Data sufficiency question

[mneeti]

In Manhattan Guide 1 - Number properties, page - 100, in testing numbers; the data sufficiency question is:

If n is an integer and n^3 is between 1 to 100, inclusive what is the value of n>
(1) n=2k+1, where k is an integer.
(2) n is a prime number

When I solved the question i found that (1) alone is sufficient to answer.
There are only four no.s i.e 1,2,3,4 whose power if raised to 3 gives result between 1 to 100. Further, only integer 3 is the result of the equation in (1) which satisfies the given problem. e.g if you put 1 as k you get n=3 , if you put 2 as k you get n=5 which is not a solution at all as 5^3 is 125. Further more, if k= -1, n=-1 and -1^3=-1 which is also not fitting into the required solution. We are only left with answer 3. Therefore, i see that (1) alone is sufficient. But that guide says that (1) & (2) together satisfy it.

Please explain where i am going wrong in solving this?

[stud.jatt]

You forgot that the set of integers includes 0 also,
substitute k = 0 and you get n = 1 and hence statement (1) alone is insufficient.

In Manhattan Guide 1 - Number properties, page - 100, in testing numbers; the data sufficiency question is:

If n is an integer and n^3 is between 1 to 100, inclusive what is the value of n>
(1) n=2k+1, where k is an integer.
(2) n is a prime number

When I solved the question i found that (1) alone is sufficient to answer.
There are only four no.s i.e 1,2,3,4 whose power if raised to 3 gives result between 1 to 100. Further, only integer 3 is the result of the equation in (1) which satisfies the given problem. e.g if you put 1 as k you get n=3 , if you put 2 as k you get n=5 which is not a solution at all as 5^3 is 125. Further more, if k= -1, n=-1 and -1^3=-1 which is also not fitting into the required solution. We are only left with answer 3. Therefore, i see that (1) alone is sufficient. But that guide says that (1) & (2) together satisfy it.

Please explain where i am going wrong in solving this?

[pranabiitkgp]

STUD is correct . Please note the wording in the qs, which says "inclusive".

Another thing to remember : 1 is neither prime nor composite .

Hence combining 1 & 2 ,we get the value 3 and hence the ans is C>.

Thanks,
VCG

[RonPurewal]

i have moved this thread to the correct folder. (please do not post MGMAT questions in the GMAT PREP folder in the future; if you do so again, we will delete the thread.)

i think you're making the mistake of assuming that k also must be greater than 0.
if so, that's not the case -- n is restricted to the values 1, 2, 3, and 4, but k isn't.

so, for statement 1, both n = 1 (which corresponds to k = 0) and n = 3 (which corresponds to k = 1) fulfill the statement. that's two different n's, so statement 1 is insufficient.