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

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Manager
Joined: 24 Aug 2010
Posts: 113
Location: Finland
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, what is [#permalink] ### Show Tags 19 Oct 2010, 10:25 2 1 00:00 Difficulty: 45% (medium) Question Stats: 64% (01:23) correct 36% (01:22) wrong based on 142 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. Math Expert Joined: 02 Sep 2009 Posts: 61385 If n is an integer and n^3 is between 1 and 100, inclusive, what is [#permalink] ### Show Tags 19 Oct 2010, 11:00 2 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$$ is between 1 and 100, inclusive, means that n could be 1, 2, 3 or 4 (but not 5 or more since 5^3 = 125 > 100). (1) n = 2k+1, where k is an integer --> n is an odd number --> n could be 1 or 3. Not sufficient. (2) n is a prime number --> n could be 2 or 3. Not sufficient. (1)+(2) n could be only 3. Sufficient. Answer: C. shekharvineet wrote: Need help on this question which is explained in the Number Properties book by Manhattan. According to Manhattan, the OA is C, but to me, the OA should be A. If n is an integer and n^3 is between 1 and 100, inclusive, what is the value of n? (1). n = 2k+1, where k is an integer. (2). n is a prime number. We know that n>0 because n^3 is between 1 and 100, so n is a positive integer. The value of n could be 1, 2, 3, and 4. Statement 1: n = 2k+1. So n is an odd number. So n is either 1 or 3. According to MGMAT, statement 1 is not sufficient to answer the question because n could be either 1 or 3 and so there is not a unique value of n as it yields two possible values. But this is where I beg to differ. According to me, the value of n could be only 3 (n = 2*1+1). Tell me where I am wrong. As for your doubt: $$n=2k+1$$, where k is an integer is a formula of an odd number so you can get ANY odd number with it, including 1: if k = 0 then $$n=2k+1=1$$. Hope it helps. _________________ Manager Joined: 24 Aug 2010 Posts: 113 Location: Finland Schools: Admitted: IESE($$),HEC, RSM,Esade
WE 1: 3.5 years international
Re: If n is an integer and n^3 is between 1 and 100, inclusive, what is  [#permalink]

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19 Oct 2010, 11:21
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.
Manager
Joined: 25 Aug 2010
Posts: 54
Re: If n is an integer and n^3 is between 1 and 100, inclusive, what is  [#permalink]

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20 Oct 2010, 05:11
(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
Manager
Joined: 02 Jun 2011
Posts: 111
Re: If n is an integer and n^3 is between 1 and 100, inclusive, what is  [#permalink]

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05 Jun 2012, 11:34
1
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.

Intern
Joined: 30 Apr 2012
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Location: India
Concentration: Finance, Human Resources
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Re: If n is an integer and n^3 is between 1 and 100, inclusive, what is  [#permalink]

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05 Jun 2012, 13:40
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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Joined: 09 Sep 2013
Posts: 14120
Re: If n is an integer and n^3 is between 1 and 100, inclusive, what is  [#permalink]

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13 Dec 2017, 22:38
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Re: If n is an integer and n^3 is between 1 and 100, inclusive, what is   [#permalink] 13 Dec 2017, 22:38
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