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# What is the value of positive integer n?

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

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28 Feb 2011, 02:31
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What is the value of positive integer n?

(1) n^4 < 25
(2) n is not equal to n^2

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-value-of-the-positive-integer-n-165408.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 14 Oct 2016, 01:44, edited 2 times in total.
Renamed the topic and edited the question.

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

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28 Feb 2011, 02:38
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We are given that n is positive and n is integer.

From 1, n^4 < 25, so n can be 1 or n can be 2 as 1^4 =1 and 2^4 = 16 whereas 3^4 would be 81 and so on. We cant fix a value for n from this information, so clearly insufficient

From 2 , n^2 is not equal to n. Now for any positive integer n, n^2 will be equal to n only when n=1, so n can be any of 2,3,4 and so on.. clearly insufficient.

Combining 1 and 2 gives us that n can only be 2, so sufficient. Answer C

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

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28 Feb 2011, 19:22
Answer is C, and the reasoning is same as explained by beyondgmatscore.
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Re: What is the value of positive integer n? [#permalink]

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22 Jan 2013, 00:52
beyondgmatscore wrote:
We are given that n is positive and n is integer.

From 1, n^4 < 25, so n can be 1 or n can be 2 as 1^4 =1 and 2^4 = 16 whereas 3^4 would be 81 and so on. We cant fix a value for n from this information, so clearly insufficient

From 2 , n^2 is not equal to n. Now for any positive integer n, n^2 will be equal to n only when n=1, so n can be any of 2,3,4 and so on.. clearly insufficient.

Combining 1 and 2 gives us that n can only be 2, so sufficient. Answer C

For statement 1 the only possible values are 1 and 2, 3 isn't possible right?

How do you solve this question using examples?
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Re: What is the value of positive integer n? [#permalink]

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24 Jan 2013, 13:48
fozzzy wrote:
beyondgmatscore wrote:
We are given that n is positive and n is integer.

From 1, n^4 < 25, so n can be 1 or n can be 2 as 1^4 =1 and 2^4 = 16 whereas 3^4 would be 81 and so on. We cant fix a value for n from this information, so clearly insufficient

From 2 , n^2 is not equal to n. Now for any positive integer n, n^2 will be equal to n only when n=1, so n can be any of 2,3,4 and so on.. clearly insufficient.

Combining 1 and 2 gives us that n can only be 2, so sufficient. Answer C

For statement 1 the only possible values are 1 and 2, 3 isn't possible right?

How do you solve this question using examples?

Fozzzy, which example method you are referring to. If $$n^4<25$$, you can consider 1 & 2 as only positive numbers which satisfy the condition.
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Re: What is the value of positive integer n? [#permalink]

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24 Jan 2013, 13:54
Statement 1: Could be 1 or could be 2. Not sufficient.
Statement 2: Could be any integer other than 0 and 1. Not sufficient.

Combined 1 + 2: Can only be 2 as all other integers would exceed 25. Sufficient.

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

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25 Jan 2013, 22:09
PraPon wrote:

Fozzzy, which example method you are referring to. If $$n^4<25$$, you can consider 1 & 2 as only positive numbers which satisfy the condition.

The earlier explanation said 3^4 was satisfying the condition so that got me confused, Only 1 and 2 satisfy the equation. when we combine 1=1^2 so this case is ruled out leaving us with the only possible value as 2.

The fastest way to approach these questions is using examples, I was wondering if there is a graphic approach or any alternative solution in case the question is complex.
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Re: What is the value of positive integer n? [#permalink]

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02 Dec 2014, 10:03
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Re: What is the value of positive integer n? [#permalink]

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13 Oct 2016, 10:33
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Re: What is the value of positive integer n? [#permalink]

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14 Oct 2016, 01:45
What is the value of positive integer n?

(1) n^4 < 25
(2) n is not equal to n^2

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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-value-of-the-positive-integer-n-165408.html
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Re: What is the value of positive integer n? [#permalink]

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15 Oct 2016, 08:35
What is the value of positive integer n?

(1) n^4 < 25
(2) n is not equal to n^2

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-value-of-the-positive-integer-n-165408.html

FROM STATEMENT - I ( INSUFFICIENT)

n = 1 , n^4 = 1
n = 2 , n^4 = 16

FROM STATEMENT - II ( INSUFFICIENT)

This statement means n = 1 , n^4 = 1 is not possible..

COMBINE I AND II

We can obtain our answer n = 2 , n^4 = 16

Hence, BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.Answer will be (C)

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Re: What is the value of positive integer n?   [#permalink] 15 Oct 2016, 08:35
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