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# If AB=10, is AB the shortest side of ∆ABC?

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If AB=10, is AB the shortest side of ∆ABC?  [#permalink]

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22 Nov 2016, 04:44
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65% (hard)

Question Stats:

51% (01:39) correct 49% (01:33) wrong based on 119 sessions

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If AB=10, is AB the shortest side of ∆ABC?

(1) The perimeter of ΔABC is 31.

(2) AC=9

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Re: If AB=10, is AB the shortest side of ∆ABC?  [#permalink]

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22 Nov 2016, 06:28
AB = 10. Is AB the shortest?

St1: Perimeter = 31 --> AB + BC + AC = 31
If AB = 10, BC = 9, AC = 12 then AB is not the shortest.
If AB = 10, BC = 10, AC = 11 then AB is the shortest.
Not Sufficient

St2: AC = 9 --> AB > AC. So AB is not the shortest.
Sufficient

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If AB=10, is AB the shortest side of ∆ABC?  [#permalink]

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22 Nov 2016, 06:59
Bunuel wrote:
If AB=10, is AB the shortest side of ∆ABC?

(1) The perimeter of ΔABC is 31.

(2) AC=9

Properties of sides of triangle

The sum of any two sides o f a triangle must be greater than the third side.

If you are given two sides of a triangle, the length of the third side must lie between the difference and the sum of the two given sides.

If we analyze statement 1 , we know that sides can be (10:11, 9:12, 8:13, 7:14, 6:15 according to properties ) and from possible arrangements both sides can be 10 or other side be the shortest, not AB.
It is not enough to answer question. ( Though I don't know whether GMAT considers side shortest if there are two short sides of same length) (Help Bunuel )

If we analyze Statement 2 alone, we can say that value of third Unknown side is between 1<X<19 , so if try any possibility there is no way that AB is the shortest side.

(Though I answered C at first )

Would appreciate Kudos if this was helpful
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Re: If AB=10, is AB the shortest side of ∆ABC?  [#permalink]

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22 Nov 2016, 07:16
1

Properties of sides of triangle

The sum of any two sides o f a triangle must be greater than the third side.

If you are given two sides of a triangle, the length of the third side must lie between the difference and the sum of the two given sides.

If we analyze statement 1 , we know that sides can be (10:11, 9:12, 8:13, 7:14, 6:15 according to properties ) and from possible arrangements there is no possibility that AB is the shortest side. It can be that both sides be 10 or any other side be the shortest, not AB.
It is enough to answer question.

If we analyze Statement 2 alone, we can say that value of third Unknown side is between 1<X<19 , so we can't say for sure what is value of AB and determine is it the shortest side.

(Though I answered C at first )

Would appreciate Kudos if this was helpful

Hi,

The question asks whether side AB has the least value. If AB = BC = 10 then the other side has the value 11. The least side value for such a triangle is 10 and AB has the least value.
But if AB = 10 and AC = 9 and BC = 12 then clearly AB does not have the least value. We do not have a unique answer and hence St1 is not sufficient to answer.

If we look at St2, we are already given that some other side is lesser than AB. So, AB cannot have the least value. In this case, we have a definite "NO" answer and hence St2 alone is sufficient.

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Re: If AB=10, is AB the shortest side of ∆ABC?  [#permalink]

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24 Nov 2016, 02:47
Vyshak wrote:

Properties of sides of triangle

The sum of any two sides o f a triangle must be greater than the third side.

If you are given two sides of a triangle, the length of the third side must lie between the difference and the sum of the two given sides.

If we analyze statement 1 , we know that sides can be (10:11, 9:12, 8:13, 7:14, 6:15 according to properties ) and from possible arrangements there is no possibility that AB is the shortest side. It can be that both sides be 10 or any other side be the shortest, not AB.
It is enough to answer question.

If we analyze Statement 2 alone, we can say that value of third Unknown side is between 1<X<19 , so we can't say for sure what is value of AB and determine is it the shortest side.

(Though I answered C at first )

Would appreciate Kudos if this was helpful

Hi,

The question asks whether side AB has the least value. If AB = BC = 10 then the other side has the value 11. The least side value for such a triangle is 10 and AB has the least value.
But if AB = 10 and AC = 9 and BC = 12 then clearly AB does not have the least value. We do not have a unique answer and hence St1 is not sufficient to answer.

If we look at St2, we are already given that some other side is lesser than AB. So, AB cannot have the least value. In this case, we have a definite "NO" answer and hence St2 alone is sufficient.

Thank you Vyshak , I edited my post based on your reply. I didn't know that shortest is considered least in GMAT and did stupid mistake in 2nd statement .

Thanks

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Re: If AB=10, is AB the shortest side of ∆ABC?  [#permalink]

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27 Jun 2018, 03:12
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Re: If AB=10, is AB the shortest side of ∆ABC? &nbs [#permalink] 27 Jun 2018, 03:12
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