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n is a positive odd integer

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Carcass
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n is a positive odd integer [#permalink] New post   26 May 2024, 22:02
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n is a positive odd integer, \(a = \frac{n-1}{2}\) and \(b = \frac{n+1}{2}\)


Quantity A
Quantity B
\(-2^a\)
\(-2^b \)




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D
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B
LuisMartinez
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Re: n is a positive odd integer [#permalink] New post   27 May 2024, 15:03
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Okay, if we make a table I think it would be easier.
n=1
a=0
b=1
A= -2^0=-1
B=-2^1= -2

n=3
a=1
b=2
A= -2^1=-2
B= -2^2=-4

Since a is always going to be smaller than b, the correct answer is A. The tricky part is differentiating -2^n and (-2)^n (I fell for it haha)
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steveharvi
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Re: n is a positive odd integer [#permalink] New post   02 Jun 2024, 01:31
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LuisMartinez wrote:
Okay, if we make a table I think it would be easier.
n=1
a=0
b=1
A= -2^0=-1
B=-2^1= -2

n=3
a=1
b=2
A= -2^1=-2
B= -2^2=-4

Since a is always going to be smaller than b, the correct answer is A. The tricky part is differentiating -2^n and (-2)^n (I fell for it haha)


-2^0 is 1 not -1, -2^2 is 4 not -4 answer should be D,
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Re: n is a positive odd integer [#permalink] New post   03 Jun 2024, 09:36
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The book reports A as answer but I agree is D

If we pick up 1 as odd number

a=0 and b =1

QA is 1 and QB is -2

A>B

However if we pick up 3

a=1 and b=2

QA= -2 and QB =4

D should be the answer
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defender007
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Re: n is a positive odd integer [#permalink] New post   17 Jul 2024, 00:26
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Easy Rule

We can remember this always Odd x Odd= Odd
Even + or - Odd = Odd

Every other operation except division results in an even number.

Now considering this a and b can either be odd or even given there is a division by 2. we just know that numerator is even in the expressions. so we cannot determine the signs of the quantity and compare.

Hence D should be the answer. Hope this helps.
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n is a positive odd integer [#permalink] New post   17 Jul 2024, 04:01
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ans is A
minus (-) sign is not powered, its just the numbers.
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KurtMeyer
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Re: n is a positive odd integer [#permalink] New post   20 Jan 2025, 04:07
shaunpant wrote:
ans is A
minus (-) sign is not powered, its just the numbers.


That is right.
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Re: n is a positive odd integer [#permalink] New post   20 Jan 2025, 04:10
defender007 wrote:
Easy Rule

We can remember this always Odd x Odd= Odd
Even + or - Odd = Odd

Every other operation except division results in an even number.

Now considering this a and b can either be odd or even given there is a division by 2. we just know that numerator is even in the expressions. so we cannot determine the signs of the quantity and compare.

Hence D should be the answer. Hope this helps.


No.

Parentheses are of utmost importance in terms of which an even exponent can be powering the signs.
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KurtMeyer
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n is a positive odd integer [#permalink] New post   20 Jan 2025, 04:10
Carcass wrote:
The book reports A as answer but I agree is D

If we pick up 1 as odd number

a=0 and b =1

QA is 1 and QB is -2

A>B

However if we pick up 3

a=1 and b=2

QA= -2 and QB =4

D should be the answer


I am totally correct in this case. Answer must be D due to absence of the brackets.
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n is a positive odd integer [#permalink]
20 Jan 2025, 04:10
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