Guys ,
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
OAc
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j_shreyans
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Brent@GMATPrepNow
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j_shreyans wrote:Guys ,
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
IMPORTANT CONCEPT
Rule #1: EVEN powers are always greater than or equal to zero. So, (POSITIVE value)^(EVEN integer) > 0, and (NEGATIVE value)^(EVEN integer) > 0
So, the correct answer here is C
C. -[a^(-2b)]
Since b is an integer, we know that -2b is an EVEN integer.
So, we get: -[a^(EVEN integer)]
By our rule, a^(EVEN integer) is greater than or equal to zero
Since a is a NON-zero integer, we can conclude that a^(EVEN integer) is GREATER THAN zero
In other words, a^(EVEN integer) is POSITIVE
This means that -[a^(EVEN integer)] is NEGATIVE
Cheers,
Brent
Last edited by Brent@GMATPrepNow on Wed Sep 03, 2014 3:52 am, edited 1 time in total.
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GMATinsight
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We check with optionsj_shreyans wrote:Guys ,
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
OAc
Option A) (-a)^-2b
for a = 1 and b = 1, (-a)^-2b = 0 therefore Not a negative number necessarily
Option B)(-a)^-3b
for a = 1 and b = 1, (-a)^-3b = 1 therefore Not a negative number necessarily
Option C)-(a^-2b)
for a = 1 and b = 1, (-a)^-3b = -1 therefore a negative number necessarily
In fact for any value of b the result will be -ve as the ive sign is outside the paranthesis
Option D)-(a^-3b)
for a = -1 and b = 1, (-a)^-3b = 1 therefore NOT a negative number necessarily
Option E) None
Answer: Option C
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Brent@GMATPrepNow wrote:j_shreyans wrote:Guys ,
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
IMPORTANT CONCEPT
Rule #1: EVEN powers are always greater than or equal to zero. So, (POSITIVE value)^(EVEN integer) > 0, and (NEGATIVE value)^(EVEN integer) > 0
So, the correct answer here is C
C. -[a^(-2b)]
Since b is an integer, we know that -2b is an EVEN integer.
So, we get: -[a^(EVEN integer)]
By our rule, a^(EVEN integer) is greater than or equal to zero
Since a is a NON-zero integer, we can conclude that a^(EVEN integer) is GREATER THAN zero
In other words, a^(EVEN integer) is POSITIVE
This means that -[a^(EVEN integer)] is NEGATIVE
Cheers,
Brent
Could you explain in the same way why each one is wrong
Thanks in advance
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Jay@ManhattanReview
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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.
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.
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.
We have a and b are nonzero integers, thus, a and b can positive or negative integers.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
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.
