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If n is an integer and n^3 is between 1 and 100 inclusive, [#permalink]
10 Aug 2011, 12:56

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.

Re: Number properties question [#permalink]
10 Aug 2011, 13:22

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.

Re: Number properties question [#permalink]
10 Aug 2011, 13:33

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.

Re: Number properties question [#permalink]
12 Aug 2011, 11:04

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"??

Re: Number properties question [#permalink]
19 Aug 2011, 21:37

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

So C is right Answer

Give Kudos if you understood it

gmatclubot

Re: Number properties question
[#permalink]
19 Aug 2011, 21:37