GMAT Exam > GMAT Questions > If x < 0, which of the following must be t...
Start Learning for Free
If x < 0, which of the following must be true?
I. x2 > 0
II. x − 2x > 0
III. x3 + x2 < 0
II. x − 2x > 0
III. x3 + x2 < 0
- a)I only
- b)I & II
- c)II & III
- d)All of the above
- e)None of the above
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If x < 0, which of the following must be true?I. x2 > 0II. x &mi...
To determine which of the given statements must be true when x < 0, let's examine each statement individually:
I. x2 > 0:
For any real number x, squaring it will always result in a non-negative value (greater than or equal to zero). However, since x < 0 in this case, x^2 will be positive. Therefore, statement I is true.
For any real number x, squaring it will always result in a non-negative value (greater than or equal to zero). However, since x < 0 in this case, x^2 will be positive. Therefore, statement I is true.
II. x − 2x > 0:
Simplifying the expression, we get -x > 0. Since x < 0, multiplying both sides of the inequality by -1 flips the sign, giving us x < 0, which is true. Therefore, statement II is true.
Simplifying the expression, we get -x > 0. Since x < 0, multiplying both sides of the inequality by -1 flips the sign, giving us x < 0, which is true. Therefore, statement II is true.
III. x3 + x2 < 0:
Substituting x = -1 into the expression, we get (-1)3 + (-1)2 = -1 + 1 = 0. Since the expression evaluates to zero, it is not less than zero. Therefore, statement III is false.
Substituting x = -1 into the expression, we get (-1)3 + (-1)2 = -1 + 1 = 0. Since the expression evaluates to zero, it is not less than zero. Therefore, statement III is false.
Based on our analysis, statements I and II are true, while statement III is false. Thus, the correct answer is (B) I & II.
|
Explore Courses for GMAT exam
|
|
Similar GMAT Doubts
Top Courses for GMATView all
If x < 0, which of the following must be true?I. x2 > 0II. x − 2x > 0III. x3 + x2 < 0a)I onlyb)I & IIc)II & IIId)All of the abovee)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
Question Description
If x < 0, which of the following must be true?I. x2 > 0II. x − 2x > 0III. x3 + x2 < 0a)I onlyb)I & IIc)II & IIId)All of the abovee)None of the aboveCorrect answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If x < 0, which of the following must be true?I. x2 > 0II. x − 2x > 0III. x3 + x2 < 0a)I onlyb)I & IIc)II & IIId)All of the abovee)None of the aboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x < 0, which of the following must be true?I. x2 > 0II. x − 2x > 0III. x3 + x2 < 0a)I onlyb)I & IIc)II & IIId)All of the abovee)None of the aboveCorrect answer is option 'B'. Can you explain this answer?.
If x < 0, which of the following must be true?I. x2 > 0II. x − 2x > 0III. x3 + x2 < 0a)I onlyb)I & IIc)II & IIId)All of the abovee)None of the aboveCorrect answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If x < 0, which of the following must be true?I. x2 > 0II. x − 2x > 0III. x3 + x2 < 0a)I onlyb)I & IIc)II & IIId)All of the abovee)None of the aboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x < 0, which of the following must be true?I. x2 > 0II. x − 2x > 0III. x3 + x2 < 0a)I onlyb)I & IIc)II & IIId)All of the abovee)None of the aboveCorrect answer is option 'B'. Can you explain this answer?.
Solutions for If x < 0, which of the following must be true?I. x2 > 0II. x − 2x > 0III. x3 + x2 < 0a)I onlyb)I & IIc)II & IIId)All of the abovee)None of the aboveCorrect answer is option 'B'. 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 If x < 0, which of the following must be true?I. x2 > 0II. x − 2x > 0III. x3 + x2 < 0a)I onlyb)I & IIc)II & IIId)All of the abovee)None of the aboveCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If x < 0, which of the following must be true?I. x2 > 0II. x − 2x > 0III. x3 + x2 < 0a)I onlyb)I & IIc)II & IIId)All of the abovee)None of the aboveCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for If x < 0, which of the following must be true?I. x2 > 0II. x − 2x > 0III. x3 + x2 < 0a)I onlyb)I & IIc)II & IIId)All of the abovee)None of the aboveCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of If x < 0, which of the following must be true?I. x2 > 0II. x − 2x > 0III. x3 + x2 < 0a)I onlyb)I & IIc)II & IIId)All of the abovee)None of the aboveCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If x < 0, which of the following must be true?I. x2 > 0II. x − 2x > 0III. x3 + x2 < 0a)I onlyb)I & IIc)II & IIId)All of the abovee)None of the aboveCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice GMAT tests.
|
|
Explore Courses for GMAT exam
|
|
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