Hi madi080,
The following rules must be clear before to attempt this question.
1. (±x)^(even) => A positive number; the sign of x does not matter
Example: a. (2)^2 = + 4; b. (-2)^2 = + 4
2a. (+x)^(odd) => A positive number
Example: a. (+2)^3 = + 8
2b. (-x)^(odd) => A negative number
Example: a. (-2)^3 = - 8
So, if the exponent is odd, the sign of base will determine whether the resultant number of positive or negative.
Let's see the question now.
If a and b are nonzero integers, which of the following must be negative?
A)(-a)^-2b
B)(-a)^-3b
C)-(a^-2b)
D)-(a^-3b)
E)None of these
We have a and b are nonzero integers, thus, a and b can positive or negative integers.
Let's discuss each option one by one.
A)(-a)^(-2b)
Since the exponent -2b is an even number, the sign of the base a will not matter, thus (-a)^(-2b) will be positive.
B)(-a)^(-3b)
Since the exponent -3b is an odd number, the sign of the base a will matter, thus (-a)^(-3b) can be positive or negative.
C)-[a^(-2b)]
Since the exponent -2b is an even number, the sign of the base a will not matter, thus [(-a)^(-2b)] will be positive, thus the sign of -[(-a)^(-2b)] will be negative. The correct answer.
D)-[a^(-3b)]
Since the exponent -3b is an odd number, the sign of the base a will matter, thus (-a)^(-3b) can be positive or negative, thus, the sign of -[a^(-3b)] can be positive or negative.
The correct answer:
C
Hope this helps!
Download free ebook:
Manhattan Review GMAT Quantitative Question Bank Guide
-Jay
_________________
Manhattan Review GMAT Prep
Locations:
New York |
Barcelona |
Manila |
Melbourne | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor!
Click here.
