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# If n is an integer and n^3 is between 1 and 100, inclusive

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Schools: Admitted: IESE($$),HEC, RSM,Esade WE 1: 3.5 years international If n is an integer and n^3 is between 1 and 100, inclusive [#permalink] ### Show Tags 19 Oct 2010, 11:25 1 This post received KUDOS 1 This post was BOOKMARKED 00:00 Difficulty: 55% (hard) Question Stats: 56% (01:08) correct 44% (01:00) wrong based on 101 sessions ### HideShow timer Statistics If n is an integer and n^3 is between 1 and 100, inclusive, what is the value of n? (1) n = 2k+1, where k is an integer. (2) n is a prime number. Need help on this question which is explained in the Number Properties book by Manhattan. According to Manhattan, the OA is C, but to me, the OA should be A. We know that n>0 because n^3 is between 1 and 100, so n is a positive integer. The value of n could be 1, 2, 3, and 4. Statement 1: n = 2k+1. So n is an odd number. So n is either 1 or 3. According to MGMAT, statement 1 is not sufficient to answer the question because n could be either 1 or 3 and so there is not a unique value of n as it yields two possible values. But this is where I beg to differ. According to me, the value of n could be only 3 (n = 2*1+1). Tell me where I am wrong. [Reveal] Spoiler: OA Kudos [?]: 99 [1], given: 18 Math Expert Joined: 02 Sep 2009 Posts: 42305 Kudos [?]: 133080 [2], given: 12403 Re: DS: MGMAT Number Properties [#permalink] ### Show Tags 19 Oct 2010, 12:00 2 This post received KUDOS Expert's post shekharvineet wrote: Need help on this question which is explained in the Number Properties book by Manhattan. According to Manhattan, the OA is C, but to me, the OA should be A. If n is an integer and n^3 is between 1 and 100, inclusive, what is the value of n? (1). n = 2k+1, where k is an integer. (2). n is a prime number. We know that n>0 because n^3 is between 1 and 100, so n is a positive integer. The value of n could be 1, 2, 3, and 4. Statement 1: n = 2k+1. So n is an odd number. So n is either 1 or 3. According to MGMAT, statement 1 is not sufficient to answer the question because n could be either 1 or 3 and so there is not a unique value of n as it yields two possible values. But this is where I beg to differ. According to me, the value of n could be only 3 (n = 2*1+1). Tell me where I am wrong. If n is an integer and n^3 is between 1 and 100, inclusive, what is the value of n? $$n$$ is an integer and $$n^3$$ is between 1 and 100, inclusive, means that $$n$$ could be 1, 2, 3 or 4 (but not 5 or more since 5^3=125>100). (1) n = 2k+1, where k is an integer --> $$n$$ is an odd number --> $$n$$ could be 1 or 3. Not sufficient. (2) n is a prime number --> $$n$$ could be 2 or 3. Not sufficient. (1)+(2) $$n$$ could be only 3. Sufficient. Answer: C. As for your doubt: $$n=2k+1$$, where $$k$$ is an integer is a fromula of odd number so you can get ANY odd number with it, including 1: if $$k=0$$ then $$n=2k+1=1$$. Hope it helps. _________________ Kudos [?]: 133080 [2], given: 12403 Manager Joined: 24 Aug 2010 Posts: 187 Kudos [?]: 99 [0], given: 18 Location: Finland Schools: Admitted: IESE($$),HEC, RSM,Esade
WE 1: 3.5 years international
Re: DS: MGMAT Number Properties [#permalink]

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19 Oct 2010, 12:21
Thanks.
It cleared my doubt, especially the last part in your solution where you talk about the value of the integer k. I simply forgot the fact that 0 is and integer and so n could be 1 or 3. thats the reason why I was getting 3 as the only value of n from the 1st statement.
+1 to you.

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Re: DS: MGMAT Number Properties [#permalink]

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20 Oct 2010, 06:11
(1) n = 2k+1, where k is an integer -->

so K can take ----- -4 -3 -2 -1 0 1 2 3 4 ----
but if i take any negative it wont be between 1 and 100 as a power cube..
so negative numbers out.
from n = 2K + 1 ===> k should be either 0 or 2 if it is 3 then n =
so i should consider only 0,1,2,3,.....

but n = 2k + 1 and n^3 is between 1 and 100 inclusive... there could be a chance of 2 values for n

if k = 0, then n = 1 ===> n^3 =1 <= 100
K = 1, then n= 3 ===> n^3 = 27 <= 100
k = 2 then n = 5 ====> n^3 = 5^3 = 125 > 100

So from 1 only 2 possible values 1 and 3 for the N

(2) n is a prime number --> could be 2 or 3 -->

So the n value from the both (1) and (2) is 3

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Re: doubt on question from manhattangmat book number properties [#permalink]

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05 Jun 2012, 12:34
1
KUDOS
given n*n*n = inclusive 1 - 100
St.1 ) n = 2k+1
implies n is odd and n*n*n = 1 - 100,
n= 1, 3 - NOT sufficient

St.2) n=prime no.
implies n= 2,3 (as again n*n*n = 1- 100) NOT sufficient

St.1) and St. 2) = 3, sufficient.

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Re: doubt on question from manhattangmat book number properties [#permalink]

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05 Jun 2012, 14:40
kashishh wrote:
given n*n*n = inclusive 1 - 100
St.1 ) n = 2k+1
implies n is odd and n*n*n = 1 - 100,
n= 1, 3 - NOT sufficient

St.2) n=prime no.
implies n= 2,3 (as again n*n*n = 1- 100) NOT sufficient

St.1) and St. 2) = 3, sufficient.

thanks a lot......i need 1 more help....while solving quant section,most of my questions on inequalities,probablity,standard deviation etc are always gettin wrong....ny idea from where should i study these......

regards,
mudit
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Re: If n is an integer and n^3 is between 1 and 100, inclusive [#permalink]

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22 Jul 2014, 04:54
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Re: If n is an integer and n^3 is between 1 and 100, inclusive   [#permalink] 22 Jul 2014, 04:54
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