Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
May 0510:00 AM PDT
-11:00 AM PDT
GMAT Inequalities is a high-frequency topic in GMAT Quant, but many students struggle because the concepts behave differently from standard algebra. Understanding the right rules, patterns, and edge cases can significantly improve both speed and accuracy.- May 06
08:30 AM PDT
-09:30 AM PDT
In Episode 3 of our GMAT Ninja Critical Reasoning series, we tackle Discrepancy, Paradox, and Explain an Oddity questions. You know the feeling: the passage gives you two facts that seem completely contradictory.... - May 08
08:00 AM PDT
-08:30 AM PDT
Join the special YouTube live-stream for selecting the winners of GMAT Club MBA Scholarships sponsored by Juno live. Watch who gets these coveted MBA scholarships offered by GMAT Club and Juno.
10 Nov 2021, 02:13
Kudos
Bookmarks
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
(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
10 Nov 2021, 02:14
Kudos
Bookmarks
Official Solution:
Is the perimeter of triangle ABC less than 15 centimetres ?
To solve this question recall the following property: the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
(1) The lengths of the sides of triangle ABC are consecutive even integers in centimetres
The smallest three consecutive positive even integers are 2, 4, and 6 but a triangle cannot have sides equal to 2, 4, and 6 centimetres because in this case the length of one side (6) is NOT smaller than the sum of two other sides (2 and 4). The next three consecutive positive even integers are 4, 6, and 8. The sum is 18. So, the perimeter of triangle ABC must be greater than 15 centimetres . Sufficient.
(2) The sum of the lengths of the shortest and longest sides of triangle ABC is 12 centimetres
The perimeter to be less than 15 centimetres, the third side (second smallest) must be less than 3 centimetres. In this case the sides would be: (less than 3), (less than 3), (more than 9). But since the sum of two sides is NOT greater than the third side ((less than 3) + (less than 3) < 9), than such a triangle is not possible. So, the perimeter of triangle ABC must be greater than 15 centimetres . Sufficient.
Answer: D
Is the perimeter of triangle ABC less than 15 centimetres ?
To solve this question recall the following property: the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
(1) The lengths of the sides of triangle ABC are consecutive even integers in centimetres
The smallest three consecutive positive even integers are 2, 4, and 6 but a triangle cannot have sides equal to 2, 4, and 6 centimetres because in this case the length of one side (6) is NOT smaller than the sum of two other sides (2 and 4). The next three consecutive positive even integers are 4, 6, and 8. The sum is 18. So, the perimeter of triangle ABC must be greater than 15 centimetres . Sufficient.
(2) The sum of the lengths of the shortest and longest sides of triangle ABC is 12 centimetres
The perimeter to be less than 15 centimetres, the third side (second smallest) must be less than 3 centimetres. In this case the sides would be: (less than 3), (less than 3), (more than 9). But since the sum of two sides is NOT greater than the third side ((less than 3) + (less than 3) < 9), than such a triangle is not possible. So, the perimeter of triangle ABC must be greater than 15 centimetres . Sufficient.
Answer: D
