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Is n^2 < n^3 ? (1) n^2 < 1 (2) n^3 < 1

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gmat1220
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Is n^2 < n^3 ? (1) n^2 < 1 (2) n^3 < 1 [#permalink] New post   Updated on: 12 Jul 2021, 07:30
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A
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C
D
E

Difficulty:

65% (hard)

Question Stats:

49% (01:34) correct 51% (01:36) wrong based on 182 sessions
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Is n^2 < n^3 ?

(1) n^2 < 1

(2) n^3 < 1

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OA is E but I have to disagree. Pls verify this reasoning.

S1 tell us that -1 < n < 1

When n = 0 the answer is NO
When n = -0.5 the answer is NO
When n = 0.5 the answer is NO
Sufficient

S2 tells us that n < 1

When n = 0 the answer is NO
When n = -0.5 the answer is NO
When n = 0.5 the answer is NO
Sufficient

Answer D
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Official Answer
D

Originally posted by gmat1220 on 14 May 2011, 21:31.
Last edited by Bunuel on 12 Jul 2021, 07:30, edited 2 times in total.
Renamed the topic and edited the question.
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Re: Is n^2 < n^3 ? (1) n^2 < 1 (2) n^3 < 1 [#permalink] New post   14 May 2011, 22:26
St 1 - is n^2 < 1 means n is between 0 and 1
in that case n^2 will be less than n^3
sufficient

St 2 - is n^3 <1 means n could be a negative integer or could be a decimal.
so n^2 could be greater than or less than n^3
not sufficient.

Answer is A
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Re: Is n^2 < n^3 ? (1) n^2 < 1 (2) n^3 < 1 [#permalink] New post   14 May 2011, 23:54
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agdimple333 wrote:
St 1 - is n^2 < 1 means n is between 0 and 1
in that case n^2 will be less than n^3
sufficient

St 2 - is n^3 <1 means n could be a negative integer or could be a decimal.
so n^2 could be greater than or less than n^3
not sufficient.

Answer is A


Not correct. What if n lies between -1,1? then also n^2<1
--------------------------------

Is n^2 < n^3 ?
=> Is n^2 ( 1- n) < 0 ?
=> is n>1

St1 n^2<1 => n lies between -1,1
Sufficient, as the answer to " is n>1 " is no.

St2. n^3< 1 => n has to be less than 1.
Hence sufficient, as the answer is no.

Hence D
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Re: Is n^2 < n^3 ? (1) n^2 < 1 (2) n^3 < 1 [#permalink] New post   24 Apr 2016, 09:56
can I solve like this?
n^3>n^2
n>0
so def n^2<n^3
so A/D

n^3<1
so n^3-1<0
cannot say
so A

however, answer is D
so Bunuel is it n^3 < 1 OR
n^3 > 1
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Re: Is n^2 < n^3 ? (1) n^2 < 1 (2) n^3 < 1 [#permalink] New post   24 Apr 2016, 09:59
Expert Reply
paidlukkha wrote:
can I solve like this?
n^3>n^2
n>0
so def n^2<n^3
so A/D

n^3<1
so n^3-1<0
cannot say
so A

however, answer is D
so Bunuel is it n^3 < 1 OR
n^3 > 1


Is n^2 < n^3 ?

Notice that the question basically asks whether n > 1.

(1) n^2 < 1 --> -1 < n < 1. The answer to the question is NO. Sufficient.

(2) n^3 < 1 --> n < 1. The answer to the question is NO. Sufficient.

Answer: D.
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Re: Is n^2 < n^3 ? (1) n^2 < 1 (2) n^3 < 1 [#permalink] New post   28 Apr 2016, 14:04
Bunuel wrote:
paidlukkha wrote:
can I solve like this?
n^3>n^2
n>0
so def n^2<n^3
so A/D

n^3<1
so n^3-1<0
cannot say
so A

however, answer is D
so Bunuel is it n^3 < 1 OR
n^3 > 1


Is n^2 < n^3 ?

Notice that the question basically asks whether n > 1.

(1) n^2 < 1 --> -1 < n < 1. The answer to the question is NO. Sufficient.

(2) n^3 < 1 --> n < 1. The answer to the question is NO. Sufficient.

Answer: D.


Why have we not considered 0 as a possible value for n?? If n=0, then we do not have a clear answer..!!!

Please suggest.
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Re: Is n^2 < n^3 ? (1) n^2 < 1 (2) n^3 < 1 [#permalink] New post   28 Apr 2016, 14:22
Expert Reply
MeghaP wrote:
Bunuel wrote:
paidlukkha wrote:
can I solve like this?
n^3>n^2
n>0
so def n^2<n^3
so A/D

n^3<1
so n^3-1<0
cannot say
so A

however, answer is D
so Bunuel is it n^3 < 1 OR
n^3 > 1


Is n^2 < n^3 ?

Notice that the question basically asks whether n > 1.

(1) n^2 < 1 --> -1 < n < 1. The answer to the question is NO. Sufficient.

(2) n^3 < 1 --> n < 1. The answer to the question is NO. Sufficient.

Answer: D.


Why have we not considered 0 as a possible value for n?? If n=0, then we do not have a clear answer..!!!

Please suggest.


Even if n = 0 we still have the same NO answer to the question whether n^2 < N^3.
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Re: Is n^2 < n^3 ? (1) n^2 < 1 (2) n^3 < 1 [#permalink] New post   13 Oct 2022, 11:42
Bunuel wrote:
paidlukkha wrote:
can I solve like this?
n^3>n^2
n>0
so def n^2<n^3
so A/D

n^3<1
so n^3-1<0
cannot say
so A

however, answer is D
so Bunuel is it n^3 < 1 OR
n^3 > 1


Is n^2 < n^3 ?

Notice that the question basically asks whether n > 1.

(1) n^2 < 1 --> -1 < n < 1. The answer to the question is NO. Sufficient.

(2) n^3 < 1 --> n < 1. The answer to the question is NO. Sufficient.

Answer: D.


Bunuel can you elaborate as to how you arrived at n>1?
Also are we assuming n to be an integer here?
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Is n^2 < n^3 ? (1) n^2 < 1 (2) n^3 < 1 [#permalink] New post   13 Oct 2022, 19:18
Expert Reply
gmat1220 wrote:
Is n^2 < n^3 ?

(1) n^2 < 1

(2) n^3 < 1


\(n^2<n^3\)

As \(n^2\) is non negative, we can divide the two sides by \(n^2\).

\(\frac{n^3}{n^2}>1………n>1\)

Thus n>1 will give a yes, while \(n\leq 1\)will give a no. \(n\leq 1\) will include n=0 as well.

(1) \(n^2 < 1\)
This means \(|n|<1………..-1<n<1\)
So the answer for ‘Is n>1?’ is NO.
Sufficient

(2) \(n^3 < 1\)
Take cube root on both sides
n<1. Again answer is NO.
Sufficient


D
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Re: Is n^2 < n^3 ? (1) n^2 < 1 (2) n^3 < 1 [#permalink] New post   30 Nov 2023, 20:07
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Re: Is n^2 < n^3 ? (1) n^2 < 1 (2) n^3 < 1 [#permalink]
30 Nov 2023, 20:07
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