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Last Month's Problem: "Dare to Compare"
<<<< This Month's Problem
x
< 0
Quantity A
2
^{x–1}
5
^{x+1}
Quantity B
3
^{x}
4
^{x–1}
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
x
is negative, and is found in the exponents of both quantities. To compare, set up a comparison or an implied inequality between the two quantities (represented for now by the double arrow), and simplify as much as possible.
Multiply both sides by 4 to eliminate the denominators, then continue simplifying.
If
x
could be 0, the simplified left side would equal exactly 10 × 1. Because the base is greater than 1 and the exponent is positive, the
part will always be greater than 1, so the simplified left side is always greater than 10, which is always greater than the 1 on the simplified right side.
The correct answer is A.
Debug Only:
Jchk