A certain roller coaster ride has fewer than 110 people waiting in lin

Question

A certain roller coaster ride has fewer than 110 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 riders are let on only in groups of 6 all riders will be able to get on the roller coaster. Which of the following could be the number of people in the line?

A. 7
B. 22
C. 52
D. 67
E. 72

A. 7
B. 22
C. 52
D. 67
E. 72

rudra316 · Answer

The number should be divisible by 6 and leave a remainder 2 when divided by 2
The number is of the form 6N or 5M+2

Only 72 satisfies both the conditions. 
Option E

manhasnoname · Answer

Total number of riders = 5p + 2 or 6q.

The first number that fits in is 12. Numbers following will be 12 + multiple of 30 ( LCM of 5 and 6).

Therefore, the total number of riders will be 30k+12.

12, 42, 72, 102 are the only possibilities as the number of riders is fewer than 110.

Among the given options 72 is the answer.

sobby · Answer

solving the question with help of options will make it easy.
for any option to be correct , it should be divisible by 6
7 is not divisible by 6.--out
22 is not divisible by 6 -out
52 is not divisible by 6 -out

67 is not divisible by 6-out
only left solution is 72.
hence e.

wayne10rooney · Answer

riders are let on only in groups of 6 all riders will be able to get on the roller coaster. Hence the total number of riders is multiple of 6.
Only option multiple of 6 is 72.

rishit1080 · Answer

From the question we can set x to the number of people in line. We know from the first sentence x < 110. We know from the second sentence that x/5 gives a remainder of 2. We know from the third sentence that x/6 give a remainder of 0.

We should plug in since there is a variable and multiple equations in the problem. 72 is the only answer choice that yields a remainder of 2 when divided by 5 and yields a remainder of 0 when divided by 6.

E

JeffTargetTestPrep · Answer

We are given that a certain roller coaster ride has fewer than 110 people waiting in line to board. If riders are let on only in groups of 5, there will be 2 riders who do not get on. If riders are let on only in groups of 6, all riders will be able to board the roller coaster. Thus, we need to find a number that when divided by 5 has a remainder of 2 and when divided by 6 has no remainder.

By quickly scanning our answer choices we see that answer choice E, 72, is the only answer choice that is a multiple of 6. (Notice that when 72 is divided by 5, the remainder is indeed 2.)

Answer: E

bumpbot · Answer

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A certain roller coaster ride has fewer than 110 people waiting in lin

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A certain roller coaster ride has fewer than 110 people waiting in lin

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