What is the Perimeter of Isosceles Triangle ABC? GMAT Data Sufficiency

Question: What is the perimeter of isosceles triangle ABC?

1. The length of side AB is 9
2.  The length of side BC is 4

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.        
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.        
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.        
4. EACH statement ALONE is sufficient.        
5. Statements (1) and (2) TOGETHER are not sufficient.

“What is the perimeter of isosceles triangle ABC?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Advanced Quant". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:
Approach Solution 1:
The model answer for this question has only 1 approach

In order to find the perimeter of an isosceles triangle, it is important to understand the rule of an isosceles triangle. This states that one side of the triangle is to be larger than the positive difference of the other two sides but smaller than the sum of the other two sides.

Considering the given case in this question, it may be identified that there are two different statements given that need to be proved to be sufficient.

The first statement of the length of the side of the isosceles triangle AB is 9 is not sufficient data because it does not mention another side or information.

Similarly, even the second statement mentions the length of the sides BC which is 4 which again is insufficient individually to find the perimeter of the triangle.

It is given that-

AB = 9
BC = 4

Therefore, AC would be equal to either 9 or 4.
Significantly, 4 cannot be the side of AC because of the isosceles triangle rule that the sum of two sides is less than the third side and if AC and BC is 4 and AB is 9 then it would not be correct.

Focusing on this aspect, it can be stated that AC is equal to 9. Accordingly, the perimeter of the isosceles triangle is 2a + b
= 2(9) +b
= 18 + 4
= 22.

Correct Answer: C

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