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SAT Exam  >  SAT Questions  >  The average (arithmetic mean) of a set of 3 p... Start Learning for Free
The average (arithmetic mean) of a set of 3 positive integers is m. If the number 24 is added to this set, what is the average (arithmetic mean) of the new set of numbers?
  • a)
  • b)
  • c)
    m + 8
  • d)
Correct answer is option 'B'. Can you explain this answer?
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The average (arithmetic mean) of a set of 3 positive integers is m. If...
Let’s call the 3 positive integers a, b, and c. If the average of these numbers is m, then

Multiply by 3: a + b + c = 3m
New average when 24 is included in the set: 
Substitute a + b + c = 3m: 
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Most Upvoted Answer
The average (arithmetic mean) of a set of 3 positive integers is m. If...
Let’s call the 3 positive integers a, b, and c. If the average of these numbers is m, then

Multiply by 3: a + b + c = 3m
New average when 24 is included in the set: 
Substitute a + b + c = 3m: 
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Question based on the following passage and supplementary material.This passage is adapted from John Bohannon, "Why You Shouldnt Trust Internet Comments." ©2013 by American Association for the Advancement of Science.The “wisdom of crowds” has become a mantra ofthe Internet age. Need to choose a new vacuumcleaner? Check out the reviews on online merchantAmazon. But a new study suggests that such online(5) scores don’t always reveal the best choice. A massivecontrolled experiment of Web users finds that suchratings are highly susceptible to irrational “herdbehavior”—and that the herd can be manipulated.Sometimes the crowd really is wiser than you. The(10) classic examples are guessing the weight of a bull orthe number of gumballs in a jar. Your guess isprobably going to be far from the mark, whereas theaverage of many people’s choices is remarkably closeto the true number.(15) But what happens when the goal is to judgesomething less tangible, such as the quality or worthof a product? According to one theory, the wisdomof the crowd still holds—measuring the aggregate ofpeople’s opinions produces a stable, reliable(20) value. Skeptics, however, argue that people’sopinions are easily swayed by those of others. Sonudging a crowd early on by presenting contraryopinions—for example, exposing them to some verygood or very bad attitudes—will steer the crowd in a(25) different direction. To test which hypothesis is true,you would need to manipulate huge numbers ofpeople, exposing them to false information anddetermining how it affects their opinions.A team led by Sinan Aral, a network scientist at(30) the Massachusetts Institute of Technology inCambridge, did exactly that. Aral has been secretlyworking with a popular website that aggregates newsstories. The website allows users to make commentsabout news stories and vote each other’s comments(35) up or down. The vote tallies are visible as a numbernext to each comment, and the position of thecomments is chronological. (Stories on the site get anaverage of about ten comments and about three votesper comment.) It’s a follow-up to his experiment(40) using people’s ratings of movies to measure howmuch individual people influence each other online(answer: a lot). This time, he wanted to know howmuch the crowd influences the individual, andwhether it can be controlled from outside.(45) For five months, every comment submitted by auser randomly received an “up” vote (positiv e); a“down” vote (negative); or as a control, no vote at all.The team then observed how users rated thosecomments. The users generated more than(50) 100,000 comments that were viewed more than10 million times and rated more than 300,000 timesby other users.At least when it comes to comments on newssites, the crowd is more herdlike than wise.(55) Comments that received fake positive votes from theresearchers were 32% more likely to receive morepositive votes compared with a control, the teamreports. And those comments were no more likelythan the control to be down-voted by the next viewer(60) to see them. By the end of the study, positivelymanipulated comments got an overall boost of about25%. However, the same did not hold true for negativemanipulation. The ratings of comments thatgot a fake down vote were usually negated by an up(65) vote by the next user to see them.“Our experiment does not reveal the psychologybehind people’s decisions,” Aral says, “but anintuitive explanation is that people are moreskeptical of negative social influence. They’re more(70) willing to go along with positive opinions from otherpeople.”Duncan Watts, a network scientist at MicrosoftResearch in New York City, agrees with thatconclusion. “[But] one question is whether the(75) positive [herding] bias is specific to this site” or truein general, Watts says. He points out that thecategory of the news items in the experiment had astrong effect on how much people could bemanipulated. “I would have thought that ‘business’ is(80) pretty similar to ‘economics,’ yet they find a muchstronger effect (almost 50% stronger) for the formerthan the latter. What explains this difference? If we’regoing to apply these findings in the real world, we’llneed to know the answers.”(85) Will companies be able to boost their products bymanipulating online ratings on a massive scale?“That is easier said than done,” Watts says. If peopledetect—or learn—that comments on a website arebeing manipulated, the herd may spook and leave(90) entirely.Mean score: mean of scores for the comments in each category, with the score for each comment being determined by the number of positive votes from website users minus the number of negative votesAdapted from Lev Muchnik, Sinan Aral, and Sean J. Taylor, “Social Influence Bias: A Randomized Experiment.” ©2013 by American Association for the Advancement of Science.Q.Which action would best address a question Watts raises about the study?

Question based on the following passage and supplementary material.This passage is adapted from John Bohannon, "Why You Shouldnt Trust Internet Comments." ©2013 by American Association for the Advancement of Science.The “wisdom of crowds” has become a mantra ofthe Internet age. Need to choose a new vacuumcleaner? Check out the reviews on online merchantAmazon. But a new study suggests that such online(5) scores don’t always reveal the best choice. A massivecontrolled experiment of Web users finds that suchratings are highly susceptible to irrational “herdbehavior”—and that the herd can be manipulated.Sometimes the crowd really is wiser than you. The(10) classic examples are guessing the weight of a bull orthe number of gumballs in a jar. Your guess isprobably going to be far from the mark, whereas theaverage of many people’s choices is remarkably closeto the true number.(15) But what happens when the goal is to judgesomething less tangible, such as the quality or worthof a product? According to one theory, the wisdomof the crowd still holds—measuring the aggregate ofpeople’s opinions produces a stable, reliable(20) value. Skeptics, however, argue that people’sopinions are easily swayed by those of others. Sonudging a crowd early on by presenting contraryopinions—for example, exposing them to some verygood or very bad attitudes—will steer the crowd in a(25) different direction. To test which hypothesis is true,you would need to manipulate huge numbers ofpeople, exposing them to false information anddetermining how it affects their opinions.A team led by Sinan Aral, a network scientist at(30) the Massachusetts Institute of Technology inCambridge, did exactly that. Aral has been secretlyworking with a popular website that aggregates newsstories. The website allows users to make commentsabout news stories and vote each other’s comments(35) up or down. The vote tallies are visible as a numbernext to each comment, and the position of thecomments is chronological. (Stories on the site get anaverage of about ten comments and about three votesper comment.) It’s a follow-up to his experiment(40) using people’s ratings of movies to measure howmuch individual people influence each other online(answer: a lot). This time, he wanted to know howmuch the crowd influences the individual, andwhether it can be controlled from outside.(45) For five months, every comment submitted by auser randomly received an “up” vote (positiv e); a“down” vote (negative); or as a control, no vote at all.The team then observed how users rated thosecomments. The users generated more than(50) 100,000 comments that were viewed more than10 million times and rated more than 300,000 timesby other users.At least when it comes to comments on newssites, the crowd is more herdlike than wise.(55) Comments that received fake positive votes from theresearchers were 32% more likely to receive morepositive votes compared with a control, the teamreports. And those comments were no more likelythan the control to be down-voted by the next viewer(60) to see them. By the end of the study, positivelymanipulated comments got an overall boost of about25%. However, the same did not hold true for negativemanipulation. The ratings of comments thatgot a fake down vote were usually negated by an up(65) vote by the next user to see them.“Our experiment does not reveal the psychologybehind people’s decisions,” Aral says, “but anintuitive explanation is that people are moreskeptical of negative social influence. They’re more(70) willing to go along with positive opinions from otherpeople.”Duncan Watts, a network scientist at MicrosoftResearch in New York City, agrees with thatconclusion. “[But] one question is whether the(75) positive [herding] bias is specific to this site” or truein general, Watts says. He points out that thecategory of the news items in the experiment had astrong effect on how much people could bemanipulated. “I would have thought that ‘business’ is(80) pretty similar to ‘economics,’ yet they find a muchstronger effect (almost 50% stronger) for the formerthan the latter. What explains this difference? If we’regoing to apply these findings in the real world, we’llneed to know the answers.”(85) Will companies be able to boost their products bymanipulating online ratings on a massive scale?“That is easier said than done,” Watts says. If peopledetect—or learn—that comments on a website arebeing manipulated, the herd may spook and leave(90) entirely.Mean score: mean of scores for the comments in each category, with the score for each comment being determined by the number of positive votes from website users minus the number of negative votesAdapted from Lev Muchnik, Sinan Aral, and Sean J. Taylor, “Social Influence Bias: A Randomized Experiment.” ©2013 by American Association for the Advancement of Science.Q.Which choice provides the best evidence for the answer to the previous question?

Question based on the following passage and supplementary material.This passage is adapted from John Bohannon, "Why You Shouldnt Trust Internet Comments." ©2013 by American Association for the Advancement of Science.The “wisdom of crowds” has become a mantra ofthe Internet age. Need to choose a new vacuumcleaner? Check out the reviews on online merchantAmazon. But a new study suggests that such online(5) scores don’t always reveal the best choice. A massivecontrolled experiment of Web users finds that suchratings are highly susceptible to irrational “herdbehavior”—and that the herd can be manipulated.Sometimes the crowd really is wiser than you. The(10) classic examples are guessing the weight of a bull orthe number of gumballs in a jar. Your guess isprobably going to be far from the mark, whereas theaverage of many people’s choices is remarkably closeto the true number.(15) But what happens when the goal is to judgesomething less tangible, such as the quality or worthof a product? According to one theory, the wisdomof the crowd still holds—measuring the aggregate ofpeople’s opinions produces a stable, reliable(20) value. Skeptics, however, argue that people’sopinions are easily swayed by those of others. Sonudging a crowd early on by presenting contraryopinions—for example, exposing them to some verygood or very bad attitudes—will steer the crowd in a(25) different direction. To test which hypothesis is true,you would need to manipulate huge numbers ofpeople, exposing them to false information anddetermining how it affects their opinions.A team led by Sinan Aral, a network scientist at(30) the Massachusetts Institute of Technology inCambridge, did exactly that. Aral has been secretlyworking with a popular website that aggregates newsstories. The website allows users to make commentsabout news stories and vote each other’s comments(35) up or down. The vote tallies are visible as a numbernext to each comment, and the position of thecomments is chronological. (Stories on the site get anaverage of about ten comments and about three votesper comment.) It’s a follow-up to his experiment(40) using people’s ratings of movies to measure howmuch individual people influence each other online(answer: a lot). This time, he wanted to know howmuch the crowd influences the individual, andwhether it can be controlled from outside.(45) For five months, every comment submitted by auser randomly received an “up” vote (positiv e); a“down” vote (negative); or as a control, no vote at all.The team then observed how users rated thosecomments. The users generated more than(50) 100,000 comments that were viewed more than10 million times and rated more than 300,000 timesby other users.At least when it comes to comments on newssites, the crowd is more herdlike than wise.(55) Comments that received fake positive votes from theresearchers were 32% more likely to receive morepositive votes compared with a control, the teamreports. And those comments were no more likelythan the control to be down-voted by the next viewer(60) to see them. By the end of the study, positivelymanipulated comments got an overall boost of about25%. However, the same did not hold true for negativemanipulation. The ratings of comments thatgot a fake down vote were usually negated by an up(65) vote by the next user to see them.“Our experiment does not reveal the psychologybehind people’s decisions,” Aral says, “but anintuitive explanation is that people are moreskeptical of negative social influence. They’re more(70) willing to go along with positive opinions from otherpeople.”Duncan Watts, a network scientist at MicrosoftResearch in New York City, agrees with thatconclusion. “[But] one question is whether the(75) positive [herding] bias is specific to this site” or truein general, Watts says. He points out that thecategory of the news items in the experiment had astrong effect on how much people could bemanipulated. “I would have thought that ‘business’ is(80) pretty similar to ‘economics,’ yet they find a muchstronger effect (almost 50% stronger) for the formerthan the latter. What explains this difference? If we’regoing to apply these findings in the real world, we’llneed to know the answers.”(85) Will companies be able to boost their products bymanipulating online ratings on a massive scale?“That is easier said than done,” Watts says. If peopledetect—or learn—that comments on a website arebeing manipulated, the herd may spook and leave(90) entirely.Mean score: mean of scores for the comments in each category, with the score for each comment being determined by the number of positive votes from website users minus the number of negative votesAdapted from Lev Muchnik, Sinan Aral, and Sean J. Taylor, “Social Influence Bias: A Randomized Experiment.” ©2013 by American Association for the Advancement of Science.Q.The author of the passage suggests that crowds may be more effective at

Question based on the following passage and supplementary material.This passage is adapted from John Bohannon, "Why You Shouldnt Trust Internet Comments." ©2013 by American Association for the Advancement of Science.The “wisdom of crowds” has become a mantra ofthe Internet age. Need to choose a new vacuumcleaner? Check out the reviews on online merchantAmazon. But a new study suggests that such online(5) scores don’t always reveal the best choice. A massivecontrolled experiment of Web users finds that suchratings are highly susceptible to irrational “herdbehavior”—and that the herd can be manipulated.Sometimes the crowd really is wiser than you. The(10) classic examples are guessing the weight of a bull orthe number of gumballs in a jar. Your guess isprobably going to be far from the mark, whereas theaverage of many people’s choices is remarkably closeto the true number.(15) But what happens when the goal is to judgesomething less tangible, such as the quality or worthof a product? According to one theory, the wisdomof the crowd still holds—measuring the aggregate ofpeople’s opinions produces a stable, reliable(20) value. Skeptics, however, argue that people’sopinions are easily swayed by those of others. Sonudging a crowd early on by presenting contraryopinions—for example, exposing them to some verygood or very bad attitudes—will steer the crowd in a(25) different direction. To test which hypothesis is true,you would need to manipulate huge numbers ofpeople, exposing them to false information anddetermining how it affects their opinions.A team led by Sinan Aral, a network scientist at(30) the Massachusetts Institute of Technology inCambridge, did exactly that. Aral has been secretlyworking with a popular website that aggregates newsstories. The website allows users to make commentsabout news stories and vote each other’s comments(35) up or down. The vote tallies are visible as a numbernext to each comment, and the position of thecomments is chronological. (Stories on the site get anaverage of about ten comments and about three votesper comment.) It’s a follow-up to his experiment(40) using people’s ratings of movies to measure howmuch individual people influence each other online(answer: a lot). This time, he wanted to know howmuch the crowd influences the individual, andwhether it can be controlled from outside.(45) For five months, every comment submitted by auser randomly received an “up” vote (positiv e); a“down” vote (negative); or as a control, no vote at all.The team then observed how users rated thosecomments. The users generated more than(50) 100,000 comments that were viewed more than10 million times and rated more than 300,000 timesby other users.At least when it comes to comments on newssites, the crowd is more herdlike than wise.(55) Comments that received fake positive votes from theresearchers were 32% more likely to receive morepositive votes compared with a control, the teamreports. And those comments were no more likelythan the control to be down-voted by the next viewer(60) to see them. By the end of the study, positivelymanipulated comments got an overall boost of about25%. However, the same did not hold true for negativemanipulation. The ratings of comments thatgot a fake down vote were usually negated by an up(65) vote by the next user to see them.“Our experiment does not reveal the psychologybehind people’s decisions,” Aral says, “but anintuitive explanation is that people are moreskeptical of negative social influence. They’re more(70) willing to go along with positive opinions from otherpeople.”Duncan Watts, a network scientist at MicrosoftResearch in New York City, agrees with thatconclusion. “[But] one question is whether the(75) positive [herding] bias is specific to this site” or truein general, Watts says. He points out that thecategory of the news items in the experiment had astrong effect on how much people could bemanipulated. “I would have thought that ‘business’ is(80) pretty similar to ‘economics,’ yet they find a muchstronger effect (almost 50% stronger) for the formerthan the latter. What explains this difference? If we’regoing to apply these findings in the real world, we’llneed to know the answers.”(85) Will companies be able to boost their products bymanipulating online ratings on a massive scale?“That is easier said than done,” Watts says. If peopledetect—or learn—that comments on a website arebeing manipulated, the herd may spook and leave(90) entirely.Mean score: mean of scores for the comments in each category, with the score for each comment being determined by the number of positive votes from website users minus the number of negative votesAdapted from Lev Muchnik, Sinan Aral, and Sean J. Taylor, “Social Influence Bias: A Randomized Experiment.” ©2013 by American Association for the Advancement of Science.Q.Data presented in the figure most directly support which idea from the passage?

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The average (arithmetic mean) of a set of 3 positive integers is m. If the number 24 is added to this set, what is the average (arithmetic mean) of the new set of numbers?a)b)c)m + 8d)Correct answer is option 'B'. Can you explain this answer?
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The average (arithmetic mean) of a set of 3 positive integers is m. If the number 24 is added to this set, what is the average (arithmetic mean) of the new set of numbers?a)b)c)m + 8d)Correct answer is option 'B'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about The average (arithmetic mean) of a set of 3 positive integers is m. If the number 24 is added to this set, what is the average (arithmetic mean) of the new set of numbers?a)b)c)m + 8d)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The average (arithmetic mean) of a set of 3 positive integers is m. If the number 24 is added to this set, what is the average (arithmetic mean) of the new set of numbers?a)b)c)m + 8d)Correct answer is option 'B'. Can you explain this answer?.
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