A certain roller coaster ride has more than 29 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 the roller coaster. If less than 112 people are in the line, which of the following is the largest possible value of number of people in the line?a)112b)108c)106d)102e)96Correct answer is option 'D'. Can you explain this answer?

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A certain roller coaster ride has more than 29 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 the roller coaster. If less than 112 people are in the line, which of the following is the largest possible value of number of people in the line?

a)
112
b)
108
c)
106
d)
102
e)
96

Correct answer is option 'D'. Can you explain this answer?

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A certain roller coaster ride has more than 29 people waiting in line ...

Let's analyze the given information:

If riders are let on only in groups of 5, there will be 2 riders that do not get on. This means the total number of riders is not divisible by 5.

If riders are let on only in groups of 6, all riders will be able to get on. This means the total number of riders is divisible by 6.

To find the largest possible value of the number of people in line, we need to find the least common multiple (LCM) of 5 and 6.

Factorizing 5: 5 = 5^1 Factorizing 6: 6 = 2 * 3^1

Taking the highest power of each prime factor: LCM(5, 6) = 2 * 3 * 5^1 = 30

Since the total number of riders must be divisible by 6, and less than 112 people are in the line, the largest possible value of the number of people in line is a multiple of 30 that is less than 112.

The largest possible value of the number of people in line is 102 (30 × 3 + 12).

Therefore, the correct answer is D.

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A certain roller coaster ride has more than 29 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 the roller coaster. If less than 112 people are in the line, which of the following is the largest possible value of number of people in the line?a)112b)108c)106d)102e)96Correct answer is option 'D'. 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 more than 29 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 the roller coaster. If less than 112 people are in the line, which of the following is the largest possible value of number of people in the line?a)112b)108c)106d)102e)96Correct answer is option 'D'. 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 more than 29 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 the roller coaster. If less than 112 people are in the line, which of the following is the largest possible value of number of people in the line?a)112b)108c)106d)102e)96Correct answer is option 'D'. Can you explain this answer?.

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