Is the triangle ABC right angled at B an isosceles triangle?Statement 1: All 3 sides are integers.Statement 2: The square of the hypotenuse is twice the product of the other two sides.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.Correct answer is option 'D'. Can you explain this answer?

EduRev

All Courses

Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity

Open App

GMAT Exam > GMAT Questions > Is the triangle ABC right angled at B an isos...

Join the Discussion on the App

Is the triangle ABC right angled at B an isosceles triangle?

Statement 1: All 3 sides are integers.
Statement 2: The square of the hypotenuse is twice the product of the other two sides.

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;
d)
EACH statement ALONE is sufficient to answer the question asked;
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.

Correct answer is option 'D'. Can you explain this answer?

FREE This question is part of

GMAT Classic Mock Test - 7

Attempt Test

Attempt this Test

Most Upvoted Answer

Is the triangle ABC right angled at B an isosceles triangle?Statement ...

Step 1: Evaluate Statement 1 ALONE
Statement 1: All 3 sides are integers.
The ratio of the sides of an isosceles right triangle is 1 : 1 : √2
Either the sides with ratio 1 or the side with ratio √2 is not an integer.
From Statement 1 we know all sides are integers. If all three sides are integers, such a right triangle cannot be isosceles.

We are able to answer the question a conclusive NO using statement 1 ALONE.
Statement 1 ALONE is SUFFICIENT.
Eliminate answer options B, C, and D.

Step 2: Evaluate Statement 2 ALONE
Statement 2: The square of the hypotenuse is twice the product of the other two sides
Let the sides be x, y, and z with z as the hypotenuse.
By Pythagoras theorem: x² + y²= z²
From statement 2: z² = 2xy
⇒ x² + y² = 2xy
⇒ x² + y² - 2xy = 0
⇒ (x - y)² = 0
⇒ x – y = 0 ⇒ x = y

If x and y are same, the triangle is an isosceles right triangle.

We are able to answer the question a conclusive YES using statement 2.

Each statement is INDEPENDENTLY sufficient to answer the question.

Choice D is the correct answer.

Answered by Talent Skill Learning · View profile

Free Test

FREE

GMAT Classic Mock Test - 7
79 Ques | 158 Min

Start Free Test

View all free GMAT tests

Community Answer

Is the triangle ABC right angled at B an isosceles triangle?Statement ...

We are able to answer the question a conclusive NO using statement 1 ALONE.
Statement 1 ALONE is SUFFICIENT.
Eliminate answer options B, C, and D.

If x and y are same, the triangle is an isosceles right triangle.

We are able to answer the question a conclusive YES using statement 2.

Each statement is INDEPENDENTLY sufficient to answer the question.

Choice D is the correct answer.

Share via Whatsapp

Attention GMAT Students!

To make sure you are not studying endlessly, EduRev has designed GMAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in GMAT.

GMAT Focus Edition Mock Test Series 2024

Quantitative for GMAT

Crash Course for GMAT

Data Insights for GMAT

View all answers Start learning for free

< Previous Question Next Question >

Explore Courses for GMAT exam

Similar GMAT Doubts

Directions: Each GMAT Data Sufficiency problem consists of a question and two statements labeled (1) and (2), that provide data. Based on the data given plus your knowledge of mathematics and everyday facts, you must decide whether the data are sufficient for answering the question. The five answer choices are the same for every data sufficiency question.What is the area of a triangle (with vertices at FCE) that is inscribed in a hexagon with vertices at ABCDE?(1) The hexagon is regular and BE = 14.(2) EC = 7√3.

View answer

Directions: Each GMAT Data Sufficiency problem consists of a question and two statements labeled (1) and (2), that provide data. Based on the data given plus your knowledge of mathematics and everyday facts, you must decide whether the data are sufficient for answering the question. The five answer choices are the same for every data sufficiency question.If the product of j and k does not equal zero, is j<0 and k>0?(1) (-j, k) lies above the x-axis and to the right of the y-axis.(2) (j, -k) lies below the x-axis and to the left of the y-axis.

View answer

Directions: Each GMAT Data Sufficiency problem consists of a question and two statements labeled (1) and (2), that provide data. Based on the data given plus your knowledge of mathematics and everyday facts, you must decide whether the data are sufficient for answering the question. The five answer choices are the same for every data sufficiency question.For integers w, x, y, and z, is wxyz = -1?(1) wx / yz = -1(2) w = -1/x and y = 1/z

View answer

Directions: Each GMAT Data Sufficiency problem consists of a question and two statements labeled (1) and (2), that provide data. Based on the data given plus your knowledge of mathematics and everyday facts, you must decide whether the data are sufficient for answering the question. The five answer choices are the same for every data sufficiency question.How many integers are there between m and n, exclusive, if m and n are themselves integers?(1) m − n = 8(2) There are 5 integers between, but not including, m − 1 and n − 1.

View answer

A={2,4,6,8,10,12,...}B={3,6,9,12,15,18...}True or false: n∈A∪BStatement 1: n is a perfect square.Statement 2: n is a multiple of 99.

View answer

Top Courses for GMATView all

GMAT Focus Edition Mock Test Series 2024

Quantitative for GMAT

Crash Course for GMAT

Data Insights for GMAT

100 RCs for GMAT

Top Courses for GMAT

View all

Is the triangle ABC right angled at B an isosceles triangle?Statement 1: All 3 sides are integers.Statement 2: The square of the hypotenuse is twice the product of the other two sides.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.Correct answer is option 'D'. Can you explain this answer?

Share with a Friend

Answer this doubt

Question Description
Is the triangle ABC right angled at B an isosceles triangle?Statement 1: All 3 sides are integers.Statement 2: The square of the hypotenuse is twice the product of the other two sides.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.Correct answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Is the triangle ABC right angled at B an isosceles triangle?Statement 1: All 3 sides are integers.Statement 2: The square of the hypotenuse is twice the product of the other two sides.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Is the triangle ABC right angled at B an isosceles triangle?Statement 1: All 3 sides are integers.Statement 2: The square of the hypotenuse is twice the product of the other two sides.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.Correct answer is option 'D'. Can you explain this answer?.

Solutions for Is the triangle ABC right angled at B an isosceles triangle?Statement 1: All 3 sides are integers.Statement 2: The square of the hypotenuse is twice the product of the other two sides.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT. Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.

Here you can find the meaning of Is the triangle ABC right angled at B an isosceles triangle?Statement 1: All 3 sides are integers.Statement 2: The square of the hypotenuse is twice the product of the other two sides.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Is the triangle ABC right angled at B an isosceles triangle?Statement 1: All 3 sides are integers.Statement 2: The square of the hypotenuse is twice the product of the other two sides.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Is the triangle ABC right angled at B an isosceles triangle?Statement 1: All 3 sides are integers.Statement 2: The square of the hypotenuse is twice the product of the other two sides.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Is the triangle ABC right angled at B an isosceles triangle?Statement 1: All 3 sides are integers.Statement 2: The square of the hypotenuse is twice the product of the other two sides.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Is the triangle ABC right angled at B an isosceles triangle?Statement 1: All 3 sides are integers.Statement 2: The square of the hypotenuse is twice the product of the other two sides.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice GMAT tests.

Explore Courses for GMAT exam