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A rectangular sheet of paper of length L units and breadth W

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A rectangular sheet of paper of length L units and breadth W  [#permalink]

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28 Oct 2017, 13:41
2
00:00

Difficulty:

85% (hard)

Question Stats:

26% (00:47) correct 74% (01:22) wrong based on 23 sessions

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A rectangular sheet of paper of length L units and breadth W units is to be cut into the least possible number of equal squares of side S units such that the sheet is totally used up. If L, W and S are integers and L and W are both greater than 1, what is the value of S?
(1) The product of L and W is 63 square units
(2) The side of the smallest square that can be made by placing side-by-side a number of sheets of length L units and breadth W units is 63 units.

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Joined: 02 Aug 2009
Posts: 7425
Re: A rectangular sheet of paper of length L units and breadth W  [#permalink]

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28 Oct 2017, 18:46
1
ManishKM1 wrote:
A rectangular sheet of paper of length L units and breadth W units is to be cut into the least possible number of equal squares of side S units such that the sheet is totally used up. If L, W and S are integers and L and W are both greater than 1, what is the value of S?
(1) The product of L and W is 63 square units
(2) The side of the smallest square that can be made by placing side-by-side a number of sheets of length L units and breadth W units is 63 units.

hi...

L and W are > 1

lets see the statements..

(1) The product of L and W is 63 square units
As L,W and S are integers......
63=9*7 or 21*3 but 63*1 is out as L and W >1
if sheet is 9*7, EQUAL square can ONLY be of side 1*1
If sheet is 21*3, the sides will be 3*3

Insuff

(2) The side of the smallest square that can be made by placing side-by-side a number of sheets of length L units and breadth W units is 63 units.
it is possible that there is ONLY 1 sheet of size 63*63
or size 7*9, where in width 7, 9 sheets are placed
and 7 sheets in length wise are placed to give 63 units on each side

Insuff

combined..
Common element in both are 7*9 rectangle
so S will be 1
suff

C
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Re: A rectangular sheet of paper of length L units and breadth W  [#permalink]

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28 Oct 2017, 20:02
1

From 1. possible numbers are 9*7 or 21*3 so two answers insufficient.
From 2. Possible numbers are 9*7 or 63*1 so two answer insufficient.
Both 1 and 2 answer should be 9*7

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Re: A rectangular sheet of paper of length L units and breadth W  [#permalink]

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12 Jan 2019, 10:52
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Re: A rectangular sheet of paper of length L units and breadth W   [#permalink] 12 Jan 2019, 10:52
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