GMAT Math : Exponents
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Example Questions
Example Question #2921 : Gmat Quantitative Reasoning
is a number not in the set .
Of the elements , which is the greatest?
Statement 1: is a negative number.
Statement 2:
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Assume both statements are known. The greatest of the three numbers must be or , since even powers of negative numbers are positive and odd powers of negative numbers are negative.
Case 1:
Case 2: ,
then
In both cases, is negative and , but in one case, is the greatest number, and in the other, is. The two statements together are inconclusive.
Example Question #801 : Data Sufficiency Questions
Philip has been assigned to write one number in the circle and one number in the square in the diagram below in order to produce a number in scientifc notation.
.
Did Philip succeed?
Statement 1: Philip wrote in the circle.
Statement 2: Philip wrote in the square.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
A number in scientific notation takes the form
where and is an integer of any sign.
Statement 1 alone proves that Philip entered a correct number into the circle, since . Statement 2 alone proves that he entered a correct number into the square, since is an integer. But each statement alone is insufficient, since each leaves uinclear whether the other number is valid. The two statements together, however, prove that Philip put correct numbers in both places, thereby writing a number in scientific notation.
Example Question #801 : Data Sufficiency Questions
is an integer. Is there a real number such that ?
Statement 1: is negative
Statement 2: is even
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
The equivalent question is "does have a real root?"
If you know only that is negative, you need to know whether is even or odd; negative numbers have real odd-numbered roots, but not real even-numbered roots.
If you know only that is even, you need to know whether is negative or nonnegative; negative numbers do not have real even-numbered roots, but nonnegative numbers do.
If you know both, however, then you know that the answer is no, since as stated before, negative numbers do not have real even-numbered roots.
Therefore, the answer is that both statements together are sufficient to answer the question, but neither statement alone is sufficient to answer the question.
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