If n is positive, is n an integer?

Question

(1)  \sqrt{n}≠ integer

(2)  \sqrt{n}<1

Kudos for a correct  solution .

TheKingInTheNorth · Answer

If n is positive, is n an integer?

(1) √n ≠ integer

Take n=1 (integer) then √n = integer 
take n=2 (integer) then √n not equal an integer .

Hence not sufficient

(2) √n<1

For all positive integer n ...√n is always greater than 1.

So if √n<1 then n is not an integer .

Hence B ans

Jonas84 · Answer

I believe the answer is B. Please see below for explanation.

0) Question asks if n an integer and tell us that n>0 this means n could either be an integer or a decimal.

I used the plug in numbers approach

(1) √n ≠ integer

if n = 2 -> √2 = 1.4 statement one true and question also true.
if n = 1/4 -> √1/4 = decimal statement one true and question not true.

we have two possibilities so statement 1 insufficient.

(2) √n<1

the only numbers that the square root is less than 1 are decimal numbers.

Answer b

rakshithbabu · Answer

Stmt1:  \sqrt{n}≠ integer 
This does not give concluding result.
eg: n=2 gives sqrt{n} = 1.4 which is not an integer.
and n=0.36 gives sqrt{n} = 0.6 which is also not an integer.

Hence n can either be integer or non integer.
-> not suff

Stmt2:  \sqrt{n}<1 
We know that sqrt{n} >=1 for all positive integers.
Hence n cannot be an integer. 
-> Suff

Answer:B

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If n is positive, is n an integer?

(1) n √ ≠integer

(2) n √ <1

There is one variable (n) and 2 equations are given, making (D) our likely answer.
Looking at the conditions,
condition 1) the condition answers the question 'yes' when sqrt (n)=sqrt(2), n=2, but 'no' when sqrt (n)=1/2, n=(1/2)^2=1/4. So this condition is insufficient.
From condition 2, the condition answers the question 'no' as sqrt (n)<1, n<1^1=1, n<1 always gives a fraction. So this is a sufficient condition, and the answer therefore becomes (B).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

ravi2107 · Answer

What about n=0 in the second statement.In that case n can be integer right ? n >0 and n^1/2 <1 ,in that case n can be 0 also..please clarify my query ?

Bunuel · Answer

Check the stem:  If n is positive , is n an integer?

0 is neither positive nor negative.

nikhilbansal08 · Answer

(1) n√≠integern≠integer

N has positive values (Given) but it can be a fraction or Integer number .. hence not sufficient.

(2) n√<1

If square root of a positive number has to be less than one than for sure the number n has to be fraction.. Thus for sure the number is not an integer.

Hence answer is B

hsbinfy · Answer

B

1)take n=35 which gives no and n=36 which gives yes

2)sqrtn<1

squaring both sides

n<1

since n is postive the range of n here is 0<n<1
Sufficient

ravi2107 · Answer

Oops !! Sorry I didnt see properly. Anyways Thanks !!

shashanksagar · Answer

Imo B. Only sqrt of a positive number less than one would be less tha one.

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If n is positive, is n an integer?

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If n is positive, is n an integer?

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