If ∆ABC is an isosceles triangle, what is the perimeter of ∆ABC?
(1) AB = 10√3
(2) AC = 8
Answer: C
Difficulty level: 600 - 650
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Challenge question: If ∆ABC is an isosceles triangle
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Last edited by Brent@GMATPrepNow on Thu Sep 20, 2018 12:06 pm, edited 1 time in total.
- fskilnik@GMATH
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Hi, Brent!
You forgot to "hide" the answer for the (nice and tricky) problem you posted above...
Regards,
Fabio.
You forgot to "hide" the answer for the (nice and tricky) problem you posted above...
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Target question: What is the perimeter of ∆ABC?Brent@GMATPrepNow wrote:If ∆ABC is an isosceles triangle, what is the perimeter of ∆ABC?
(1) AB = 10√3
(2) AC = 8
Given: ∆ABC is an isosceles triangle
Statement 1: AB = 10√3
We only know the measurement of ONE side of the triangle.
So, there's no way to determine the triangle's perimeter.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: AC = 8
We only know the measurement of ONE side of the triangle.
So, there's no way to determine the triangle's perimeter.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that AB = 10√3
Statement 2 tells us that AC = 8
We also know that ∆ABC is an isosceles triangle, so two sides have the same length.
This means there are two possible cases: the sides have length 10√3, 10√3 and 8 OR the sides have length 10√3, 8 and 8
Since we have two different sets of lengths, we might incorrectly conclude that the statements COMBINED are not sufficient.
However, there's an important rule about the side lengths of a triangle:
If two sides of a triangle have lengths A and B, then . . .
DIFFERENCE between A and B < length of third side < SUM of A and B
In other words, the length of ONE side of a triangle cannot be longer than the sum of the other TWO sides.
For the GMAT, all students should have the following approximations memorized:
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2
So, 10√3 ≈ (10)(1.7) ≈ 17
Let's rewrite our two possible cases: the sides have length 17, 17 and 8 OR the sides have length 17, 8 and 8
Notice that, in the second case, the side with length 17 is longer than the sum of the other two sides (8 and 8)
This means the 17, 8, 8 triangle CANNOT EXIST
Since the first case (17, 17, 8) does not break any rules, we can be certain that ∆ABC has lengths 10√3, 10√3 and 8, which means we can definitely determine the perimeter.
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer: C