GMAT Exam > GMAT Questions > The rectangle ABCD has its side lengths equal...
Start Learning for Free
The rectangle ABCD has its side lengths equal to x and y respectively, where x and y are prime numbers greater than 2. Which of the following cannot be equal to the sum of all the sides of the rectangle ABCD?
I. 64
II. 82
III. 146
I. 64
II. 82
III. 146
- a)I only
- b)II only
- c)III only
- d)I and II only
- e)II and III only
Correct answer is option 'E'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The rectangle ABCD has its side lengths equal to x and y respectively,...
Given
- ABCD is a rectangle with side lengths equal to x and y respectively
- x, y are prime numbers > 2
- Thus, x and y are odd
To Find
- Values in the options that cannot be equal to 2(x+y)
Approach and Working
- As we are asked to find a value in the options that is not equal to 2(x+y), we will first find a constraint on 2(x+y).
- We will then evaluate the 3 options as per the constraint on 2(x+y)
- Since x and y are both odd, x + y = even, i.e. it will at least be a multiple of 2, if not its higher powers
- So, 2(x+y) will at least be a multiple of 4, if not the higher powers of 2
- Hence an integer that is not divisible by 4 can never be equal to 2(x+y)
1. Option-I: 64 → Is divisible by 4, can be equal to 2(x+y)
2. Option-II: 82 → Is not divisible by 4, can never be equal to 2(x+y)
3. Option-III: 146 → Is not divisible by 4, can never be equal to 2(x+y)
Thus, options II and III can never be equal to the value of 2(x+y).
Hence the correct answer is OPTION E
2. Option-II: 82 → Is not divisible by 4, can never be equal to 2(x+y)
3. Option-III: 146 → Is not divisible by 4, can never be equal to 2(x+y)
Thus, options II and III can never be equal to the value of 2(x+y).
Hence the correct answer is OPTION E
Most Upvoted Answer
The rectangle ABCD has its side lengths equal to x and y respectively,...
Given information:
- Rectangle ABCD has side lengths x and y, where x and y are prime numbers greater than 2.
- We need to find which of the following cannot be equal to the sum of all the sides of the rectangle ABCD: 64, 82, 146.
Approach:
- We know that the sum of all the sides of the rectangle ABCD is 2(x+y).
- We need to check which of the given options cannot be expressed as 2(x+y) for some prime numbers x and y greater than 2.
- We can eliminate the options one by one until we are left with the answer.
Solution:
I. 64
- 2(x+y) = 64
- x+y = 32
- Since x and y are prime numbers greater than 2, their sum cannot be 32.
- Therefore, option I cannot be equal to the sum of all the sides of the rectangle ABCD.
II. 82
- 2(x+y) = 82
- x+y = 41
- 41 is a prime number greater than 2.
- Therefore, option II can be equal to the sum of all the sides of the rectangle ABCD.
III. 146
- 2(x+y) = 146
- x+y = 73
- 73 is a prime number greater than 2.
- Therefore, option III can be equal to the sum of all the sides of the rectangle ABCD.
Final Answer:
- Option E) II and III only cannot be equal to the sum of all the sides of the rectangle ABCD.
- Rectangle ABCD has side lengths x and y, where x and y are prime numbers greater than 2.
- We need to find which of the following cannot be equal to the sum of all the sides of the rectangle ABCD: 64, 82, 146.
Approach:
- We know that the sum of all the sides of the rectangle ABCD is 2(x+y).
- We need to check which of the given options cannot be expressed as 2(x+y) for some prime numbers x and y greater than 2.
- We can eliminate the options one by one until we are left with the answer.
Solution:
I. 64
- 2(x+y) = 64
- x+y = 32
- Since x and y are prime numbers greater than 2, their sum cannot be 32.
- Therefore, option I cannot be equal to the sum of all the sides of the rectangle ABCD.
II. 82
- 2(x+y) = 82
- x+y = 41
- 41 is a prime number greater than 2.
- Therefore, option II can be equal to the sum of all the sides of the rectangle ABCD.
III. 146
- 2(x+y) = 146
- x+y = 73
- 73 is a prime number greater than 2.
- Therefore, option III can be equal to the sum of all the sides of the rectangle ABCD.
Final Answer:
- Option E) II and III only cannot be equal to the sum of all the sides of the rectangle ABCD.
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.
|
Explore Courses for GMAT exam
|
|
Similar GMAT Doubts
Top Courses for GMATView all
The rectangle ABCD has its side lengths equal to x and y respectively, where x and y are prime numbers greater than 2. Which of the following cannot be equal to the sum of all the sides of the rectangle ABCD?I. 64II. 82III. 146a)I onlyb)II onlyc)III onlyd)I and II onlye)II and III onlyCorrect answer is option 'E'. Can you explain this answer?
Question Description
The rectangle ABCD has its side lengths equal to x and y respectively, where x and y are prime numbers greater than 2. Which of the following cannot be equal to the sum of all the sides of the rectangle ABCD?I. 64II. 82III. 146a)I onlyb)II onlyc)III onlyd)I and II onlye)II and III onlyCorrect answer is option 'E'. 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 The rectangle ABCD has its side lengths equal to x and y respectively, where x and y are prime numbers greater than 2. Which of the following cannot be equal to the sum of all the sides of the rectangle ABCD?I. 64II. 82III. 146a)I onlyb)II onlyc)III onlyd)I and II onlye)II and III onlyCorrect answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The rectangle ABCD has its side lengths equal to x and y respectively, where x and y are prime numbers greater than 2. Which of the following cannot be equal to the sum of all the sides of the rectangle ABCD?I. 64II. 82III. 146a)I onlyb)II onlyc)III onlyd)I and II onlye)II and III onlyCorrect answer is option 'E'. Can you explain this answer?.
The rectangle ABCD has its side lengths equal to x and y respectively, where x and y are prime numbers greater than 2. Which of the following cannot be equal to the sum of all the sides of the rectangle ABCD?I. 64II. 82III. 146a)I onlyb)II onlyc)III onlyd)I and II onlye)II and III onlyCorrect answer is option 'E'. 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 The rectangle ABCD has its side lengths equal to x and y respectively, where x and y are prime numbers greater than 2. Which of the following cannot be equal to the sum of all the sides of the rectangle ABCD?I. 64II. 82III. 146a)I onlyb)II onlyc)III onlyd)I and II onlye)II and III onlyCorrect answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The rectangle ABCD has its side lengths equal to x and y respectively, where x and y are prime numbers greater than 2. Which of the following cannot be equal to the sum of all the sides of the rectangle ABCD?I. 64II. 82III. 146a)I onlyb)II onlyc)III onlyd)I and II onlye)II and III onlyCorrect answer is option 'E'. Can you explain this answer?.
Solutions for The rectangle ABCD has its side lengths equal to x and y respectively, where x and y are prime numbers greater than 2. Which of the following cannot be equal to the sum of all the sides of the rectangle ABCD?I. 64II. 82III. 146a)I onlyb)II onlyc)III onlyd)I and II onlye)II and III onlyCorrect answer is option 'E'. 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 The rectangle ABCD has its side lengths equal to x and y respectively, where x and y are prime numbers greater than 2. Which of the following cannot be equal to the sum of all the sides of the rectangle ABCD?I. 64II. 82III. 146a)I onlyb)II onlyc)III onlyd)I and II onlye)II and III onlyCorrect answer is option 'E'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The rectangle ABCD has its side lengths equal to x and y respectively, where x and y are prime numbers greater than 2. Which of the following cannot be equal to the sum of all the sides of the rectangle ABCD?I. 64II. 82III. 146a)I onlyb)II onlyc)III onlyd)I and II onlye)II and III onlyCorrect answer is option 'E'. Can you explain this answer?, a detailed solution for The rectangle ABCD has its side lengths equal to x and y respectively, where x and y are prime numbers greater than 2. Which of the following cannot be equal to the sum of all the sides of the rectangle ABCD?I. 64II. 82III. 146a)I onlyb)II onlyc)III onlyd)I and II onlye)II and III onlyCorrect answer is option 'E'. Can you explain this answer? has been provided alongside types of The rectangle ABCD has its side lengths equal to x and y respectively, where x and y are prime numbers greater than 2. Which of the following cannot be equal to the sum of all the sides of the rectangle ABCD?I. 64II. 82III. 146a)I onlyb)II onlyc)III onlyd)I and II onlye)II and III onlyCorrect answer is option 'E'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The rectangle ABCD has its side lengths equal to x and y respectively, where x and y are prime numbers greater than 2. Which of the following cannot be equal to the sum of all the sides of the rectangle ABCD?I. 64II. 82III. 146a)I onlyb)II onlyc)III onlyd)I and II onlye)II and III onlyCorrect answer is option 'E'. Can you explain this answer? tests, examples and also practice GMAT tests.
|
|
Explore Courses for GMAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup