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Is the perimeter of triangle ABC less than 15 centimetres ?

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Is the perimeter of triangle ABC less than 15 centimetres ?  [#permalink]

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New post 20 Aug 2018, 05:28
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GMAT CLUB TESTS' FRESH QUESTION:



Is the perimeter of triangle ABC less than 15 centimetres ?

(1) The lengths of the sides of triangle ABC are consecutive even integers in centimetres
(2) The sum of the lengths of the shortest and longest sides of triangle ABC is 12 centimetres

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Re: Is the perimeter of triangle ABC less than 15 centimetres ?  [#permalink]

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New post Updated on: 20 Aug 2018, 06:00
Imo d

St1: 2 is the least possible side of a triangle ( 0 is even but side with 0 units is not possible)

2,4,6-- possible pair
But as we know sum of 2 sides should be greater than 3rd side. Difference of 2 sides should be less than 3rd side.

6-2< 4 < 6+4
4< 4 < 10.. (not possible)

Next pair will always have perimeter greater than 15

Sufficient

St2: let sides be x, y, z

X+z= 12
We can infer that y should be less than 12

1+11---> 3rd side is between 10 to 12
It cannot be greater than 11 [ greatest side]. In all cases, perimeter is >15


7+5--> 3rd side is between 2 to 12
It can be but we need > or equal to 5 [ greater than smallest side]
Permimeter will always be >15



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Originally posted by sumit411 on 20 Aug 2018, 05:51.
Last edited by sumit411 on 20 Aug 2018, 06:00, edited 1 time in total.
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Re: Is the perimeter of triangle ABC less than 15 centimetres ?  [#permalink]

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New post 20 Aug 2018, 05:54
1
Is the perimeter of triangle ABC less than 15 centimetres ?

(1) The lengths of the sides of triangle ABC are consecutive even integers in centimetres
so the sides are 2n, 2n+2, 2n+4
Minimum value of n is 1, so min sides are 2,4,6... But the largest side is EQUAL to sum of other two sides, so it will not be a triangle..
Next values - 4, 6, 8.....sum=4+6+8=18>15
Ans NO
Sufficient

(2) The sum of the lengths of the shortest and longest sides of triangle ABC is 12 centimetres
So if perimeter is LESS than 15, the third side can have a max value as just less than 3
The smallest side has to be less than this too, so sides are <3, <3, ~9
But such a triangle is not possible as sum of the smallest sides is LESS than the largest side.
So Ans NO
Sufficient

D
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: Is the perimeter of triangle ABC less than 15 centimetres ?  [#permalink]

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New post 20 Aug 2018, 05:55
sumit411 wrote:
Imo A

St1: 2 is the least possible side of a triangle ( 0 is even but side with 0 units is not possible)

2,4,6-- possible pair
But as we know sum of 2 sides should be greater than 3rd side. Difference of 2 sides should be less than 3rd side.

6-2< 4 < 6+4
4< 4 < 10.. (not possible)

Next pair will always have perimeter greater than 15

Sufficient

St2: let sides be x, y, z

X+z= 12
We can only infer that y should be less than 12

Not sufficient

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You are missing out on the rule that the sum of the smaller two sides has to be greater than the largest side, so statement II is also sufficient
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: Is the perimeter of triangle ABC less than 15 centimetres ?  [#permalink]

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New post 20 Aug 2018, 06:16
chetan2u wrote:
Is the perimeter of triangle ABC less than 15 centimetres ?

(1) The lengths of the sides of triangle ABC are consecutive even integers in centimetres
so the sides are 2n, 2n+2, 2n+4
Minimum value of n is 1, so min sides are 2,4,6... But the largest side is EQUAL to sum of other two sides, so it will not be a triangle..
Next values - 4, 6, 8.....sum=4+6+8=18>15
Ans NO
Sufficient

(2) The sum of the lengths of the shortest and longest sides of triangle ABC is 12 centimetres
So if perimeter is LESS than 15, the third side can have a max value as just less than 3
The smallest side has to be less than this too, so sides are <3, <3, ~9
But such a triangle is not possible as sum of the smallest sides is LESS than the largest side.
So Ans NO
Sufficient

D
Great explanation sir :)


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Re: Is the perimeter of triangle ABC less than 15 centimetres ? &nbs [#permalink] 20 Aug 2018, 06:16
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