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18 Jun 2022, 20:45
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
28% (02:49) correct
72%
(02:19)
wrong
based on 32
sessions
History
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Time
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Not Attempted Yet
A long thin strip of paper is 256 units in length, 1 unit in width, and is divided into 256 unit squares. The strip of paper is kept in such a manner that the longer side is in the left-right orientation. The squares are numbered 1 through 256 starting from the left most square. The paper is folded into half repeatedly. For the first fold, the right end of the paper is folded over to coincide with and lie on top of the left end. Then the paper is cut at the fold. There are now two strips of paper 1 × 128 in dimensions. Next, the right end of these two strips together is folded over to coincide with and lie on top of the left end, resulting in 4 strips of paper 1 × 64 in dimention. The strip is again cut at the folds. This process is repeated till it becomes a stack of 256 unit squares. What is the number written on the square that is at the 128th position from the bottom?
(A) 3
(B) 4
(C) 128
(D) 129
(E) None of these
Are You Up For the Challenge: 700 Level Questions
(A) 3
(B) 4
(C) 128
(D) 129
(E) None of these
Are You Up For the Challenge: 700 Level Questions
21 Jun 2022, 04:45
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As stated in the question, every time the paper is folded/cut the number of pieces doubles.
So the number of pieces at the left end proceeds as follows:
1 2 4 8 16 32 64 128 256
After 7 folds and cuts there will be 128 pieces of paper each with two numbers, one stacked on the leftmost square and the other immediately to the right.
The topmost number on the left is the one in the 128th position from the bottom after the 8th and final fold/cut.
This number was the bottommost number on the right after the 6th fold/cut.
As the folds are made, the rightmost number on the bottom strip of paper reduces backwards from 256 as the numbers to its right are brought to the top due to the folding, as follows
256 128 64 32 16 8 4 2 1
After 6 folds, the rightmost number on the bottom will be 4, which will be the number 128th from the bottom after all numbers are stacked to the left.
Posted from my mobile device
So the number of pieces at the left end proceeds as follows:
1 2 4 8 16 32 64 128 256
After 7 folds and cuts there will be 128 pieces of paper each with two numbers, one stacked on the leftmost square and the other immediately to the right.
The topmost number on the left is the one in the 128th position from the bottom after the 8th and final fold/cut.
This number was the bottommost number on the right after the 6th fold/cut.
As the folds are made, the rightmost number on the bottom strip of paper reduces backwards from 256 as the numbers to its right are brought to the top due to the folding, as follows
256 128 64 32 16 8 4 2 1
After 6 folds, the rightmost number on the bottom will be 4, which will be the number 128th from the bottom after all numbers are stacked to the left.
Posted from my mobile device
