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Viggo has 25 hardcover books that he is arranging upright on the top

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Bunuel
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Viggo has 25 hardcover books that he is arranging upright on the top [#permalink] New post   30 Oct 2019, 23:11
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Viggo has 25 hardcover books that he is arranging upright on the top shelf of a bookcase. Will the 25 books fit on the top shelf?

(1) The top shelf of Viggo’s bookcase has a length of 36 inches.
(2) The average (arithmetic mean) thickness of the 25 books is at most 3/2 inches.
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Viggo has 25 hardcover books that he is arranging upright on the top [#permalink] New post   31 Oct 2019, 00:58
Bunuel wrote:
Viggo has 25 hardcover books that he is arranging upright on the top shelf of a bookcase. Will the 25 books fit on the top shelf?

(1) The top shelf of Viggo’s bookcase has a length of 36 inches.
(2) The average (arithmetic mean) thickness of the 25 books is at most 3/2 inches.


total book thickness not know
#1 insufficient
#2
at most total books thickness = 37.5
from 1 &2
insufficient as answer is Yes/ NO
IMO E
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Re: Viggo has 25 hardcover books that he is arranging upright on the top [#permalink] New post   02 Nov 2019, 20:48
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Archit3110 wrote:
Bunuel wrote:
Viggo has 25 hardcover books that he is arranging upright on the top shelf of a bookcase. Will the 25 books fit on the top shelf?

(1) The top shelf of Viggo’s bookcase has a length of 36 inches.
(2) The average (arithmetic mean) thickness of the 25 books is at most 3/2 inches.


total book thickness not know
#1 insufficient
#2
at most total books thickness = 37.5
from 1 &2
insufficient as answer is Yes/ NO
IMO E





Could you please elaborate on what you mean when you say "at most total books thickness = 37.5"????
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Re: Viggo has 25 hardcover books that he is arranging upright on the top [#permalink] New post   02 Nov 2019, 21:00
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Viggo has 25 hardcover books that he is arranging upright on the top shelf of a bookcase. Will the 25 books fit on the top shelf?

Will depend on the SUM of thicknesses of all 25 books, if \(\leq{}\) thickness of shelf.. yes, and if >thickness of shelf..No

(1) The top shelf of Viggo’s bookcase has a length of 36 inches.
SO if the SUM of thicknesses of all 25 books \(\leq{36}\) thickness of shelf.. yes, and if >36..No
But we do not know the thickness of books

(2) The average (arithmetic mean) thickness of the 25 books is at most 3/2 inches.
AT MOST 3/2 inches ..\(\leq{\frac{3}{2}}\)..
We can say the SUM of thickness \(\leq\) 25*average thickness = 25*3/2=37.5
Nothing about thickness of shelf

Combined..
SUM\(\leq\)37.5If between 36 and 37.5...NO, otherwise yes
Insuff

E
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Re: Viggo has 25 hardcover books that he is arranging upright on the top [#permalink] New post   03 Nov 2019, 04:59
Jashan25
at most means <= to the value ; which is 37.5 inches in this case .. so its yes and no that books will fit on shelf..


Jashan25 wrote:
Archit3110 wrote:
Bunuel wrote:
Viggo has 25 hardcover books that he is arranging upright on the top shelf of a bookcase. Will the 25 books fit on the top shelf?

(1) The top shelf of Viggo’s bookcase has a length of 36 inches.
(2) The average (arithmetic mean) thickness of the 25 books is at most 3/2 inches.


total book thickness not know
#1 insufficient
#2
at most total books thickness = 37.5
from 1 &2
insufficient as answer is Yes/ NO
IMO E





Could you please elaborate on what you mean when you say "at most total books thickness = 37.5"????
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Re: Viggo has 25 hardcover books that he is arranging upright on the top [#permalink] New post   03 Nov 2019, 05:22
"At most average" means maximum average. Means there might be lowest average.
In given problem statement 2, we can have two extreme averages.

Jashan25 wrote:
Archit3110 wrote:
Bunuel wrote:
Viggo has 25 hardcover books that he is arranging upright on the top shelf of a bookcase. Will the 25 books fit on the top shelf?

(1) The top shelf of Viggo’s bookcase has a length of 36 inches.
(2) The average (arithmetic mean) thickness of the 25 books is at most 3/2 inches.


total book thickness not know
#1 insufficient
#2
at most total books thickness = 37.5
from 1 &2
insufficient as answer is Yes/ NO
IMO E





Could you please elaborate on what you mean when you say "at most total books thickness = 37.5"????
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Re: Viggo has 25 hardcover books that he is arranging upright on the top [#permalink] New post   12 Jan 2021, 04:44
I'm not 100% sure why E is the right answer. I understand the previous comments regarding the fact that the books will not fit on the shelf with the two statements. However the answer E states "Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked." , and IMO with both statements we can answer the question asked, even though the answer is no.

Can someone please explain why when choosing E in these types of questions we mean that the answer is no? Instead of choosing the answer C, in which we are saying that we have sufficient information to answer the questions, regardless of whether the answer is a yes or no.
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Viggo has 25 hardcover books that he is arranging upright on the top [#permalink] New post   15 Jan 2021, 00:21
The second statement states that the average thickness is atmost 3/2 . Which does'nt give a clear picture about the total thickness. Isn't this the reason why we chose E over C?
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Re: Viggo has 25 hardcover books that he is arranging upright on the top [#permalink] New post   16 Jan 2021, 05:55
ansana wrote:
The second statement states that the average thickness is atmost 3/2 . Which does'nt give a clear picture about the total thickness. Isn't this the reason why we chose E over C?


Yes that is correct. it says that the total thickness cannot be more than 37.5, however, we can't tell if its more than 36 or not.
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Re: Viggo has 25 hardcover books that he is arranging upright on the top [#permalink] New post   16 Jan 2021, 05:59
pmp00 wrote:
I'm not 100% sure why E is the right answer. I understand the previous comments regarding the fact that the books will not fit on the shelf with the two statements. However the answer E states "Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked." , and IMO with both statements we can answer the question asked, even though the answer is no.

Can someone please explain why when choosing E in these types of questions we mean that the answer is no? Instead of choosing the answer C, in which we are saying that we have sufficient information to answer the questions, regardless of whether the answer is a yes or no.


pmp00, Like you've correctly mentioned whether the answer is yes or no is not our concern. We just need a definite answer in such questions. However, we don't have a definite answer here. As per the 2nd statements the avg thickness is "at most" 3/2 inches. At most is key here. It means that the maximum total thickness cannot be more than 37.5, but it might very well be less than 36 or more than 36.

If thickness = 35, the answer would b yes. If the thickness, would be 36.5, the answer would be no. (Note that the both 35 and 36.5 are valid as per the statements)
Hence, the answer is E.

Hope this helps!
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Re: Viggo has 25 hardcover books that he is arranging upright on the top [#permalink]
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