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The document walks through multiple worked answers, using clear intermediate steps such as mass and units conversion, proportional counting with boxes and slices, finding unknown values from diagram relationships, time and angle calculations, and multi-step reasoning with totals and differences. It also includes tips for comparing numbers and interpreting graphical or geometric information.",{"@graph":69,"@context":122},[70,84,105],{"@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/selective-high-school-placement-test-mathematical-reasoning-explained-answers-for-practice-test-3/389530/",{"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/selective-high-school-placement-test-mathematical-reasoning-explained-answers-for-practice-test-3/389530.png","ImageObject",300,407,{"name":92,"@type":93},"Pentious","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-09-25",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What kind of content does Practice Test 3 include?","Question",{"text":112,"@type":113},"It contains explained answers for a Mathematical Reasoning placement test, showing step-by-step solution methods for multiple questions.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How are answers typically derived in the document?",{"text":117,"@type":113},"Solutions commonly use intermediate calculations such as totals minus parts, unit conversions (e.g., kg to grams), and diagram-based relationships.",{"name":119,"@type":110,"acceptedAnswer":120},"Does the document include any tips for solving questions faster?",{"text":121,"@type":113},"Yes. 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Rana eats 2 slices.  \nPenny eats 4 slices.  \nJoshua eats 4 slices, because 59 of the pizza is 2 slices and 69 of the pizza is 4 slices.(If the pizza is divided into 5 equal parts, or fifths, then each fifth is made of 2 slices. )  \nStatement 1: They eat the whole pizza.  \nThe number of slices they eat altogether is 2 + 4 + 4 = 10. This is all of the slices. Statement 1 is correct.  \nStatement 2: Joshua eats the least pizza.  \nJoshua eats 4 slices. Rana eats the least pizza, as she only eats 2 slices.  \nStatement 2 is incorrect.  \nStatement 3: Penny eats twice as much pizza as Joshua. Penny and Joshua eat the same amount: 4 slices each. Statement 3 is incorrect.  \nThe correct answer is A statement 1 only  \n5 There are 60 seconds in every minute. There are 60 minutes in every hour.  \nSo in 1 hour, there are 60 × 60 seconds.  \nThere are 24 hours in every day.  \nSo in 1 day, there are 24 × 60 × 60 seconds.  \nTip: Changing the order of numbers in a multiplication does not change the result – so if your answer is 60 × 60 × 24 × 24, it is the same as 24 × 24 × 60 × 60.  \nIn 24 days, there are 24 times as many seconds, or 24 × 24 × 60 × 60 seconds.  \nSo the correct answer is E 24 × 24 × 60 × 60  \n6 We can answer the question in three steps:  \nStep 1: Work out the graph scale using the size of Class 3.  \nStep 2: Use the scale to find the total number of children in Classes 1 to 5.  \nStep 3: Subtract this from 160 to find the size of Class 6.  \nStep 1:  \nIn Class 3, there are 30 children, and the column for Class 3 is 15 divisions high.  \nSo one division on the graph represents 30 ÷ 15 = 2 children.  \nStep 2:  \nThe heights of all the columns shown on the graph are:  \nClass 1 – 10 divisions  \nClass 2 – 14 divisions  \nClass 3 – 15 divisions  \nClass 4 – 13 divisions  \nClass 5 – 12 divisions  \nThe total height of these four columns is 10 + 14 + 15 + 13 + 12 = 64 divisions.  \nThis represents 64 × 2 = 128 children.  \nStep 3:  \nThere are 160 children in the school, so the number of children in Class 6 is 160 − 128 = 32.  \nSo the correct answer is C 32  \n7 Imagine taking objects off the scales. If we take objects of equal mass from both sides, the scales will still balance.  \nTaking  and  from each side leaves:  \n on the left, and  on the right.  \nSince each has mass 6 g, the total mass on the right is now 3 × 6 g = 18 g.  \nSo the total mass on the left is also 18 g.  \nIf the mass of  is 18 g, the mass of  is 18 g ÷ 2 = 9 g.  \nSo the correct answer is D 9 g  \n8 The fastest drivers are the drivers with the lowest times. All of the times have the same number of whole seconds.  \nTenths (in the first place after the decimal point) are larger than hundredths (in the second place) . So to compare decimals:  \n􀁸 First compare the tenths. If one number has more tenths, it must be larger.  \n􀁸 If both numbers have the same number of tenths, compare the hundredths (and then the thousandths) .  \nAdams was fastest, because 58.046 has no tenths and so it is the shortest time.  \nSmith was second fastest, because 58.117 has only one tenth.  \nCruz’s and Batra’s times, 58.208","cbCaiazJWuc0mQqg","https://ap.wps.com/l/cbCaiazJWuc0mQqg","pdf",1491756,"English","# Mathematical Reasoning - Practice Test 3\n## Worked Answers 1-12","[{\"question\":\"What kind of content does Practice Test 3 include?\",\"answer\":\"It contains explained answers for a Mathematical Reasoning placement test, showing step-by-step solution methods for multiple questions.\"},{\"question\":\"How are answers typically derived in the document?\",\"answer\":\"Solutions commonly use intermediate calculations such as totals minus parts, unit conversions (e.g., kg to grams), and diagram-based relationships.\"},{\"question\":\"Does the document include any tips for solving questions faster?\",\"answer\":\"Yes. For example, it provides guidance on number comparison in decimals and how rearranging multiplication factors does not change the result.\"}]","Selective High School Placement Test - Mathematical Reasoning - Explained answers for Practice Test 3 | PDF",1790323435,48]