Cbr>SAT | Test\u003Cbr>Math | Domain\u003Cbr>Problem-Solving and Data Analysis | Skill\u003Cbr>Percentages | Difficulty\u003Cbr>|\n| --- | --- | --- | --- | --- |\n\nID: 954943a4  \nJennifer bought a box of Crunchy Grain cereal. The nutrition facts on the box state  \nthat a serving size of the cereal is  cup and provides 210 calories, 50 of which are calories from fat. In addition, each serving of the cereal provides 180 milligrams of potassium, which is 5% of the daily allowance for adults. If p percent of an adult’s daily allowance of potassium is provided by x servings of Crunchy Grain cereal per day, which of the following expresses p in terms of x ?  \nA.   \nB.   \nC.   \nD.   \nID: 954943a4 Answer  \nCorrect Answer: B  \nRationale  \nChoice B is correct. It’s given that each serving of Crunchy Grain cereal provides 5% of an adult’s daily allowance of potassium, so x servings would provide x times 5% . The percentage of an adult’s daily allowance of potassium, p, is 5 times the number of servings, x. Therefore, the percentage of an adult’s daily allowance of potassium can be expressed as  .  \nChoices A, C, and D are incorrect and may result from incorrectly converting 5% to its decimal equivalent, which isn’t necessary since p is expressed as a percentage. Additionally, choices C and D are incorrect because the context should be represented by a linear relationship, not by an exponential relationship.  \nQuestion Difficulty: Hard  \nQuestion ID 65c49824  \n\n| Assessment\u003Cbr>SAT | Test\u003Cbr>Math | Domain\u003Cbr>Problem-Solving and Data Analysis | Skill\u003Cbr>Percentages | Difficulty\u003Cbr>|\n| --- | --- | --- | --- | --- |\n\nID: 65c49824  \nA school district is forming a committee to discuss plans for the construction of anew high school. Of those invited to join the committee, 15% are parents of students, 45% are teachers from the current high school, 25% are school and district administrators, and the remaining 6 individuals are students. How many more teachers were invited to join the committee than school and district administrators?  \nID: 65c49824 Answer  \nRationale  \nThe correct answer is 8. The 6 students represent  of those invited to join the committee. If  \nx people were invited to join the committee, then  . Thus, there were  people invited to join the committee. It follows that there were  teachers and  school and district administrators invited to join the committee. Therefore, there were 8 more teachers than school and district administrators invited to join the committee.  \nQuestion Difficulty: Hard  \nQuestion ID 0ea56bb2  \n\n| Assessment\u003Cbr>SAT | Test\u003Cbr>Math | Domain\u003Cbr>Problem-Solving and Data Analysis | Skill\u003Cbr>Percentages | Difficulty\u003Cbr>|\n| --- | --- | --- | --- | --- |\n\nID: 0ea56bb2  \n\n| Year | Subscriptions sold |\n| --- | --- |\n| 2012 | 5,600 |\n| 2013 | 5,880 |\n\nThe manager of an online news service received the report above on the number of subscriptions sold by the service. The manager estimated that the percent increase from 2012 to 2013 would be double the percent increase from 2013 to 2014. How many subscriptions did the manager expect would be sold in 2014?  \nA. 6,020  \nB. 6,027  \nC. 6,440  \nD. 6,468  \nID: 0ea56bb2 Answer  \nCorrect Answer: B  \nRationale  \nChoice B is correct. The percent increase from 2012 to 2013 was , or 5% . Since the percent increase  \nfrom 2012 to 2013 was estimated to be double the percent increase from 2013 to 2014, the percent increase from 2013 to 2014 was expected to be 2. 5% .  \nTherefore, the number of subscriptions sold in 2014 is expected to be the number of subscriptions sold in 2013 multiplied by  \n, or  .  \nChoice A is incorrect and is the result of adding half of the value of the increase from 2012 to 2013 to the 2013 result. Choice C is incorrect and is the result adding twice the value of the increase from 2012 to 2013 to the 2013 result. Choice Dis incorrect and is the result of interpreting the percent increase from 2013 to 2014 as double the percent increase from 2012 to 2013.  ","cbCaidNlssQz9Q0W","https://ap.wps.com/l/cbCaidNlssQz9Q0W","pdf",625009,17,"English","# SAT Math - Percentages (Hard)\n## Questions and Solutions","[{\"question\":\"How do you express an adult potassium allowance percentage (p) in terms of cereal servings (x)?\",\"answer\":\"Use the given per-serving allowance percentage: x servings provide x times that percentage, so p scales linearly with x.\"},{\"question\":\"Why do percent-change prediction problems typically use multiplication by (1 + rate) for each step?\",\"answer\":\"The percent increase from one year to the next is applied as a multiplicative factor to the previous year’s amount; combining stages uses the expected rates for each interval.\"},{\"question\":\"How is a percent decrease computed from two values on a graph?\",\"answer\":\"Compute the difference (original minus new), divide by the original value, then multiply by 100 to convert to a percentage.\"}]","HARD percentages KEY | PDF",43]