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by Brent@GMATPrepNow » Wed Sep 03, 2014 3:32 am
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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by GMATinsight » Wed Sep 03, 2014 3:35 am
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

OAc
We check with options

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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by madi080 » Tue Aug 29, 2017 9:51 am
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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by Jay@ManhattanReview » Tue Aug 29, 2017 10:01 pm
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!

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