Problem Solving

In a set of five books, no two of which have the same number of pages, the longest book has 150 pages and the shortest book has 130 pages. If x pages is the average(arithmetic mean) of the number of pages in the five-book set, which of the following best indicates all possible values of x and only possible values of x?
(A) 130 < x < 150
(B) 131 < x < 149
(C) 133 < x < 145
(D) 134 < x < 145
(E) 135 < x < 145

sanju09 wrote:In a set of five books, no two of which have the same number of pages, the longest book has 150 pages and the shortest book has 130 pages. If x pages is the average(arithmetic mean) of the number of pages in the five-book set, which of the following best indicates all possible values of x and only possible values of x?
(A) 130 < x < 150
(B) 131 < x < 149
(C) 133 < x < 145
(D) 134 < x < 145
(E) 135 < x < 145

As we want to find a range for the average. Let's consider a scenario were the other three books have the next lowest number of pages. i.e 131

x= (130+131+131+131+180)/5 = 134
Since only one answer starts with 134, we can stop right here. D is the answer

Least number of pages - 130
Greatest number of pages - 150

Least possible pages of other books - 131, 132 ,133.

Average = 130+131+132+133+150/5 = 676/5= 135.2

So x > 135

similarly Greatest possible pages = 130+147+148+149+150 = 724
Average = 144.8

x < 145
So 135< x< 145 . Option E

sl750 wrote:

sanju09 wrote:In a set of five books, no two of which have the same number of pages, the longest book has 150 pages and the shortest book has 130 pages. If x pages is the average(arithmetic mean) of the number of pages in the five-book set, which of the following best indicates all possible values of x and only possible values of x?
(A) 130 < x < 150
(B) 131 < x < 149
(C) 133 < x < 145
(D) 134 < x < 145
(E) 135 < x < 145

As we want to find a range for the average. Let's consider a scenario were the other three books have the next lowest number of pages. i.e 131

x= (130+131+131+131+180)/5 = 134
Since only one answer starts with 134, we can stop right here. D is the answer

no two books have the same pages.

so minimum value of x is X=(130+131+132+133+150)/5=676/5=135.2

Can this 0.2 make a difference .
yes , indeed I go with E.

baladon99 wrote:Least number of pages - 130
Greatest number of pages - 150

Least possible pages of other books - 131, 132 ,133.

Average = 130+131+132+133+150/5 = 676/5= 135.2

So x > 135

similarly Greatest possible pages = 130+147+148+149+150 = 724
Average = 144.8

x < 145
So 135< x< 145 . Option E

Excellent