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SAT Exam  >  SAT Questions  >  Every athlete in a group of 60 female varsity... Start Learning for Free
Every athlete in a group of 60 female varsity athletes at Greenwich High School either runs track, plays soccer, or does both. If one-third of the athletes in this group who play on the soccer team also run on the track team, and one-half of the athletes in this group who run on the track team also play on the soccer team, which of the following statements must be true?
  • a)
    This group contains 40 soccer players.
  • b)
    This group contains 20 athletes who play soccer but do not run track.
  • c)
    This group contains 20 athletes who play both track and soccer.
  • d)
    The number of soccer players in this group is 15 greater than the number of track team members in this group.
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Every athlete in a group of 60 female varsity athletes at Greenwich Hi...
Given Information:
- There are 60 female varsity athletes at Greenwich High School.
- All the athletes in this group either run track, play soccer, or do both.
- One-third of the athletes who play soccer also run on the track team.
- One-half of the athletes who run on the track team also play on the soccer team.

To Find:
Which of the following statements must be true?

Analysis:
Let's use the process of elimination to determine which statement(s) must be true.

Eliminating Statement A:
Statement A claims that the group contains 40 soccer players. However, we cannot confirm this statement based on the given information.

Eliminating Statement B:
Statement B claims that the group contains 20 athletes who play soccer but do not run track. However, we cannot confirm this statement based on the given information.

Eliminating Statement C:
Statement C claims that the group contains 20 athletes who play both track and soccer. However, we cannot confirm this statement based on the given information.

Statement D:
Statement D claims that the number of soccer players in this group is 15 greater than the number of track team members in this group. Let's analyze this statement in detail.

Explanation of Statement D:
Let's assume the number of athletes who play soccer is x and the number of athletes who run track is y.

According to the given information:
- One-third of the soccer players also run track. Therefore, the number of soccer players who run track is (1/3)x.
- One-half of the track team members also play soccer. Therefore, the number of track team members who play soccer is (1/2)y.

Since every athlete in the group either runs track, plays soccer, or does both, the total number of athletes can be represented as:
x + y - (1/3)x - (1/2)y

Simplifying this expression, we get:
(2/3)x + (1/2)y

According to Statement D, the number of soccer players is 15 greater than the number of track team members. So we can write:
x = y + 15

Substituting this value in the expression for the total number of athletes:
(2/3)(y + 15) + (1/2)y

Simplifying further:
(2/3)y + 10 + (1/2)y

Combining like terms:
(4/6)y + (3/6)y + 10

Simplifying:
(7/6)y + 10

Since the total number of athletes in the group is given as 60, we can set up the equation:
(7/6)y + 10 = 60

Solving for y:
(7/6)y = 50
y = (6/7) * 50
y = 42.86

Since the number of athletes cannot be a decimal, we can round down to the nearest whole number:
y ≈ 42

Therefore, the number of soccer players is x = y + 15 = 42 + 15 = 57.

Conclusion:
Based on the calculations, Statement D is true. The number of soccer players in this group is 15 greater than the number of track team members in this
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Community Answer
Every athlete in a group of 60 female varsity athletes at Greenwich Hi...
Let’s let s = the total number of athletes in the group who play soccer, and t = the number of athletes in the group who run track. We can set up a Venn diagram to show the relationship between these two overlapping sets.

Since one-third of the soccer players also run track, we must put 1/3s in the overlapping region between soccer and track, and therefore the number who play only soccer is 2/3s. Likewise, since one-half of the athletes who run track also play soccer, we must put 1/2t in the overlapping region, and therefore the number of athletes who only run track is 1/2t.
Since there are 60 athletes in total: 
Simplify: 
Multiply by 3 to simplify: 2s + 3t = 180
The number of soccer players who run track must equal the number of track athletes who play soccer: 
Multiply by 6 (the common denominator): 2s = 3t
Substitute 2s = 3t into the previous equation: 3t + 3t = 180
Simplify: 6t = 180 Divide by 6: t = 30
Substitute t = 30 into the other equation to solve for s: 2s = 3(30)
Simplify: 2s = 90
Divide by 2: s = 45
Now we can use these values to complete the Venn diagram: 

From this diagram, we can see that the only true statement among the choices is (D).
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Question based on the following passage.This passage is adapted from Joshua Foer, Moonwalking with Einstein: The Art and Science of Remembering Everything. ©2011 by Joshua Foer.In 2000, a neuroscientist at University CollegeLondon named Eleanor Maguire wanted to find outwhat effect, if any, all that driving around thelabyrinthine streets of London might have on(5)cabbies’ brains. When she brought sixteen taxidrivers into her lab and examined their brains in anMRI scanner, she found one surprising andimportant difference. The right posteriorhippocampus, a part of the brain known to be(10)involved in spatial navigation, was 7 percent largerthan normal in the cabbies—a small but verysignificant difference. Maguire concludedthat all of that way-finding around London had physicallyaltered the gross structure oftheir brains. The more(15)years a cabbie had been on the road, the morepronounced the effect.The brain is a mutable organ, capable—withinlimits—of reorganizing itself and readapting to newkinds of sensory input, a phenomenon known as(20)neuroplasticity. It had long been thought that theadult brain was incapable ofspawning newneurons—that while learning caused synapses torearrange themselves and new links between braincells to form, the brain’s basic anatomical structure(25)was more or less static. Maguire’s study suggested theold inherited wisdom was simply not true.After her groundbreaking study of Londoncabbies, Maguire decided to turn her attention tomental athletes. She teamed up with Elizabeth(30)Valentine and John Wilding, authors of the academicmonograph Superior Memory, to study tenindividuals who had finished near the top of theWorld Memory Championship. They wanted to findout if the memorizers’ brains were—like the London(35)cabbies’—structurally different from the rest of ours,or if they were somehow just making better use ofmemory abilities that we all possess.The researchers put both the mental athletes and agroup of matched control subjects into MRI scanners(40)and asked them to memorize three-digit numbers,black-and-white photographs of people’s faces, andmagnified images of snowflakes, while their brainswere being scanned. Maguire and her team thought itwas possible that they might discover anatomical(45)differences in the brains of the memory champs,evidence that their brains had somehow reorganizedthemselves in the process of doing all that intensiveremembering. But when the researchers reviewed theimaging data, not a single significant structural(50)difference turned up. The brains of the mentalathletes appeared to be indistinguishable from thoseof the control subjects. What’s more, on every singletest of general cognitive ability, the mental athletes’scores came back well within the normal range. The(55)memory champs weren’t smarter, and they didn’thave special brains.But there was one telling difference between thebrains of the mental athletes and the control subjects:When the researchers looked at which parts of the(60)brain were lighting up when the mental athletes werememorizing, they found that they were activatingentirely different circuitry. According to thefunctional MRIs [fMRIs], regions of the brain thatwere less active in the control subjects seemed to be(65)working in overdrive for the mental athletes.Surprisingly, when the mental athletes werelearning new information, they were engagingseveral regions of the brain known to be involved intwo specific tasks: visual memory and spatial(70)navigation, including the same right posteriorhippocampal region that the London cabbies hadenlarged with all their daily way-finding. At firstglance, this wouldn’t seem to make any sense.Why would mental athletes be conjuring images in(75)their mind’s eye when they were trying to learnthree-digit numbers? Why should they be navigatinglike London cabbies when they’re supposed to beremembering the shapes of snowflakes?Maguire and her team asked the mental athletes(80)to describe exactly what was going through theirminds as they memorized. The mental athletes saidthey were consciously converting the informationthey were being asked to memorize into images, anddistributing those images along familiar spatial(85)journeys. They weren’t doing this automatically, orbecause it was an inborn talent they’d nurtured sincechildhood. Rather, the unexpected patterns of neuralactivity that Maguire’s fMRIs turned up were theresult of training and practice.Q.The main purpose of the fifth paragraph (lines 57-65) is to

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Every athlete in a group of 60 female varsity athletes at Greenwich High School either runs track, plays soccer, or does both. If one-third of the athletes in this group who play on the soccer team also run on the track team, and one-half of the athletes in this group who run on the track team also play on the soccer team, which of the following statements must be true?a)This group contains 40 soccer players.b)This group contains 20 athletes who play soccer but do not run track.c)This group contains 20 athletes who play both track and soccer.d)The number of soccer players in this group is 15 greater than the number of track team members in this group.Correct answer is option 'D'. Can you explain this answer?
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Every athlete in a group of 60 female varsity athletes at Greenwich High School either runs track, plays soccer, or does both. If one-third of the athletes in this group who play on the soccer team also run on the track team, and one-half of the athletes in this group who run on the track team also play on the soccer team, which of the following statements must be true?a)This group contains 40 soccer players.b)This group contains 20 athletes who play soccer but do not run track.c)This group contains 20 athletes who play both track and soccer.d)The number of soccer players in this group is 15 greater than the number of track team members in this group.Correct answer is option 'D'. 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 Every athlete in a group of 60 female varsity athletes at Greenwich High School either runs track, plays soccer, or does both. If one-third of the athletes in this group who play on the soccer team also run on the track team, and one-half of the athletes in this group who run on the track team also play on the soccer team, which of the following statements must be true?a)This group contains 40 soccer players.b)This group contains 20 athletes who play soccer but do not run track.c)This group contains 20 athletes who play both track and soccer.d)The number of soccer players in this group is 15 greater than the number of track team members in this group.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Every athlete in a group of 60 female varsity athletes at Greenwich High School either runs track, plays soccer, or does both. If one-third of the athletes in this group who play on the soccer team also run on the track team, and one-half of the athletes in this group who run on the track team also play on the soccer team, which of the following statements must be true?a)This group contains 40 soccer players.b)This group contains 20 athletes who play soccer but do not run track.c)This group contains 20 athletes who play both track and soccer.d)The number of soccer players in this group is 15 greater than the number of track team members in this group.Correct answer is option 'D'. Can you explain this answer?.
Solutions for Every athlete in a group of 60 female varsity athletes at Greenwich High School either runs track, plays soccer, or does both. If one-third of the athletes in this group who play on the soccer team also run on the track team, and one-half of the athletes in this group who run on the track team also play on the soccer team, which of the following statements must be true?a)This group contains 40 soccer players.b)This group contains 20 athletes who play soccer but do not run track.c)This group contains 20 athletes who play both track and soccer.d)The number of soccer players in this group is 15 greater than the number of track team members in this group.Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for SAT. Download more important topics, notes, lectures and mock test series for SAT Exam by signing up for free.
Here you can find the meaning of Every athlete in a group of 60 female varsity athletes at Greenwich High School either runs track, plays soccer, or does both. If one-third of the athletes in this group who play on the soccer team also run on the track team, and one-half of the athletes in this group who run on the track team also play on the soccer team, which of the following statements must be true?a)This group contains 40 soccer players.b)This group contains 20 athletes who play soccer but do not run track.c)This group contains 20 athletes who play both track and soccer.d)The number of soccer players in this group is 15 greater than the number of track team members in this group.Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Every athlete in a group of 60 female varsity athletes at Greenwich High School either runs track, plays soccer, or does both. If one-third of the athletes in this group who play on the soccer team also run on the track team, and one-half of the athletes in this group who run on the track team also play on the soccer team, which of the following statements must be true?a)This group contains 40 soccer players.b)This group contains 20 athletes who play soccer but do not run track.c)This group contains 20 athletes who play both track and soccer.d)The number of soccer players in this group is 15 greater than the number of track team members in this group.Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Every athlete in a group of 60 female varsity athletes at Greenwich High School either runs track, plays soccer, or does both. If one-third of the athletes in this group who play on the soccer team also run on the track team, and one-half of the athletes in this group who run on the track team also play on the soccer team, which of the following statements must be true?a)This group contains 40 soccer players.b)This group contains 20 athletes who play soccer but do not run track.c)This group contains 20 athletes who play both track and soccer.d)The number of soccer players in this group is 15 greater than the number of track team members in this group.Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Every athlete in a group of 60 female varsity athletes at Greenwich High School either runs track, plays soccer, or does both. If one-third of the athletes in this group who play on the soccer team also run on the track team, and one-half of the athletes in this group who run on the track team also play on the soccer team, which of the following statements must be true?a)This group contains 40 soccer players.b)This group contains 20 athletes who play soccer but do not run track.c)This group contains 20 athletes who play both track and soccer.d)The number of soccer players in this group is 15 greater than the number of track team members in this group.Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Every athlete in a group of 60 female varsity athletes at Greenwich High School either runs track, plays soccer, or does both. If one-third of the athletes in this group who play on the soccer team also run on the track team, and one-half of the athletes in this group who run on the track team also play on the soccer team, which of the following statements must be true?a)This group contains 40 soccer players.b)This group contains 20 athletes who play soccer but do not run track.c)This group contains 20 athletes who play both track and soccer.d)The number of soccer players in this group is 15 greater than the number of track team members in this group.Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice SAT tests.
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