GMAT Exam > GMAT Questions > GMAT Challenging Math Question | Arithmetic |...
Start Learning for Free
GMAT Challenging Math Question | Arithmetic | Number Properties DS Practice
Is |x| > x?
Is |x| > x?
Statement 1: x2 + y2 = 4
Statement 2: x3 + y2 = 0
Statement 2: x3 + y2 = 0
- 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 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
GMAT Challenging Math Question | Arithmetic | Number Properties DS Pra...
Step 1: Decode the Question Stem and Simplify it
What does "Is |x| > x?| mean?
The modulus of a number gives the magnitude of that number.
Substitute a positive value for x: |x| = x
Substitute zero for x: |x| = x
Substitute a negative value for x: |x| > x
So, the question ultimately boils down to Is x < 0?
What does "Is |x| > x?| mean?
The modulus of a number gives the magnitude of that number.
Substitute a positive value for x: |x| = x
Substitute zero for x: |x| = x
Substitute a negative value for x: |x| > x
So, the question ultimately boils down to Is x < 0?
Step 2: Evaluate Statement 1 ALONE
Statement 1: x2 + y2 = 4
Squares of real numbers are non-negative.
So, both x2 and y2 are non negative.
So, x2 could be 0 or positive.
Statement 1: x2 + y2 = 4
Squares of real numbers are non-negative.
So, both x2 and y2 are non negative.
So, x2 could be 0 or positive.
If x2 = 0, x is 0.
Answer to the question "Is x < 0?" is NO.
Answer to the question "Is x < 0?" is NO.
If x2 is positive, x may be positive or negative.
Answer to the question "Is x < 0?" is NO or YES
Answer to the question "Is x < 0?" is NO or YES
We are not able to find a conclusive answer to the question using statement 1 ALONE.
Statement 1 alone is NOT Sufficient.
Eliminate answer options A and D.
Statement 1 alone is NOT Sufficient.
Eliminate answer options A and D.
Step 3: Evaluate Statement 2 ALONE
Statement 2: x3 + y2 = 0
Squares of real numbers are non-negative. So, y2 is definitely not a negative number.
Statement 2: x3 + y2 = 0
Squares of real numbers are non-negative. So, y2 is definitely not a negative number.
Two possibilities exist for x3 and y2
Possibility 1: Both x3 and y2 are 0.
If x3 = 0, the value of x = 0.
The answer to the question "Is x < 0?" is NO.
Possibility 1: Both x3 and y2 are 0.
If x3 = 0, the value of x = 0.
The answer to the question "Is x < 0?" is NO.
Possibility 2: x3 is negative and y2 is positive.
If x3 < 0, x < 0
The answer to the question "Is x < 0?" is YES.
If x3 < 0, x < 0
The answer to the question "Is x < 0?" is YES.
We are not able to find a conclusive answer to the question using statement 2 ALONE.
Statement 2 alone is NOT Sufficient.
Eliminate answer option B.
Statement 2 alone is NOT Sufficient.
Eliminate answer option B.
Step 4: Evaluate Statements TOGETHER
Statement 1: x2 + y2 = 4
Statement 2: x3 + y2 = 0
Statement 1: x2 + y2 = 4
Statement 2: x3 + y2 = 0
From Statement 1, if x = 0, y2 = 4
And from statement 2, if x = 0, y2 = 0.
So, if x = 0, the statements contradict each other.
So, x cannot be 0.
And from statement 2, if x = 0, y2 = 0.
So, if x = 0, the statements contradict each other.
So, x cannot be 0.
Therefore, y2 has to be positive and x3 has to be negative to satisfy both statements.
If x3 < 0, we can deduce that x < 0.
Answer to the question "Is x < 0?" is a conclusive YES.
If x3 < 0, we can deduce that x < 0.
Answer to the question "Is x < 0?" is a conclusive YES.
We are able to answer the question by combining the two statements.
Choice C is the correct answer.
Free Test
FREE
| Start Free Test |
Community Answer
GMAT Challenging Math Question | Arithmetic | Number Properties DS Pra...
Step 1: Decode the Question Stem and Simplify it
What does "Is |x| > x?| mean?
The modulus of a number gives the magnitude of that number.
Substitute a positive value for x: |x| = x
Substitute zero for x: |x| = x
Substitute a negative value for x: |x| > x
So, the question ultimately boils down to Is x < 0?
What does "Is |x| > x?| mean?
The modulus of a number gives the magnitude of that number.
Substitute a positive value for x: |x| = x
Substitute zero for x: |x| = x
Substitute a negative value for x: |x| > x
So, the question ultimately boils down to Is x < 0?
Step 2: Evaluate Statement 1 ALONE
Statement 1: x2 + y2 = 4
Squares of real numbers are non-negative.
So, both x2 and y2 are non negative.
So, x2 could be 0 or positive.
Statement 1: x2 + y2 = 4
Squares of real numbers are non-negative.
So, both x2 and y2 are non negative.
So, x2 could be 0 or positive.
If x2 = 0, x is 0.
Answer to the question "Is x < 0?" is NO.
Answer to the question "Is x < 0?" is NO.
If x2 is positive, x may be positive or negative.
Answer to the question "Is x < 0?" is NO or YES
Answer to the question "Is x < 0?" is NO or YES
We are not able to find a conclusive answer to the question using statement 1 ALONE.
Statement 1 alone is NOT Sufficient.
Eliminate answer options A and D.
Statement 1 alone is NOT Sufficient.
Eliminate answer options A and D.
Step 3: Evaluate Statement 2 ALONE
Statement 2: x3 + y2 = 0
Squares of real numbers are non-negative. So, y2 is definitely not a negative number.
Statement 2: x3 + y2 = 0
Squares of real numbers are non-negative. So, y2 is definitely not a negative number.
Two possibilities exist for x3 and y2
Possibility 1: Both x3 and y2 are 0.
If x3 = 0, the value of x = 0.
The answer to the question "Is x < 0?" is NO.
Possibility 1: Both x3 and y2 are 0.
If x3 = 0, the value of x = 0.
The answer to the question "Is x < 0?" is NO.
Possibility 2: x3 is negative and y2 is positive.
If x3 < 0, x < 0
The answer to the question "Is x < 0?" is YES.
If x3 < 0, x < 0
The answer to the question "Is x < 0?" is YES.
We are not able to find a conclusive answer to the question using statement 2 ALONE.
Statement 2 alone is NOT Sufficient.
Eliminate answer option B.
Statement 2 alone is NOT Sufficient.
Eliminate answer option B.
Step 4: Evaluate Statements TOGETHER
Statement 1: x2 + y2 = 4
Statement 2: x3 + y2 = 0
Statement 1: x2 + y2 = 4
Statement 2: x3 + y2 = 0
From Statement 1, if x = 0, y2 = 4
And from statement 2, if x = 0, y2 = 0.
So, if x = 0, the statements contradict each other.
So, x cannot be 0.
And from statement 2, if x = 0, y2 = 0.
So, if x = 0, the statements contradict each other.
So, x cannot be 0.
Therefore, y2 has to be positive and x3 has to be negative to satisfy both statements.
If x3 < 0, we can deduce that x < 0.
Answer to the question "Is x < 0?" is a conclusive YES.
If x3 < 0, we can deduce that x < 0.
Answer to the question "Is x < 0?" is a conclusive YES.
We are able to answer the question by combining the two statements.
Choice C is the correct answer.
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
GMAT Challenging Math Question | Arithmetic | Number Properties DS PracticeIs |x| > x?Statement 1: x2 + y2 = 4Statement 2: x3 + y2 = 0a)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 'C'. Can you explain this answer?
Question Description
GMAT Challenging Math Question | Arithmetic | Number Properties DS PracticeIs |x| > x?Statement 1: x2 + y2 = 4Statement 2: x3 + y2 = 0a)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 'C'. 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 GMAT Challenging Math Question | Arithmetic | Number Properties DS PracticeIs |x| > x?Statement 1: x2 + y2 = 4Statement 2: x3 + y2 = 0a)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 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for GMAT Challenging Math Question | Arithmetic | Number Properties DS PracticeIs |x| > x?Statement 1: x2 + y2 = 4Statement 2: x3 + y2 = 0a)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 'C'. Can you explain this answer?.
GMAT Challenging Math Question | Arithmetic | Number Properties DS PracticeIs |x| > x?Statement 1: x2 + y2 = 4Statement 2: x3 + y2 = 0a)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 'C'. 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 GMAT Challenging Math Question | Arithmetic | Number Properties DS PracticeIs |x| > x?Statement 1: x2 + y2 = 4Statement 2: x3 + y2 = 0a)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 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for GMAT Challenging Math Question | Arithmetic | Number Properties DS PracticeIs |x| > x?Statement 1: x2 + y2 = 4Statement 2: x3 + y2 = 0a)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 'C'. Can you explain this answer?.
Solutions for GMAT Challenging Math Question | Arithmetic | Number Properties DS PracticeIs |x| > x?Statement 1: x2 + y2 = 4Statement 2: x3 + y2 = 0a)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 'C'. 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 GMAT Challenging Math Question | Arithmetic | Number Properties DS PracticeIs |x| > x?Statement 1: x2 + y2 = 4Statement 2: x3 + y2 = 0a)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 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
GMAT Challenging Math Question | Arithmetic | Number Properties DS PracticeIs |x| > x?Statement 1: x2 + y2 = 4Statement 2: x3 + y2 = 0a)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 'C'. Can you explain this answer?, a detailed solution for GMAT Challenging Math Question | Arithmetic | Number Properties DS PracticeIs |x| > x?Statement 1: x2 + y2 = 4Statement 2: x3 + y2 = 0a)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 'C'. Can you explain this answer? has been provided alongside types of GMAT Challenging Math Question | Arithmetic | Number Properties DS PracticeIs |x| > x?Statement 1: x2 + y2 = 4Statement 2: x3 + y2 = 0a)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 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice GMAT Challenging Math Question | Arithmetic | Number Properties DS PracticeIs |x| > x?Statement 1: x2 + y2 = 4Statement 2: x3 + y2 = 0a)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 'C'. 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup