How many isosceles triangles with integer sides are possible? GMAT Problem Solving

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.

Suggested GMAT Problem Solving Questions:

• If g is an integer what is the value of(−1)g4−1(−1)g4−1? GMAT Problem Solving
• What is the Area of the Triangle with the following Vertices L(1,3) M(5,1) and N(3,5)? GMAT Problem Solving
• If P2−QR=10P2−QR=10, Q2+PR=10Q2+PR=10, R2+PQ=10R2+PQ=10 GMAT Problem Solving
• If y (u-c) = 0 and j (u-k) = 0, Which of the Following Must be True, Assuming c < kc < k? GMAT Problem Solving
• What is the Remainder when 333²²² is Divided by 7? GMAT Problem Solving
• In a College of 300 Students, Every Student Reads 5 Newspapers and every Newspaper is Read by 60 Students GMAT Problem Solving
• If 4 People are Selected from a Group of 6 Married Couples, What is the Probability That none of Them would be Married to Each Other? GMAT Problem Solving
• If the Equation |x|+|y|= 5 Encloses a Certain Region on the Graph, What is the Area of that Region? GMAT Problem Solving
• If x = ¾ and y = ⅖ , What is the Value of √(x2+6x+9)(x2+6x+9) - √(y2−2y+1)(y2−2y+1)? GMAT Problem Solving
• A Chord of a Circle is Equal to its Radius. GMAT Problem Solving
• A Clock loses a Minute Every Three Hours for 4 Days and Gains 1% in the Subsequent 6 Days. GMAT Problem Solving
• The Population of the Bacteria Colony Doubles Every Day GMAT Problem Solving
• If tu=xytu=xyand ty=uxty=ux Where t, u, x, and y are Non-Zero Integers GMAT Problem Solving
• A Farm has Chickens, Cows and Sheep. The Number of Chickens and Cows Combined is 3 Times the Number of Sheep. GMAT Problem Solving
• In how Many Different Ways Can a Group of 8 People be Divided into 4 Teams of 2 People Each? GMAT Problem Solving
• If m is Three Times n, and if 2n + 3 is 20% of 25, What is the value of m? GMAT Problem Solving
• If Ben Were to Lose the Championship, Mike would be the Winner GMAT Problem Solving
• A Train Travelling at a Certain Constant Speed takes 30 seconds GMAT Problem Solving
• The product of the first 10 prime numbers is closest to which of the following? GMAT Problem Solving
• There is a 120 liter mixture of alcohol and water. The ratio of alcohol to water is 7 : 5 GMAT Problem Solving
• An equilateral triangle ABC is inscribed in square ADEF, forming three right triangles GMAT Problem Solving
• A Furniture Store Sells Only Two Models of Desks, Model A and Model B. The Selling Price of Model A is $120 GMAT Problem Solving
• A contractor combined x tons of a gravel mixture that contained 10 percent gravel G GMAT Problem Solving
• There are 100 Apples in a Bag of which 98% are Green and Rest are Red GMAT Problem Solving
• How many litres of a 90% solution of concentrated acid needs to be mixed with a 75% solution GMAT Problem Solving
• Jug Contains Water And Orange Juice In The Ratio 5:7 . Another Jug Contains Water And Orange J GMAT Problem Solving
• The number of ways in which 8 different flowers can be seated to form a garland so that 4 particular flowers are never separated GMAT Problem Solving
• A train travels from Albany to Syracuse, a distance of 120 miles, at an average rate of 50 miles per hour GMAT Problem Solving
• The hexagon ABCDEF is regular. That means all its sides are the same length and all its interior angles are the same size. GMAT Problem Solving
• y varies directly as x and when x = 6, y = 24. What is the value of y, when x = 5? GMAT Problem Solving
• If k is an Integer and 2 < k < 7, for How Many Different Values of k is There a Triangle With Sides of Lengths 2, 7, and k? GMAT Problem Solving
• How many factors does 36² have? GMAT Problem Solving
• A number when divided successively by 4 and 5 leaves remainder 1 and 4 respectively GMAT Problem Solving
• Walking at 6/7 th of his usual speed, a man is 25 min too late GMAT Problem Solving
• An Inlet Pipe can Fill in an Empty Cistern in 30 minutes Whereas a leak in the Bottom of the Cistern can Empty a Filled Tank in 40 minutes GMAT Problem Solving
• A milkman cheats his customers by adding water to the milk he sells GMAT Problem Solving
• if 80 lamps can be lighted, 5 hours per day for 10 days for $21.25, then the number of lamps, GMAT Problem Solving
• Few of the corporate contributions to the earthquake relief fund, aside from Pterocom GMAT Problem Solving
• X is Older Than Y, Z Is Younger Than W And V Is Older Than Y GMAT Problem Solving
• What is the Largest Power of 3 Contained in 200! GMAT Problem Solving
• Find the Greatest Number That Will Divide 43,91 and 183 So as to Leave GMAT Problem Solving
• A Right Angled Triangle has its Sides in Arithmetic Progression and Being Integers GMAT Problem Solving
• Out of 7 Consonants and 4 Vowels, How Many Words of 3 Consonants and 2 Vowels Can be Formed? GMAT Problem Solving
• 4 Bells Toll Together at 9:00 A.M. They Toll After 7, 8, 11 and 12 seconds Respectively GMAT Problem Solving
• A Man can Hit a Target Once with 4 Shots. If He Fires 4 Shots in Success GMAT Problem Solving
• A is twice as good a workman as B and together they finish a piece of GMAT Problem Solving
• Frances can complete a job in 12 hours, and Joan can complete the same GMAT Problem Solving
• The Average Age of Chief Executive Officers (CEO’s) in a Large Sample of Companies is 57 GMAT Problem Solving
• Running at the Same Constant Rate, 6 Identical Machines can GMAT Problem Solving
• If a and b are positive integers such that a – b and a/b are both even GMAT Problem Solving