This data sufficiency problem consists of a q...
This data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in a leap year or the meaning of the word counterclockwise), you must indicate whether -
Q.
Is x3 > x2?
1. x > 0
2. x < 1
Numbers: All numbers used are real numbers.
• a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
• b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
• c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
• d)
• e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

### Related Test

 DIVYA DHARSHINI.R Aug 08, 2019
Related This data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in a leap year or the meaning of the word counterclockwise), you must indicate whether -Q.Is x3> x2?1. x > 02.x < 1Numbers:All numbers used are real numbers.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.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 specific to the problem are needed.Correct answer is option 'B'. Can you explain this answer?
Step 1 of solving this GMAT DS question: Understand the question stem and when the data is sufficient
What kind of an answer will the question fetch?
The question is an "Is" question. Answer to an "is" question is either YES or NO.
When is the data sufficient?
The data is sufficient if we are able to get a DEFINITE YES or a DEFINITE NO from the information given in the statements.
If from the statements we get an answer that x3 > x2 in some instances and it is otherwise in other instances, the data is NOT sufficient.
Step 2 of solving this GMAT DS question: Evaluate Statement (1) ALONE
Statement 1: x > 0
We know that x is a positive number.
Interval 1: If 0 < x < 1, then x3 < x2.
For example, (0.5)3 = 0.125, which is lesser than (0.5)2 = 0.25
The answer to the question is NO.
Interval 2: If x > 1, then x3 > x2
For example, 23 = 8 which is greater than 22 = 4
The answer to the question is YES.
We do NOT have a DEFINITE answer using statement 1.
Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C or E.
Step 3 of solving this GMAT DS question: Evaluate Statement (2) ALONE
Statement 2: x < 1
Interval 1: For positive values of x, i.e., 0 < x < 1, we know x3 < x2.
The answer to the question is NO.
Interval 2:For negative values of x, x3 will be a negative number and x2 will be a positive number.
Hence, x3 < x2
The answer to the question is NO.
Lastly, what is the answer if x = 0?
When x = 0, x3 = x2.
The answer to the question is NO.
Hence, if we know that x < 1, we can conclude that x3 is NOT GREATER THAN x2.
We have a DEFINITE answer, even if it is NO.
Statement 2 ALONE is sufficient. Eliminate choices C and E.

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