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# What is the value of the positive integer n ?

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What is the value of the positive integer n ? [#permalink]

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03 Jan 2014, 06:17
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

What is the value of the positive integer n ?

(1) n^4 < 25
(2) $$n\neq{n^2}$$

Data Sufficiency
Question: 18
Category: Arithmetic Arithmetic operations
Page: 154
Difficulty: 600

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Re: What is the value of the positive integer n ? [#permalink]

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03 Jan 2014, 06:17
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SOLUTION

What is the value of the positive integer n ?

Notice that we are told that n is a $$positive integer$$.

(1) n^4 < 25. Since n is a positive integer, then n can be 1 or 2. Not sufficient.

(2) $$n\neq{n^2}$$ --> $$n)\neq{1}$$. Not sufficient.

(1)+(2) Since from (2) $$n)\neq{1}$$, then from (1) n=2. Sufficient.

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Re: What is the value of the positive integer n ? [#permalink]

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03 Jan 2014, 12:24
2
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

What is the value of the positive integer n ?

(1) n^4 < 25
(2) $$n\neq{n^2}$$

Data Sufficiency
Question: 18
Category: Arithmetic Arithmetic operations
Page: 154
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

Its C..

STATEMENT 1===== n4<25.. n can 1 AND 2.. 1^4=1 that is less than 25. N2=16 that is less than 25.

Statement 2====== n is not equal to n2 .. from this we can say this n is not 1..bt we dont knw n cud be 2 ,3 or 4 not sufficient.

Both statement togather are sufficient. n is 2 because from statement 1 we got that n cud be 2 or 1 ..and from statement 2 we got that n can not 1..so n is 2..sufficient.
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Re: What is the value of the positive integer n ? [#permalink]

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04 Jan 2014, 10:31
1. The 2 numbers that have 4th power less than 25 are 1 and 2; 1 and 16
2. From this, n is anything but 1;

Both together, clearly, gives the value as 2. Sufficient.

(C).
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Re: What is the value of the positive integer n ? [#permalink]

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05 Jan 2014, 11:33
1
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

What is the value of the positive integer n ?

(1) n^4 < 25
(2) $$n\neq{n^2}$$

Statement 1) n^4 < 25, both the values of n = 1 or 2 satisfies the statement. Not Sufficient.
Statement 2) n is not equal to n^2. We cannot determine any value of n from this statement. Not Sufficient.

Combining the two statement, only n = 2 satisfies both the condition. Hence Option C)
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Re: What is the value of the positive integer n ? [#permalink]

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05 Jan 2014, 12:12
SOLUTION

What is the value of the positive integer n ?

Notice that we are told that n is a $$positive integer$$.

(1) n^4 < 25. Since n is a positive integer, then n can be 1 or 2. Not sufficient.

(2) $$n\neq{n^2}$$ --> $$n)\neq{1}$$. Not sufficient.

(1)+(2) Since from (2) $$n)\neq{1}$$, then from (1) n=2. Sufficient.

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Re: What is the value of the positive integer n ? [#permalink]

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18 Sep 2015, 03:08
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What is the value of the positive integer n ? [#permalink]

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20 Sep 2015, 00:59
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.

What is the value of the positive integer n ?

(1) n^4 < 25
(2) n≠n 2

In the original condition there is 1 variable (n) and in order to match the number of variable and equation, we need 1 equation. Since there is 1 each in 1) and 2), D has high probability of being the answer.

in case of 1), n=1,2 the answer is not unique, therefore the condition is NOT sufficient.
in case of 2), n=2,3.4.... and the answer is not unique. therefore the condition is NOT sufficient.
Using both 1) & 2) together, the answer is unique and therefore the conditions are sufficient. Thus the answer is C

Normally 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 D has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) separately. Here, there is 59 % chance that D is the answer, while A or B has 38% chance. There is 3% chance that C or E is the answer for the case. Since D is most likely to be the answer according to DS definition, we solve the question assuming D would be our answer hence using 1) and 2) separately. Obviously there may be cases where the answer is A, B, C or E.
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Re: What is the value of the positive integer n ? [#permalink]

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20 Sep 2015, 07:53
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.

What is the value of the positive integer n ?

(1) n^4 < 25
(2) n≠n 2

In the original condition there is 1 variable (n) and in order to match the number of variable and equation, we need 1 equation. Since there is 1 each in 1) and 2), D has high probability of being the answer.

in case of 1), n=1,2 the answer is not unique, therefore the condition is NOT sufficient.
in case of 2), n=2,3.4.... and the answer is not unique. therefore the condition is NOT sufficient.
Using both 1) & 2) together, the answer is unique and therefore the conditions are sufficient. Thus the answer is C

Normally 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 D has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) separately. Here, there is 59 % chance that D is the answer, while A or B has 38% chance. There is 3% chance that C or E is the answer for the case. Since D is most likely to be the answer according to DS definition, we solve the question assuming D would be our answer hence using 1) and 2) separately. Obviously there may be cases where the answer is A, B, C or E.

Hi,
using 1 and 2 separately is true for any of the options... be it A,B,C,D,E..
i do not think the observation of any two equations given would be the same.. equality and inequality of equations will have a great say on the possiblity of that equation giving us the answer so 59% may not be true for eq using < or >...
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Re: What is the value of the positive integer n ?   [#permalink] 20 Sep 2015, 07:53
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