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D
Carcass
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Joined: 18 Apr 2015
Posts: 18279
GRE 1: Q160 V160
n < - 1 [#permalink] New post  20 Oct 2017, 02:45
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\(n < - 1\)

Quantity A
Quantity B
\(n^2 * n^4\)
\((n^2)^4\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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IlCreatore
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Re: n < - 1 [#permalink] New post  20 Oct 2017, 04:56
2
Quantity A is equal to \(n^2*n^4 = n^{2+4} = n^6\). While quantity B is equal to \((n^2)^4 = n^{2*4} = n^8\). Thus, since the exponents are positive, the higher the exponent, the higher the quantity. Then, quantity B is greater!
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shahab1987
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Re: n < - 1 [#permalink] New post  27 Feb 2019, 22:31
I think the answer should be D, because when we put -1/2 A is bigger than B and if we put -2 so B is bigger than A, so i think the answer should be D
please help me
It is kind of you!
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Carcass
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Joined: 18 Apr 2015
Posts: 18279
GRE 1: Q160 V160
Re: n < - 1 [#permalink] New post  28 Feb 2019, 01:07
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QA is \(n^6\)

QB is \(n^8\)

Even you plug in a quantity < -1 such as \(\frac{3}{2} = 1.5\) the result will be in the first case 11.39 and in the second quantity 25.6.

So the answer is always B

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chetan2u
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Re: n < - 1 [#permalink] New post  28 Feb 2019, 09:46
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shahab1987 wrote:
I think the answer should be D, because when we put -1/2 A is bigger than B and if we put -2 so B is bigger than A, so i think the answer should be D
please help me
It is kind of you!



Hi, we are looking for n<-1..

when you take n as -1/2, it is >-1, and thus outside the range n<-1.
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html
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GreenlightTestPrep
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Re: n < - 1 [#permalink] New post  28 Feb 2019, 09:58
1
Expert Reply
Carcass wrote:



\(n < - 1\)

Quantity A
Quantity B
\(n^2 * n^4\)
\((n^2)^4\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Given:
Quantity A: (n²)(n⁴)
Quantity B: (n²)⁴

Simplify:
Quantity A: n⁶
Quantity B: n⁸

From here, we can solve this question using matching operations

Since n⁶ must be POSITIVE, we can safely divide both quantities by n⁶ to get:
Quantity A: 1
Quantity B: n²

Since n < -1, we know that n² is greater than 1

Answer: B

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