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If 1 < n < 0, which of the following expressions has the greatest val

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carcass
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If 1 < n < 0, which of the following expressions has the greatest val [#permalink] New post   16 Sep 2022, 00:31
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If −1 < n < 0, which of the following expressions has the greatest value?

(A) n
(B) n^2
(C) n^3
(D) (1 − n)^2
(E) (1 − n)^3

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Re: If 1 < n < 0, which of the following expressions has the greatest val [#permalink] New post   16 Sep 2022, 01:12
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for given range -1<n<0
n = -0.5
(A) n ; -0.5
(B) n^2 ; .25
(C) n^3; -.125
(D) (1 − n)^2 ; ( 2.25)
(E) (1 − n)^3 ; (3.3)
OPTION E is greatest


carcass wrote:
If −1 < n < 0, which of the following expressions has the greatest value?

(A) n
(B) n^2
(C) n^3
(D) (1 − n)^2
(E) (1 − n)^3

3
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Re: If 1 < n < 0, which of the following expressions has the greatest val [#permalink] New post   16 Sep 2022, 01:42
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carcass wrote:
If −1 < n < 0, which of the following expressions has the greatest value?

(A) n
(B) n^2
(C) n^3
(D) (1 − n)^2
(E) (1 − n)^3

Solution:
  • Apart from plugging an easy value like -0.5 or -0.2, there is a logical and faster way to approach this problem

  • We know n is negative, right?
  • If we look at options A, B and C, we will notice that option B has even power n thereby making is positive
  • Thus option B is definitely bigger than A and C and we can eliminate option A and C

  • Anothe thing to notice here is the range of n is −1 < n < 0 which means the value of 1 - n will always be positive and greater than 1
  • This means between options D and E, the later will be bigger because or higher power 3
  • Thus, we can eliminate option D

  • Now the choice is between options B and E
  • Option B is the square of numbers like -0.2, -0.5, -0.9 and so on. The value of which will only tend to touch 1
  • Whereas option E is the cube of 1 - n, which in itself is greater than 1


Hence the right answer is Option E
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Re: If 1 < n < 0, which of the following expressions has the greatest val [#permalink] New post   16 Sep 2022, 07:03
carcass wrote:
If −1 < n < 0, which of the following expressions has the greatest value?

(A) n
(B) n^2
(C) n^3
(D) (1 − n)^2
(E) (1 − n)^3



Looking at the answer choices, we can choose a value for n (plugging in purposes) which can help us remove options quickly, in this case it is: \(n = -0.2\)

We have squares in the answer choices so yes there is going to be positive answer choices and since we are searching for the greatest value, we can safely eliminate the answer choices which give us negative values

Options A and C eliminated

Now, between options B and D: B gives us \((-0.02)^2\), and D gives us \((1.2)^2\), thus eliminate B

D v/s E
D: \(1.2^2\)
E: \(1.2^3\)

We DO NOT need to calculate because for values > 1, number increases with increasing powers

Answer - E
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Re: If 1 < n < 0, which of the following expressions has the greatest val [#permalink]
16 Sep 2022, 07:03
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