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

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Intern
Joined: 02 Aug 2011
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If n is an integer and n^3 is between 1 and 100 inclusive, [#permalink]

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10 Aug 2011, 13:56
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.

This is an example question from Manhattan Gmat Numbers Properties guide 1. When I initially did the question, I chose statement 1. as sufficient on its own.

Firstly, in the question stem you can narrow down the choices for n as being between 1 and 4. I then tested numbers in the equation in statement 1 and felt able to conclude that n was 3, as plugging any other integers higher than 1 for k made n>4. Statement 2 only allows me to narrow the choice down to 2 or 3 so its insufficient.
BUT when i read through the answer explanation, they dismiss statement 1 as only telling us that n is odd, meaning it leaves us with a choice of 1 or 3, therefore, you'd need both statements to be able to conclude that n was 3.

Could someone tell me where I went wrong?
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10 Aug 2011, 14:06
K can be zero and zero is an integer. Thus, I don't think statement 1 alone is sufficient.
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10 Aug 2011, 14:08
k might also have been a negative integer but given that n^3 is between 1 and 100, this part of the number line is ruled out.
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10 Aug 2011, 14:22
schemer wrote:
K can be zero and zero is an integer. Thus, I don't think statement 1 alone is sufficient.

yes, it can be zero! that'll give me 1 as the answer.
I guess I'm not out of the habit of think of integers as 1 and beyond. i don't think i'll forget the importance of the almighty zero from now on! thanks for the quick response.
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10 Aug 2011, 14:33
meshell wrote:
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.

This is an example question from Manhattan Gmat Numbers Properties guide 1. When I initially did the question, I chose statement 1. as sufficient on its own.

Firstly, in the question stem you can narrow down the choices for n as being between 1 and 4. I then tested numbers in the equation in statement 1 and felt able to conclude that n was 3, as plugging any other integers higher than 1 for k made n>4. Statement 2 only allows me to narrow the choice down to 2 or 3 so its insufficient.

BUT when i read through the answer explanation, they dismiss statement 1 as only telling us that n is odd, meaning it leaves us with a choice of 1 or 3, therefore, you'd need both statements to be able to conclude that n was 3.

Could someone tell me where I went wrong?

If n is an integer and n^3 is between 1 and 100 inclusive, what is the value of n

From the question n can be only be positive integers: either 1 or 2 or 3 or 4.

(1) If n = 2k +1, where k is an integer:
Here, k can only be 0 and 1 and n could be 1 or 3. not sufficient.

(2) If n is a prime number, n could be 2 or 3.

from 1 and 2, n is 3. So that's C.
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12 Aug 2011, 12:04
Fistail wrote:
meshell wrote:
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.

This is an example question from Manhattan Gmat Numbers Properties guide 1. When I initially did the question, I chose statement 1. as sufficient on its own.

Firstly, in the question stem you can narrow down the choices for n as being between 1 and 4. I then tested numbers in the equation in statement 1 and felt able to conclude that n was 3, as plugging any other integers higher than 1 for k made n>4. Statement 2 only allows me to narrow the choice down to 2 or 3 so its insufficient.

BUT when i read through the answer explanation, they dismiss statement 1 as only telling us that n is odd, meaning it leaves us with a choice of 1 or 3, therefore, you'd need both statements to be able to conclude that n was 3.

Could someone tell me where I went wrong?

If n is an integer and n^3 is between 1 and 100 inclusive, what is the value of n

From the question n can be only be positive integers: either 1 or 2 or 3 or 4.

(1) If n = 2k +1, where k is an integer:
Here, k can only be 0 and 1 and n could be 1 or 3. not sufficient.

(2) If n is a prime number, n could be 2 or 3.

from 1 and 2, n is 3. So that's C.

Can you pls help me understand why K will ONLY b "0" or "1"??
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12 Aug 2011, 12:09
DeeptiM wrote:
Can you pls help me understand why K will ONLY b "0" or "1"??

Because possible values of n = 1,2,3,4 (only there cubes will lie between 1 and 100)

and if n = 2k+1 => k = 1 (n = 3), 0 (n=1)
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14 Aug 2011, 17:48
1
KUDOS
 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.

[strike]n = -1, n^3 = -1[/strike]
[strike]n = 0, n^3 = 0[/strike]
n = 1, n^3 = 1
n = 2, n^3 = 8
n = 3, n^3 = 27
n = 4, n^3 = 64
[strike]n = 5, n^3 = 125[/strike]

1 <= n^3 <= 100, so 1 <= n <= 4.

Rephrase the question stem: "n = 1, 2, 3, or 4. What is n?"

Statement 1) "n is odd", so n could be 1 or 3. Insufficient.

Statement 2) n is prime, so n could be 2 or 3. Insufficient.

Combined) n is an odd prime number, so 3 is the only possibility. Sufficient.

[Reveal] Spoiler:
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15 Aug 2011, 09:09
c..
1. n can be 1 or 3 (when k=0 and 1 repectively)
2.n can be 2,3

combine both stmnts,we have n=3
Intern
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17 Aug 2011, 17:00
Yup .Its C.

We should not miss considering K=0.
Director
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17 Aug 2011, 19:18
n is an integer

n^3 lies between 1 and 100.

=> n can only be positive integer and n can be 1 or 2 or 3 or 4

1. Not Sufficient

n is odd integer => n can be 1 or 3

2. Not sufficient

n is 2 or 3

Together,

Its sufficient , n =3.

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17 Aug 2011, 19:56
anordinaryguy wrote:
DeeptiM wrote:
Can you pls help me understand why K will ONLY b "0" or "1"??

Because possible values of n = 1,2,3,4 (only there cubes will lie between 1 and 100)

and if n = 2k+1 => k = 1 (n = 3), 0 (n=1)

Ahh..revisited the ques n got to knw d mistake..

Thanks for the explanation..kudos to u!!
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19 Aug 2011, 21:47
+1 for C.

Agree with bodleyev's explanation. Kudos to him

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19 Aug 2011, 22:37
From Question n^3 is between 1 & 100 so n can not be negative
now 1^3=1
2^3=8
3^3=27
4^=64
values greater than 4 ruled out
1. n = 2k+1, not sufficient to identify the answer
2. n= Prime number not sufficient to identify the answer

combining both k can be 0 or 1 as we are restricted to values of n=1, 2, 3 & 4 so 4 is also ruled out we are left with 1, 2 & 3
Now A natural number is called a prime number (or a prime) if it is bigger than one and has no divisors other than 1 and itself.
So left with 2 & 3
now here k value becomes 1 so answer come to 3

Give Kudos if you understood it
Re: Number properties question   [#permalink] 19 Aug 2011, 22:37
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