All Courses
Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity Get the App Login Join for Free
Sign in Open App
GMAT Exam  >  GMAT Questions  >  A certain roller coaster ride has between 29 ... Start Learning for Free
A certain roller coaster ride has between 29 and 150 people waiting in line to board. If riders are let on only in groups of 5 there will be 2 riders that do not get on. If the riders are let on only in groups of 6 all riders will be able to get on. Which of the following is the sum of the greatest possible number of people in the line and the least possible number of people in the line?
  • a)
    269
  • b)
    184
  • c)
    174
  • d)
    169
  • e)
    142
Correct answer is option 'C'. Can you explain this answer?
Clear all your GMAT doubts with EduRev
Most Upvoted Answer
A certain roller coaster ride has between 29 and 150 people waiting in...
Given:
- Number of people waiting in line to board: between 29 and 150
- Riders are let on in groups of 5, 2 riders do not get on
- Riders are let on in groups of 6, all riders get on

To find:
The sum of the greatest possible number of people in the line and the least possible number of people in the line.

Solution:
Let's first consider the scenario where riders are let on in groups of 5. In this case, 2 riders do not get on the roller coaster. We need to find the greatest possible number of people in the line.

Since 2 riders do not get on, the number of people waiting in line must be a multiple of 5 plus 2. The greatest multiple of 5 less than or equal to 150 is 145. Therefore, the greatest possible number of people in the line is 145 + 2 = 147.

Now let's consider the scenario where riders are let on in groups of 6. In this case, all riders get on the roller coaster. We need to find the least possible number of people in the line.

Since all riders get on, the number of people waiting in line must be a multiple of 6. The least multiple of 6 greater than or equal to 29 is 30. Therefore, the least possible number of people in the line is 30.

Finally, we need to find the sum of the greatest possible number of people in the line (147) and the least possible number of people in the line (30).

Sum = 147 + 30 = 177

Therefore, the correct answer is option (C) 174.
Free Test
FREE
Start Free Test
Start Free Test
Community Answer
A certain roller coaster ride has between 29 and 150 people waiting in...
To find the total number of riders, we can express it as either 5p + 2 or 6q, where p and q are positive integers.
By analyzing the given conditions, we observe that the first valid number of riders is 12, and the subsequent valid numbers follow a pattern of 12 + multiples of 30 (the least common multiple of 5 and 6).
Thus, the total number of riders can be represented as 30k + 12.
Considering the range of riders between 29 and 150, the valid options are 42, 72, 102, and 132.
Among the provided answer choices, the sum of the greatest possible number of people in line and the least possible number of people in line is 42 + 132, which equals 174. Therefore, option C (174) is the correct answer.
Explore Courses for GMAT exam

Similar GMAT Doubts

Directions: Read the given passage carefully and answer the question as follow.The Law of Nations is founded, I have said, on the general principles of right and justice, on the broad fundamental distinctions between right and wrong, or as Montesquieu defines it, “on the principle that nations ought in time of peace to do each as much good, and in time of war as little harm as possible.” These are the principles from which any rule must be shown to spring, before it can be said to be a rule for international guidance. But what are the principles of right and wrong? These are not left to the individual reason of the interpreter of the law for the time being, but are to be decided by the public opinion of the civilized world, as it stands at the time when the case arises.It may immediately be asked—How is that public opinion to be ascertained? The answer is—By ascertaining the differences in opinion between the present and the past. For this purpose it must be observed, that the views of a past age are easily ascertainable, in matters of law, from theoretical writings, history, and judicial decisions; and these views may be reduced to definition. Modern universal intelligence will either agree or disagree in these views. In the mass of instances it will agree, as progress on such points is at all times slow; and not only will the points of disagreement be few, but they will be salient, striking, and generally of popular notoriety. Present, universal, or international opinion, has therefore two portions. 1. That in which it accords with the views of a past generation, which has become historical. 2. That in which it differs from or contradicts those views.Q.Based on the information in the passage, in which of the following situations would it become difficult to ascertain public opinion?

A team of researchers has been able to successfully study the highly complex molecular structure of mitoribosomes, which are the ribosomes of mitochondria. Ribosomes are found in the cells of all living organisms, and they serve as a primary location for biological protein synthesis, but certain organisms such as fungi, plants, animals, and humans contain much more complex ribosomes than bacteria do. In organisms with complex cells, ribosomes can also be divided into two types: those in the cytosol -- which comprises the majority of the cell -- and those found in the mitochondria or power houses of cells. Mitochondria are found only in eukaryotes. Every ribosome consists of two subunits. The smaller subunit uses transfer ribonucleic acids to decode the genetic code, which is stored in the DNA, it receives in the form of messenger ribonucleic acids, while the larger subunit joins the amino acids delivered by the transfer ribonucleic acids together like a string of pearls.Since they are found only in small amounts and are difficult to isolate, mitochondrial ribosomes or mitoribosomes are particularly difficult to study. But because of the recent technical advances in cryo-electron microscopy and the development of direct electron detection cameras that can correct for specimen motion during the exposure, it recently became possible to capture images of biomolecules at a resolution high enough to capture the details, especially those of the peptidyl transferase centre (PTC).This research is of special importance to producing the right kind of antibiotics for humans. PTC is where the amino acid building blocks are combined, leading to protein synthesis. As per the researchers, this process of synthesizing proteins is medically relevant as the tunnel through which the proteins pass, after being synthesized, is a target for specific antibiotics. The antibiotic blocks the tunnel, preventing the proteins that have just been synthesized from leaving the tunnel. However, for an antibiotic to be used in humans, it must not attack human ribosomes and should inhibit protein synthesis only in the ribosomes of bacteria. The problem arises since mitochondrial ribosomes resemble those of bacteria, which is why certain antibiotics also interfere with mitoribosomes, possibly leading to serious side effects. The findings of the research will make it possible in the future to design antibiotics that inhibit only bacterial and not mitochondrial ribosomes, the one basic requirement for using them in clinical applications.Which of the following can be inferred from the passage?

A team of researchers has been able to successfully study the highly complex molecular structure of mitoribosomes, which are the ribosomes of mitochondria. Ribosomes are found in the cells of all living organisms, and they serve as a primary location for biological protein synthesis, but certain organisms such as fungi, plants, animals, and humans contain much more complex ribosomes than bacteria do. In organisms with complex cells, ribosomes can also be divided into two types: those in the cytosol -- which comprises the majority of the cell -- and those found in the mitochondria or power houses of cells. Mitochondria are found only in eukaryotes. Every ribosome consists of two subunits. The smaller subunit uses transfer ribonucleic acids to decode the genetic code, which is stored in the DNA, it receives in the form of messenger ribonucleic acids, while the larger subunit joins the amino acids delivered by the transfer ribonucleic acids together like a string of pearls.Since they are found only in small amounts and are difficult to isolate, mitochondrial ribosomes or mitoribosomes are particularly difficult to study. But because of the recent technical advances in cryo-electron microscopy and the development of direct electron detection cameras that can correct for specimen motion during the exposure, it recently became possible to capture images of biomolecules at a resolution high enough to capture the details, especially those of the peptidyl transferase centre (PTC).This research is of special importance to producing the right kind of antibiotics for humans. PTC is where the amino acid building blocks are combined, leading to protein synthesis. As per the researchers, this process of synthesizing proteins is medically relevant as the tunnel through which the proteins pass, after being synthesized, is a target for specific antibiotics. The antibiotic blocks the tunnel, preventing the proteins that have just been synthesized from leaving the tunnel. However, for an antibiotic to be used in humans, it must not attack human ribosomes and should inhibit protein synthesis only in the ribosomes of bacteria. The problem arises since mitochondrial ribosomes resemble those of bacteria, which is why certain antibiotics also interfere with mitoribosomes, possibly leading to serious side effects. The findings of the research will make it possible in the future to design antibiotics that inhibit only bacterial and not mitochondrial ribosomes, the one basic requirement for using them in clinical applications.The author is primarily concerned with

A team of researchers has been able to successfully study the highly complex molecular structure of mitoribosomes, which are the ribosomes of mitochondria. Ribosomes are found in the cells of all living organisms, and they serve as a primary location for biological protein synthesis, but certain organisms such as fungi, plants, animals, and humans contain much more complex ribosomes than bacteria do. In organisms with complex cells, ribosomes can also be divided into two types: those in the cytosol -- which comprises the majority of the cell -- and those found in the mitochondria or power houses of cells. Mitochondria are found only in eukaryotes. Every ribosome consists of two subunits. The smaller subunit uses transfer ribonucleic acids to decode the genetic code, which is stored in the DNA, it receives in the form of messenger ribonucleic acids, while the larger subunit joins the amino acids delivered by the transfer ribonucleic acids together like a string of pearls.Since they are found only in small amounts and are difficult to isolate, mitochondrial ribosomes or mitoribosomes are particularly difficult to study. But because of the recent technical advances in cryo-electron microscopy and the development of direct electron detection cameras that can correct for specimen motion during the exposure, it recently became possible to capture images of biomolecules at a resolution high enough to capture the details, especially those of the peptidyl transferase centre (PTC).This research is of special importance to producing the right kind of antibiotics for humans. PTC is where the amino acid building blocks are combined, leading to protein synthesis. As per the researchers, this process of synthesizing proteins is medically relevant as the tunnel through which the proteins pass, after being synthesized, is a target for specific antibiotics. The antibiotic blocks the tunnel, preventing the proteins that have just been synthesized from leaving the tunnel. However, for an antibiotic to be used in humans, it must not attack human ribosomes and should inhibit protein synthesis only in the ribosomes of bacteria. The problem arises since mitochondrial ribosomes resemble those of bacteria, which is why certain antibiotics also interfere with mitoribosomes, possibly leading to serious side effects. The findings of the research will make it possible in the future to design antibiotics that inhibit only bacterial and not mitochondrial ribosomes, the one basic requirement for using them in clinical applications.Which of the following is mentioned in the passage?

Top Courses for GMATView all

Top Courses for GMAT

A certain roller coaster ride has between 29 and 150 people waiting in line to board. If riders are let on only in groups of 5 there will be 2 riders that do not get on. If the riders are let on only in groups of 6 all riders will be able to get on. Which of the following is the sum of the greatest possible number of people in the line and the least possible number of people in the line?a)269b)184c)174d)169e)142Correct answer is option 'C'. Can you explain this answer?
Question Description
A certain roller coaster ride has between 29 and 150 people waiting in line to board. If riders are let on only in groups of 5 there will be 2 riders that do not get on. If the riders are let on only in groups of 6 all riders will be able to get on. Which of the following is the sum of the greatest possible number of people in the line and the least possible number of people in the line?a)269b)184c)174d)169e)142Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A certain roller coaster ride has between 29 and 150 people waiting in line to board. If riders are let on only in groups of 5 there will be 2 riders that do not get on. If the riders are let on only in groups of 6 all riders will be able to get on. Which of the following is the sum of the greatest possible number of people in the line and the least possible number of people in the line?a)269b)184c)174d)169e)142Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain roller coaster ride has between 29 and 150 people waiting in line to board. If riders are let on only in groups of 5 there will be 2 riders that do not get on. If the riders are let on only in groups of 6 all riders will be able to get on. Which of the following is the sum of the greatest possible number of people in the line and the least possible number of people in the line?a)269b)184c)174d)169e)142Correct answer is option 'C'. Can you explain this answer?.
Solutions for A certain roller coaster ride has between 29 and 150 people waiting in line to board. If riders are let on only in groups of 5 there will be 2 riders that do not get on. If the riders are let on only in groups of 6 all riders will be able to get on. Which of the following is the sum of the greatest possible number of people in the line and the least possible number of people in the line?a)269b)184c)174d)169e)142Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT. Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.
Here you can find the meaning of A certain roller coaster ride has between 29 and 150 people waiting in line to board. If riders are let on only in groups of 5 there will be 2 riders that do not get on. If the riders are let on only in groups of 6 all riders will be able to get on. Which of the following is the sum of the greatest possible number of people in the line and the least possible number of people in the line?a)269b)184c)174d)169e)142Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A certain roller coaster ride has between 29 and 150 people waiting in line to board. If riders are let on only in groups of 5 there will be 2 riders that do not get on. If the riders are let on only in groups of 6 all riders will be able to get on. Which of the following is the sum of the greatest possible number of people in the line and the least possible number of people in the line?a)269b)184c)174d)169e)142Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A certain roller coaster ride has between 29 and 150 people waiting in line to board. If riders are let on only in groups of 5 there will be 2 riders that do not get on. If the riders are let on only in groups of 6 all riders will be able to get on. Which of the following is the sum of the greatest possible number of people in the line and the least possible number of people in the line?a)269b)184c)174d)169e)142Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A certain roller coaster ride has between 29 and 150 people waiting in line to board. If riders are let on only in groups of 5 there will be 2 riders that do not get on. If the riders are let on only in groups of 6 all riders will be able to get on. Which of the following is the sum of the greatest possible number of people in the line and the least possible number of people in the line?a)269b)184c)174d)169e)142Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A certain roller coaster ride has between 29 and 150 people waiting in line to board. If riders are let on only in groups of 5 there will be 2 riders that do not get on. If the riders are let on only in groups of 6 all riders will be able to get on. Which of the following is the sum of the greatest possible number of people in the line and the least possible number of people in the line?a)269b)184c)174d)169e)142Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice GMAT tests.
Explore Courses for GMAT exam

Top Courses for GMAT

Explore Courses
SaveJoin the Discussion on the App for FREE
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Get App
© EduRev
Education Revolution
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup