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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?
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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.
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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.
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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?
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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.
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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.
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