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# What is the perimeter of a recangle having an area of 105

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Senior Manager
Joined: 29 Jun 2005
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What is the perimeter of a recangle having an area of 105  [#permalink]  29 Jul 2005, 02:17
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What is the perimeter of a recangle having an area of 105

1. The length is greater than twice the width
2. The length and width of the rectangle are each integers greater than 5
SVP
Joined: 14 Dec 2004
Posts: 1707
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Kudos [?]: 52 [0], given: 0

ANS = 44.

My workout:
--------------
L > 5, W > 5 (also, both integrers)
&
L > 2w

For L*W = 105, L has to be less than 10, since 10*20 itself is 200.
L=6 ...can't be (105/6 is not an integer)
L=7 ...YES... (105/7 = 15) also, 15 meets L > 2w. (cross check...L=8, L=9 can't be)

So, L = 7 & w = 15.
Perimeter = 2*(7+15) = 44.

Is this correct?
Senior Manager
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This DS question.
Senior Manager
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Hi Dilshod,
It is pretty clear it is DS question, so no problem.

My answer is B, because according to condition 1, l > 2w let us say

l = 2w + x (wherw x is always positive and greater than 0)

perimeter is 2(3w + x) and this is true when the w, l values are 3, 35 and 5, 21 or 7,15

From condition 2, the only factors of 105 that satisfies the condition is 15*7

_________________

Fear Mediocrity, Respect Ignorance

Senior Manager
Joined: 29 Jun 2005
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Kudos [?]: 15 [0], given: 0

The OA is B.
You are right.
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