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M21-15

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M21-15 [#permalink]

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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
[Reveal] Spoiler: OA

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Re M21-15 [#permalink]

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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.


Answer: B
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Re M21-15 [#permalink]

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New post 06 Sep 2015, 09:54
I think this is a high-quality question and I agree with explanation.
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Re: M21-15 [#permalink]

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New post 14 Sep 2015, 23:03
amazing question...
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Re: M21-15 [#permalink]

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New post 08 Sep 2016, 21:38
Really well crafted question.
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Re: M21-15 [#permalink]

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New post 17 Sep 2016, 03:45
Amazing short-cut explanation. Thanks Bunuel
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Re: M21-15 [#permalink]

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New post 12 May 2017, 05:39
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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Re: M21-15 [#permalink]

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New post 12 May 2017, 05:59
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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M21-15 [#permalink]

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New post 12 May 2017, 10:02
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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Re: M21-15 [#permalink]

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New post 12 May 2017, 10:05
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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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M21-15 [#permalink]

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New post 12 May 2017, 10:12
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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M21-15   [#permalink] 12 May 2017, 10:12
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