Which of the following inequalities has a solution set that, when graphed on the number line, is a single segment of finite length ?
A x4 greater or equal 1
B x3 lesser or equal 27
C x2 greater or equal 16
D 2 lesser or equal|x|lesser or equal 5
E 2 lesser or equal 3x + 4 lesser or equal 6
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candygal79
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Hi candygal79,
The equations in this question can be physically drawn or handled as a Number Property concept:
Note that the question asks for a SINGLE SEGMENT of FINITE LENGTH. This means that the group of numbers that make up the solution set would be consecutive and limited (as opposed to non-consecutive and/or infinite).
Here are the Number Properties:
A: X^4 >= 1
X can be 1, 2, 3, etc. or -1, -2, -3, etc. This group of answers is infinite and non-consecutive. Eliminate A.
B: X^3 <= 27
X can be 3, 2, 1, 0, -1, etc. This group is infinite. Eliminate B.
C: X^2 >= 16
X can be 4, 5, 6, etc. or -4, -5, -6, etc. This group is infinite and non-consecutive. Eliminate C.
D: 2 <= |X| <= 5
X can be 2, 3, 4, 5 or -2, -3, -4, -5, This group is finite BUT non-consecutive. Eliminate D.
E: 2 <= 3X + 4 <= 6
Let's simplify with algebra...
-2 <= 3X <= 2
-2/3 <= X <= 2/3
X is a finite set of answers and the answers are consecutive. This is a MATCH to what we're looking for.
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
The equations in this question can be physically drawn or handled as a Number Property concept:
Note that the question asks for a SINGLE SEGMENT of FINITE LENGTH. This means that the group of numbers that make up the solution set would be consecutive and limited (as opposed to non-consecutive and/or infinite).
Here are the Number Properties:
A: X^4 >= 1
X can be 1, 2, 3, etc. or -1, -2, -3, etc. This group of answers is infinite and non-consecutive. Eliminate A.
B: X^3 <= 27
X can be 3, 2, 1, 0, -1, etc. This group is infinite. Eliminate B.
C: X^2 >= 16
X can be 4, 5, 6, etc. or -4, -5, -6, etc. This group is infinite and non-consecutive. Eliminate C.
D: 2 <= |X| <= 5
X can be 2, 3, 4, 5 or -2, -3, -4, -5, This group is finite BUT non-consecutive. Eliminate D.
E: 2 <= 3X + 4 <= 6
Let's simplify with algebra...
-2 <= 3X <= 2
-2/3 <= X <= 2/3
X is a finite set of answers and the answers are consecutive. This is a MATCH to what we're looking for.
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
