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# If # denotes one of the four arithmetic operations addition

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Intern
Joined: 02 Jan 2010
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03 Feb 2010, 19:08
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69% (00:58) correct 31% (01:15) wrong based on 432 sessions

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If # denotes one of the four arithmetic operations addition, subtraction, multiplication and division, what is the value of 1 # 2?

(1) n # 0 = n for all integers n
(2) n # n = 0 for all integers n
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Joined: 02 Sep 2009
Posts: 55231
Re: GMAT Prep Problem on arithmetic operation  [#permalink]

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04 Feb 2010, 05:12
1
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MrEasy wrote:
Guys I have a question, in the GMAT prep I came across this question (See attachment).

I wonder, does it not make a difference when someone assumes that n could be 0 as it is not explicitly stated in the question that it is not?

If # denotes one of the four arithmetic operations addition, subtraction, multiplication and division, what is the value of 1 # 2?
(1) n # 0 = n for all integers n
(2) n # n = 0 for all integers n

The key here is the bold part of the statement, which tells us that statements MUST be true for all integers. I guess your concern is about the statement (2):

n # n = 0 --> means # can denote only subtraction to be true for ALL integers. Though if n=0 it can denote addition and multiplication as well but one value of n can not determine #.

Hope it's clear.
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Re: If # denotes one of the four arithmetic operations addition  [#permalink]

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29 Oct 2015, 16:01
Bunuel wrote:
MrEasy wrote:
Though if n=0 it can denote addition and multiplication as well but one value of n can not determine #.

Hope it's clear.

Hi Bunnel,

Can you please elaborate why the answer should not be E ? In my opinion in the statement two if the value of n=0 then the sign could be any and if the value of n is not equalt to 0 then the sign is subtraction. So clearly we have two answers hence the statement should be insufficient.

Please correct me what am I missing ?

Thanks
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Re: If # denotes one of the four arithmetic operations addition  [#permalink]

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29 Oct 2015, 16:10
2
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SD007 wrote:
Bunuel wrote:
MrEasy wrote:
Though if n=0 it can denote addition and multiplication as well but one value of n can not determine #.

Hope it's clear.

Hi Bunnel,

Can you please elaborate why the answer should not be E ? In my opinion in the statement two if the value of n=0 then the sign could be any and if the value of n is not equalt to 0 then the sign is subtraction. So clearly we have two answers hence the statement should be insufficient.

Please correct me what am I missing ?

Thanks

Let me try to answer. The question mentions that the "#" symbol should denote an operation satisfied for ALL integers and not just 1.

You are restricting the interpretation of statement 2 by only assuming that n=0 is the only value. This is not true. Whatever operation you choose, must be applicable for ALL integers.

Per statement 2, n#n=0 ---> only n-n = 0 is the applicable solution. n+n=2n , n*n=n^2, n/n=1. Thus the only case possible is the # = subtraction.

Hope this helps.
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Re: If # denotes one of the four arithmetic operations addition  [#permalink]

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17 Mar 2016, 04:30
Bunuel wrote:
MrEasy wrote:
Guys I have a question, in the GMAT prep I came across this question (See attachment).

I wonder, does it not make a difference when someone assumes that n could be 0 as it is not explicitly stated in the question that it is not?

If # denotes one of the four arithmetic operations addition, subtraction, multiplication and division, what is the value of 1 # 2?
(1) n # 0 = n for all integers n
(2) n # n = 0 for all integers n

The key here is the bold part of the statement, which tells us that statements MUST be true for all integers. I guess your concern is about the statement (2):

n # n = 0 --> means # can denote only subtraction to be true for ALL integers. Though if n=0 it can denote addition and multiplication as well but one value of n can not determine #.

Hope it's clear.

why the option D is not the answer. please explain. I think in stmt 1 the operation can be addition?
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Joined: 02 Sep 2009
Posts: 55231
Re: If # denotes one of the four arithmetic operations addition  [#permalink]

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17 Mar 2016, 04:50
robu wrote:
Bunuel wrote:
MrEasy wrote:
Guys I have a question, in the GMAT prep I came across this question (See attachment).

I wonder, does it not make a difference when someone assumes that n could be 0 as it is not explicitly stated in the question that it is not?

If # denotes one of the four arithmetic operations addition, subtraction, multiplication and division, what is the value of 1 # 2?
(1) n # 0 = n for all integers n
(2) n # n = 0 for all integers n

The key here is the bold part of the statement, which tells us that statements MUST be true for all integers. I guess your concern is about the statement (2):

n # n = 0 --> means # can denote only subtraction to be true for ALL integers. Though if n=0 it can denote addition and multiplication as well but one value of n can not determine #.

Hope it's clear.

why the option D is not the answer. please explain. I think in stmt 1 the operation can be addition?

It can be addition as well as subtraction. So, 1 # 2 can be 1 + 2 = 3 as well as 1 - 2 = -1.
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Re: If # denotes one of the four arithmetic operations addition  [#permalink]

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06 Sep 2018, 01:31
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Re: If # denotes one of the four arithmetic operations addition   [#permalink] 06 Sep 2018, 01:31
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