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# What is the value of the integer n? (1) n(n + 2) = 15 (2) (n

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What is the value of the integer n? (1) n(n + 2) = 15 (2) (n [#permalink]

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30 Dec 2010, 16:27
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What is the value of the integer n?

(1) n(n + 2) = 15
(2) (n + 2)^n = 125

I am not sure if the given ans is right
[Reveal] Spoiler: OA

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Ajit

Last edited by Bunuel on 10 Jul 2013, 00:54, edited 1 time in total.
Edited the OA.

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Re: What is the value of the integer n....Exponents [#permalink]

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30 Dec 2010, 16:45
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ajit257 wrote:
What is the value of the integer n?

(1) n(n + 2) = 15
(2) (n + 2)^n = 125

I am not sure if the given ans is right

What is the value of the integer n?

(1) n(n + 2) = 15 --> $$n^2+2n-15=0$$ --> $$(n+5)(n-3)=0$$ --> $$n=-5$$ or $$n=3$$. Not sufficient.

(2) (n + 2)^n = 125 --> as $$n$$ is an integer then $$(n + 2)^n=125^1=5^3$$ (125 can be written as integer^integer only in those two ways), only $$n=3$$ works: $$(2+3)^3=5^3=125$$. Sufficient.

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Re: What is the value of the integer n....Exponents [#permalink]

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30 Dec 2010, 16:53
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Bunuel,
Thanks for the confirmation. I got the same. The given ans is wrong ...should be B.
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Re: What is the value of the integer n....Exponents [#permalink]

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31 Dec 2010, 17:04
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C it is

statment 2) is not sufficient coz N can be a decimal value

from statement 1) we know that N= -5 or 3
by sustituting these values in statement 2), we know that N=3

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Re: What is the value of the integer n....Exponents [#permalink]

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01 Jan 2011, 00:28
girishkakkar wrote:
C it is

statment 2) is not sufficient coz N can be a decimal value

from statement 1) we know that N= -5 or 3
by sustituting these values in statement 2), we know that N=3

The question clearly states
"What is the value of the integer n?"

So the answer should be B.

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Re: What is the value of the integer n....Exponents [#permalink]

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01 Jan 2011, 07:12
but talking about statement 2), cant value of N be 3 or ANY decimal number? Since it is NOT stated in the question that "N is an integer". Correct me if I am wrong.

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Re: What is the value of the integer n....Exponents [#permalink]

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01 Jan 2011, 07:18
girishkakkar wrote:
but talking about statement 2), cant value of N be 3 or ANY decimal number? Since it is NOT stated in the question that "N is an integer". Correct me if I am wrong.

Question is: What is the value of the integer n? So the stem explicitly says that n is an integer.
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Re: What is the value of the integer n? (1) n(n + 2) = 15 (2) (n [#permalink]

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04 Jan 2012, 09:18

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Re: What is the value of the integer n? (1) n(n + 2) = 15 (2) (n [#permalink]

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04 Jan 2012, 13:14
Agree with Buneul. If n is integer, them then S2 has to be an integer.

1. Clearly insufficient, two roots = -5,3
2. Since n is integer, only n that satisfies this equation is n = 3. Sufficient

+B.
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Re: What is the value of the integer n....Exponents [#permalink]

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03 Jan 2013, 02:13
curtis0063 wrote:
Bunuel wrote:
ajit257 wrote:
What is the value of the integer n?

(1) n(n + 2) = 15
(2) (n + 2)^n = 125

What is the value of the integer n?

(1) n(n + 2) = 15 --> $$n^2+2n-15=0$$ --> $$(n+5)(n-3)=0$$ --> $$n=-5$$ or $$n=3$$. Not sufficient.

Dear Bunuel,

My fist approach for statement 1 is 15=3X5, so my reasoning is n(n+2)=3X5. Only n=3 match to that equation, so I pick up D. Could you tell me any thing wrong from my reasoning? THX!

You need to brush up fundamentals.

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Re: What is the value of the integer n? (1) n(n + 2) = 15 (2) (n [#permalink]

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04 Sep 2014, 06:10
curtis0063 wrote:
Bunuel wrote:
ajit257 wrote:
What is the value of the integer n?

(1) n(n + 2) = 15
(2) (n + 2)^n = 125

What is the value of the integer n?

(1) n(n + 2) = 15 --> $$n^2+2n-15=0$$ --> $$(n+5)(n-3)=0$$ --> $$n=-5$$ or $$n=3$$. Not sufficient.

Dear Bunuel,

My fist approach for statement 1 is 15=3X5, so my reasoning is n(n+2)=3X5. Only n=3 match to that equation, so I pick up D. Could you tell me any thing wrong from my reasoning? THX!

15 can also be written as -3 * -5... if n= -5 then n(n+2) => -5 * -3= 15
So A cannot provide an unique solution.

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Re: What is the value of the integer n? (1) n(n + 2) = 15 (2) (n [#permalink]

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22 Sep 2015, 03:52
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 integer n?

(1) n(n + 2) = 15
(2) (n + 2)^n = 125

In the original condition there is 1 variable (n) and thus we need 1 equation to match the number of variable and equation. Since there is 1 each in 1) and 2), D has high probability of being the answer.
In case of 1), n^2+2n-15=0, (n+5)(n-3)=0 and thus n=-5,3. The answer is not unique, therefore the condition is not sufficient.
In case of 2), n=3, therefore the answer is unique and the condition is sufficient. Therefore the answer is B.

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 integer n? (1) n(n + 2) = 15 (2) (n [#permalink]

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14 Jul 2017, 11:20
In statement one: n(n+2)=15 can we say that either n = 15 or n+2=15 n =13. Am i wrong?? Or is this method too correct??

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Re: What is the value of the integer n? (1) n(n + 2) = 15 (2) (n [#permalink]

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14 Jul 2017, 11:41
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longhaul123 wrote:
In statement one: n(n+2)=15 can we say that either n = 15 or n+2=15 n =13. Am i wrong?? Or is this method too correct??

Nope.
if you say that, you're meaning to say that 15*13 = 15 which is not possible.
You can only say that when n(n+2) = 0
i.e. n = 0,-2 <= 2 solutions for the equation.

n^{2} + 2n -15 = 0
n = -5,3

Alternatively
You can plug in values.
n(n+2) = 15
15 = 1*15 or 3*5

n = 3
3*5 =15

But if n = -5
n+2 = -3
-3*(-5) = 15

2 values so the statement is not sufficient.

Hope this helps.
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Re: What is the value of the integer n? (1) n(n + 2) = 15 (2) (n [#permalink]

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29 Nov 2017, 11:44
Also, doesn't the rule says that we can compare exponents only if the bases are same. We cannot assume n+2 and 5 are equal so we need help of statement I to know that n can take 5 as value. Pls correct me if I am wrong

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Re: What is the value of the integer n? (1) n(n + 2) = 15 (2) (n [#permalink]

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29 Nov 2017, 19:55
narayani20 wrote:
Also, doesn't the rule says that we can compare exponents only if the bases are same. We cannot assume n+2 and 5 are equal so we need help of statement I to know that n can take 5 as value. Pls correct me if I am wrong

n = 5 does not fit. Please check here: https://gmatclub.com/forum/what-is-the- ... ml#p843731
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Re: What is the value of the integer n? (1) n(n + 2) = 15 (2) (n [#permalink]

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30 Nov 2017, 21:59
I got the answer B as correct one.

But i plugged in values to find the answer.

What is the value of the integer n?

(1) n(n + 2) = 15
N can be either 3 or -5. We get 2 possible options so Not Sufficient.

(2) (n + 2)^n = 125
N can only be 3. Only one answer. - Sufficient.

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Re: What is the value of the integer n? (1) n(n + 2) = 15 (2) (n   [#permalink] 30 Nov 2017, 21:59
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