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A certain roller coaster ride has between 29 and 150 people waiting in

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Bunuel
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A certain roller coaster ride has between 29 and 150 people waiting in [#permalink] New post   06 Nov 2016, 09:15
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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
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C
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Re: A certain roller coaster ride has between 29 and 150 people waiting in [#permalink] New post   07 Nov 2016, 07:49
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Bunuel wrote:
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


Answer: in One line by Option Elimination

A certain roller coaster ride has between 29 and 150 people

If riders are let on only in groups of 5 there will be 2 riders that do not get on i.e. Number of the form 5a+2

If the riders are let on only in groups of 6 all riders will be able to get on i.e. a multiple of 6

Greatest + Least such number = a multiple of 6+a multiple of 6 = a multiple of 6
Option A, B, D, E ruled out

Answer: Option C
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Re: A certain roller coaster ride has between 29 and 150 people waiting in [#permalink] New post   06 Nov 2016, 19:49
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Bunuel wrote:
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


Let x be the number of people

x=5m+2

x=6n

x=30p+12

Least = 30+12= 42

Highest = 30*4+12 = 132

Total = 174

C


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Re: A certain roller coaster ride has between 29 and 150 people waiting in [#permalink] New post   07 Nov 2016, 07:16
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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.

42, 72, 102, 132 are the only possibilities as the number of riders should be between 29 and 150.

Among the given options (42+132 =174) is the answer.
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Re: A certain roller coaster ride has between 29 and 150 people waiting in [#permalink] New post   07 Nov 2016, 07:47
We are looking for a number which is divisible by 6 and leaves 2 as reminder when divided by 5. For sure, this number is even (as divisible by 6). So odd options are ruled out. Also minimum and max number will not cross 200+ so even 269 (option 1 is ruled out)
Now only 2 options are left.
First number which statisfy the condition is 12. Next number will be 12 + (LCM of 5,6) ie 12+ 30 = 42. So min number is 42. other numbers are 12+60 ie 72, 12+90 ie 102, 12+120 ie 132. So max number is 132.
42+ 132 is 174 ie option C
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Re: A certain roller coaster ride has between 29 and 150 people waiting in [#permalink] New post   07 Jun 2022, 01:56
If riders are let only in groups of 5, and there are 2 riders left,
Then total people waiting = 5x+2, where x can be any positive integer, and 29 <= 5x+2 <= 150.

Also, groups of 6 will completely exhaust the list.
Thus, 5x+2 is divisible by 6.

The highest value of x, such that 5x+2 <= 150 and divisible by 6 is 22.
Thus, the total number of people waiting in this case = 132.

The lowest value of x, such that 5x+2 <= 29 and divisible by 6 is 8.
Thus, the total number of people waiting, in this case, is 42.

So, the sum of least and most possible number of people = 132 + 42 = 174.

Thus, the correct option is C.
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Re: A certain roller coaster ride has between 29 and 150 people waiting in [#permalink]
07 Jun 2022, 01:56
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