Bunuel wrote:
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
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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