Will the first 10 volumes of a 20-volume encyclopedia fit

Will the first 10 volumes of a 20-volume encyclopedia fit upright in the bookrack shown above?

(1) x = 50 centimeters. Clearly insufficient.

(2) Twelve of the volumes have an average (arithmetic mean) thickness of 5 centimeters. You most certainly can not assume that thickness of each of the 20 volumes is 5 centimeters, moreover you can not even assume that thickness of each of theses 12 volumes is 5 centimeters. Yes, the total thickness of these 12 volumes is 12*5=60 centimeters, but individual thicknesses could be {1, 1, 1, ..., 1, 49} or {2, 2, 2, ..., 2, 38} ... Next, you don't know which 12 volumes have an average thickness of 5 centimeters: first 12? last 12? first 6 and last 6? So, this statement is not sufficient.

(1)+(2) It's certainly possible that all 20 volumes to have thicknesses of 5 centimeters and in this case the first 10 volumes will fit in the bookrack of 50 centimeters but it's also possible that the last 12 volumes to have an average thickness of 5 centimeters and the first 8 volumes have thicknesses of 100 meters each (why not?) and in this case the first 10 volumes will NOT fit in the bookrack of 50 centimeters. Not sufficient.

Answer: E.

Hope it's clear.
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Target question: Will the first 10 volumes of a 20-volume encyclopedia fit upright in the bookrack shown above?

Statement 1: x = 50 centimeters.
We have no idea how THICK the first 10 volumes are.
They COULD each be 1 mm thick, in which case the 10 volumes will easily fit in the 50 cm rack
Or they COULD each be 1 km thick, in which case the 10 volumes will NOT fit in the 50 cm rack
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Twelve of the volumes have an average (arithmetic mean) thickness of 5 centimeters.
We have no idea how wide the book rack is.
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
We have no info about the thickness of the 10 volumes to be placed in the rack.
Consider these two possible cases:

Case a: Each of the 12 volumes noted above in statement 2 are 5 cm thick. Two of those 5-cm-thick volumes are added to eight volumes that are each 1 mm thick. In this case, the 10 volumes will easily fit in the 50 cm rack
Case b: Each of the 12 volumes noted above in statement 2 are 5 cm thick. Two of those 5-cm-thick volumes are added to eight volumes that are each 1 km thick. In this case, the 10 volumes will NOT fit in the 50 cm rack

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
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Hello Brent,

Hope you doing great!!

I just had a doubt here.The question says

Will the first 10 volumes of a 20-volume encyclopedia fit upright in the bookrack shown above?

1.Does that mean we are only concerned about it upright (through height) in the stack and not about the base overflowing or not fitting properly across the rack base?

Length Breadth and Height..((so height being point of concern here.))

2.Query 2
What is implied meaning of thickness .Is it he height of the book standing upright.


((I came across an official question wherein a glass had to be fitted completely on the table so length breadth role was important))

The idea here is that the books are arranged like this


So, the thickness is the horizontal distance.

I hope that helps.

Cheers,
Brent
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Thanks a lot.

You got it straight what was wrong in my thinking.I didn't realise that .Thanks again

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