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# A project requires a rectangular sheet of cardboard satisfying the fol

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Manager
Joined: 01 Sep 2016
Posts: 208

Kudos [?]: 184 [0], given: 33

GMAT 1: 690 Q49 V35
A project requires a rectangular sheet of cardboard satisfying the fol [#permalink]

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19 Sep 2017, 12:50
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Difficulty:

95% (hard)

Question Stats:

30% (01:34) correct 70% (01:50) wrong based on 47 sessions

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A project requires a rectangular sheet of cardboard satisfying the following requirement: When the sheet is cut into identical rectangular halves, each of the resulting rectangles has the same ratio of length to width as the original sheet. Which of the following sheets comes closest to satisfying the requirement?

(A) A sheet measuring 7 inches by 10 inches
(B) A sheet measuring 8 inches by 14 inches
(C) A sheet measuring 10 inches by 13 inches
(D) A sheet measuring 3 feet by 5 feet
(E) A sheet measuring 5 feet by 8 feet
[Reveal] Spoiler: OA

_________________

we shall fight on the beaches,
we shall fight on the landing grounds,
we shall fight in the fields and in the streets,
we shall fight in the hills;
we shall never surrender!

Kudos [?]: 184 [0], given: 33

Manager
Joined: 01 Sep 2016
Posts: 208

Kudos [?]: 184 [0], given: 33

GMAT 1: 690 Q49 V35
A project requires a rectangular sheet of cardboard satisfying the fol [#permalink]

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19 Sep 2017, 13:02
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The first and the foremost thing to realize is that one side of the figure would be cut by half. Now when you go through the options, please make sure on thing. There is no need to half the smaller side in the option, as it would be the total waste of time. For example, if you have a rectangular figure with a ratio of 1:4, then halfing the smaller side would bring the ration to .5 to 4, which means that the ratio will decrease further rather than remaining the same.

So now let's go to the option choices:
a) Sheet measuring 7*10 : Lets half the larger side"10", we get 7:5, now is 5/7 equal to 7/10. I would say pretty close- lets keep.
b) A sheet measuring 8 inches by 14 inches: Half the larger side we get, 7/8 vs 8/14: No chance of being close- eliminate
c) A sheet measuring 10 inches by 13 inches: Half the larger side we get, 6.5/10 vs 10/13: Not close- eliminate
d) A sheet measuring 3 feet by 5 feet: 2.5/3 vs 3/5 : No chance
e) A sheet measuring 5 feet by 8 feet: 4/5 vs 5/8: Not close

_________________

we shall fight on the beaches,
we shall fight on the landing grounds,
we shall fight in the fields and in the streets,
we shall fight in the hills;
we shall never surrender!

Kudos [?]: 184 [0], given: 33

Manager
Joined: 01 Sep 2016
Posts: 208

Kudos [?]: 184 [0], given: 33

GMAT 1: 690 Q49 V35
Re: A project requires a rectangular sheet of cardboard satisfying the fol [#permalink]

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19 Sep 2017, 13:09
Algebraic Solution
Say the original sheet measures L by W, with L > W, so that the cut yields two rectangular halves measuring L/2 by W each.

Per the project requirements, the ratio of these new dimensions must be the same as the ratio of L to W.  Consider both possible ways in which the ratio might be set up. If the ratio of original to new is set up as L : W = L/2 : W, then it reduces to 1 = 1/2, an impossible condition. (Or, if you prefer to reason theoretically, it is impossible to reduce L by half but leave W unchanged and have the ratio stay the same.)

Therefore, the width (W) of the original rectangle, must become the longer side for the smaller rectangles. The ratio must be set up as L : W = W : L/2.

Set up the ratio:
$$L/W = 2L/W$$
L/W= 1.4 ( $$Root 2 = 1.4$$)

The condition thus requires original dimensions that come as close as possible to satisfying , or, equivalently, .

The one closest to 1.4 is the correct answer.

(A) 10/7 = approximately 1.4
(B) 14/8 = 7/4 = 1.75
(C) 13/10 = 1.3
(D) 5/3 =  = approximately 1.7
(E) 8/5 = = 1.6
Choice A comes closest to the requirement. The correct answer is (A).
_________________

we shall fight on the beaches,
we shall fight on the landing grounds,
we shall fight in the fields and in the streets,
we shall fight in the hills;
we shall never surrender!

Kudos [?]: 184 [0], given: 33

Re: A project requires a rectangular sheet of cardboard satisfying the fol   [#permalink] 19 Sep 2017, 13:09
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