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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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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Great explanation sir


Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
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Statement 1) The lengths are consecutive even integers. Let's start by taking the shortest lengths, say, 2,4,6 perimeter=12, but these values don't form a triangle since triangle has a property that for any value of a, b and c, a+b>c. Here, 2+4= or 2+4 isn't greater than 6. Let's move forward. Take lengths as 4,6,8. Perimeter =18 and 4+6>8. For each next value, perimeter increases by 6 than the last value. for example, 6,8,10, perimeter =24. So, the perimeter is always greater than 15. Sufficient.

Statement 2) Let the shortest length be a and longest be b. So, a+b =12. Let a= 5, b=7. Assume second longest be x. So, in this case, 5<x<7. The perimeter will be x+12. Say, perimeter=y, Then, 12+5 <y<12+7. 17<y<19, for this case. Let's investigate further, Assume a to the least and b to be the longest, So, a=1, b=11, 1+x>11, x>10, y>1+11+10, y>22. So, the perimeter will be always greater than 15 cm. Hence, Sufficient.

The correct answer is Option D.
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