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# If n is positive, is n an integer?

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Math Expert
Joined: 02 Sep 2009
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If n is positive, is n an integer?  [#permalink]

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24 Sep 2015, 22:33
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70% (01:14) correct 30% (01:06) wrong based on 144 sessions

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If n is positive, is n an integer?

(1) $$\sqrt{n}≠ integer$$

(2) $$\sqrt{n}<1$$

Kudos for a correct solution.

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Re: If n is positive, is n an integer?  [#permalink]

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24 Sep 2015, 23:32
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
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Re: If n is positive, is n an integer?  [#permalink]

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28 Sep 2015, 11:05

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.

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Re: If n is positive, is n an integer?  [#permalink]

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24 Oct 2015, 22:07
Bunuel wrote:
If n is positive, is n an integer?

(1) $$\sqrt{n}≠ integer$$

(2) $$\sqrt{n}<1$$

Kudos for a correct solution.

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

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Re: If n is positive, is n an integer?  [#permalink]

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26 Oct 2015, 01:21
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.
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Re: If n is positive, is n an integer?  [#permalink]

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07 Jul 2016, 06:10
MathRevolution wrote:
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.

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 ?
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Re: If n is positive, is n an integer?  [#permalink]

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07 Jul 2016, 06:12
ravi2107 wrote:
MathRevolution wrote:
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.

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 ?

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

0 is neither positive nor negative.
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Re: If n is positive, is n an integer?  [#permalink]

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07 Jul 2016, 06:56
(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.

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Re: If n is positive, is n an integer?  [#permalink]

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07 Jul 2016, 07:20
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
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Re: If n is positive, is n an integer?  [#permalink]

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07 Jul 2016, 09:13
Bunuel wrote:
ravi2107 wrote:
MathRevolution wrote:
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.

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 ?

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

0 is neither positive nor negative.

Oops !! Sorry I didnt see properly. Anyways Thanks !!
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Re: If n is positive, is n an integer?  [#permalink]

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07 Jul 2016, 09:14
Imo B. Only sqrt of a positive number less than one would be less tha one.

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Re: If n is positive, is n an integer?  [#permalink]

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09 Jun 2018, 02:19
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Re: If n is positive, is n an integer? &nbs [#permalink] 09 Jun 2018, 02:19
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