Question: How many isosceles triangles with integer sides are possible such that sum of two of the side is 12?

A. 11
B. 6
C. 17
D. 23
E. 27

Answer: C

Solution and Explanation:

Approach Solution 1:
To answer this GMAT question, apply the data provided in the question. These issues pertain to many different branches of mathematics. This query relates to geometry. Because of how the options are set up, it is hard to choose the best one. Applicants must be able to understand the proper strategy for getting the desired response. There is only one correct answer out of the five options offered.
It is asked in the question to find out the number of isosceles triangles with integer sides possible with the sum of two sides as 12.
The triangle with two sides and six (according to triangle conditions) added to its two sides (6+6) < x < (0)
makes 11 potential triangles ( x.6,6) Set X as (1 to 11)
2nd instance ( sum of the unequal side of the triangle is 12)
such that (1,11,11)
(2,10,10)
(3,9,9)
(4,8,8)
(5,7,7)
(5,5,7)
Total number of possible triangles = 11 + 6 = 17 triangles
Correct option: C

Approach Solution 2:
To answer this GMAT question, apply the data that was provided in the question. These issues pertain to many different branches of mathematics. This query relates to geometry. It is challenging to choose the best option due to the way the options are presented. Applicants must be able to understand the proper strategy for getting the desired response. There is only one correct answer out of the five options offered.
There are two options: Two equal sides might equal 12 or two unequal sides added together would equal 12.
2 unequal sides added up equals 12
=> The triangle's sides should be 6, 6, and x if the sum of its two equal sides is 12.
What variations can x have?
From 1 to 11, there are 11 possible integer values for x.
Now, 2 unequal sides add up to 12. This could be 1 + 11 or 2 + 10 or 3 + 9 or 4 + 8 or 5 + 7.
Triangles with the above combination:
1, 11, 11
2, 10, 10
3, 9, 9
4, 8, 8
5, 7, 7
5, 5, 7
Triplets like (1, 1, 11), (2, 2, 10), and so forth are disregarded since the sum of the two lesser numbers is less than the greatest value. A triangle cannot be made out of these.
11 plus 6 is a total of 17 options.
Thus, the response is 17.
Correct option: C

Approach Solution 3:
To answer this GMAT question, apply the data that was provided in the question. These issues pertain to many different branches of mathematics. This query relates to probability. It is challenging to choose the best option due to the way the options are presented. Applicants must be able to understand the proper strategy for getting the desired response. There is only one correct answer out of the five options offered.
There are two options: the sum of two equal sides equals 12, and the sum of two unequal sides equals 12.
The first possibility is that the sum of the two equal sides is twelve.
As a result, the triangle's two equal sides add up to 12, which looks like (A, 6, 6) and has an A value between 1 and 11.
There are 11 integers available, then, for the first possibility.
Second Option: The total of the two uneven sides is 12.
As a result, integers suitable for this scenario are:
(1, 11, 11), (2, 10, 10), (3, 9, 9), (4, 8, 8), and (5, 7) are all possible (5, 5, 7)
These are not viable cases since the total of the two smaller digits is less than the larger number. { (1, 1, 11), (2, 2, 10), (3, 3, 9), (4, 4, 8) }
There are 6 integers available, then, for the second choice.
So,
There are (11 + 6) = 17 isosceles triangles with integer sides that can have a side sum of 12 or more.
Correct option: C

“How many isosceles triangles with integer sides are possible?" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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