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# M21-15

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 01:10
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Difficulty:

75% (hard)

Question Stats:

43% (01:17) correct 57% (01:19) wrong based on 160 sessions

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Is the perimeter of a rectangle greater than 8 inches?

(1) The diagonal of the rectangle is twice as long as its shorter side

(2) The diagonal of the rectangle is 4 inches longer than its shorter side

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Joined: 02 Sep 2009
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16 Sep 2014, 01:10
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Official Solution:

The question asks whether $$Perimeter=2(a+b) \gt 8$$, or whether $$a+b \gt 4$$, (where $$a$$ and $$b$$ are the length of the sides of the rectangle).

(1) The diagonal of the rectangle is twice as long as its shorter side. Clearly insufficient, we know the shape of the rectangle but not its size.

(2) The diagonal of the rectangle is 4 inches longer than its shorter side. This statement basically says that the length of the diagonal is greater than 4 inches: $$d \gt 4$$. Now, consider the triangle made by the diagonal and the two sides of the rectangle: since the length of any side of a triangle must be smaller than the sum of the other two sides, then we have that $$a+b \gt d$$, so $$a+b \gt d \gt 4$$. Sufficient.

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06 Sep 2015, 10:54
I think this is a high-quality question and I agree with explanation.
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15 Sep 2015, 00:03
amazing question...
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Joined: 29 Oct 2015
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GMAT 1: 690 Q44 V40

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08 Sep 2016, 22:38
Really well crafted question.
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17 Sep 2016, 04:45
Amazing short-cut explanation. Thanks Bunuel
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12 May 2017, 06:39
Bunuel wrote:
Is the perimeter of a rectangle greater than 8 inches?

(1) The diagonal of the rectangle is twice as long as its shorter side

(2) The diagonal of the rectangle is 4 inches longer than its shorter side

Can we not say from st1 that it is a 30:60:90 triangle and hence sufficient?
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Siva Rama Krishna Meka

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12 May 2017, 06:59
Sirakri wrote:
Bunuel wrote:
Is the perimeter of a rectangle greater than 8 inches?

(1) The diagonal of the rectangle is twice as long as its shorter side

(2) The diagonal of the rectangle is 4 inches longer than its shorter side

Can we not say from st1 that it is a 30:60:90 triangle and hence sufficient?

Yes, but do we know numerical value of any of the sides?
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Joined: 11 Oct 2015
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WE: General Management (Entertainment and Sports)

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12 May 2017, 11:02
Bunuel wrote:
Sirakri wrote:
Bunuel wrote:
Is the perimeter of a rectangle greater than 8 inches?

(1) The diagonal of the rectangle is twice as long as its shorter side

(2) The diagonal of the rectangle is 4 inches longer than its shorter side

Can we not say from st1 that it is a 30:60:90 triangle and hence sufficient?

Yes, but do we know numerical value of any of the sides?

But we can answer YES or No, right?

Thanks for your quick response Bunuel, you're a star
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Siva Rama Krishna Meka

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12 May 2017, 11:05
Sirakri wrote:
But we can answer YES or No, right?

Thanks for your quick response Bunuel, you're a star

No, you cannot. The question asks: is the perimeter of a rectangle greater than 8 inches? Just knowing the ratio is not giving any actual lengths, so you cannot answer the question.
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12 May 2017, 11:12
Bunuel wrote:
Sirakri wrote:
But we can answer YES or No, right?

Thanks for your quick response Bunuel, you're a star

No, you cannot. The question asks: is the perimeter of a rectangle greater than 8 inches? Just knowing the ratio is not giving any actual lengths, so you cannot answer the question.

Thanks for the clarification

Actually, am I missing something? If let's say the least possible side is 0.---------1, we can frame other sides. No? Sorry, I've some problem with the understanding.

Thanks again for your time.
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Siva Rama Krishna Meka

M21-15 &nbs [#permalink] 12 May 2017, 11:12
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