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# If # denotes one of the four arithmetic operations addition, subtracti

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Joined: 02 Jan 2010
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If # denotes one of the four arithmetic operations addition, subtracti  [#permalink]

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03 Feb 2010, 19:08
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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
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Re: If # denotes one of the four arithmetic operations addition, subtracti  [#permalink]

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28 Nov 2010, 15:05
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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

The key here is the bold part of the statements, which tells us that statements MUST be true for all integers.

(1) n # 0 = n for all integers n --> # may denote both addition and subtraction (as n+0=n and n-0=n is true for all integers n), which gives two different values for 1 # 2. Not sufficient.

(2) n # n = 0 for all integers n --> # may denote only subtraction to be true for ALL integers (n-n=0 is true for all integers n), though if n=0 it can denote addition and multiplication as well but one value of n can not determine #. So 1 # 2 = 1 - 2 = -1. Sufficient.

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

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28 Nov 2010, 15:49
Bunuel wrote:
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 statements, which tells us that statements MUST be true for all integers.

(1) n # 0 = n for all integers n --> # may denote both addition and subtraction (as n+0=n and n-0=n is true for all integers n), which gives two different values for 1 # 2. Not sufficient.

(2) n # n = 0 for all integers n --> # may denote only subtraction to be true for ALL integers (n-n=0 is true for all integers n), though if n=0 it can denote addition and multiplication as well but one value of n can not determine #. So 1 # 2 = 1 - 2 = -1. Sufficient.

Hope it's clear.

Bunuel so on stmt 2 does this mean since the stmt says all integers N the rule has to apply to all zeros not just 0? Therefore only subtraction can be true? Thanks
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Re: If # denotes one of the four arithmetic operations addition, subtracti  [#permalink]

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28 Nov 2010, 15:55
gettinit wrote:
Bunuel wrote:
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 statements, which tells us that statements MUST be true for all integers.

(1) n # 0 = n for all integers n --> # may denote both addition and subtraction (as n+0=n and n-0=n is true for all integers n), which gives two different values for 1 # 2. Not sufficient.

(2) n # n = 0 for all integers n --> # may denote only subtraction to be true for ALL integers (n-n=0 is true for all integers n), though if n=0 it can denote addition and multiplication as well but one value of n can not determine #. So 1 # 2 = 1 - 2 = -1. Sufficient.

Hope it's clear.

Bunuel so on stmt 2 does this mean since the stmt says all integers N the rule has to apply to all zeros not just 0? Therefore only subtraction can be true? Thanks

I'm not sure understoond your question.

Anyway, "n # n = 0 for all integers n", means that n # n = 0 must be true (for some operation denoted by #) no matter what integers you substitute for n.
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Re: If # denotes one of the four arithmetic operations addition, subtracti  [#permalink]

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28 Nov 2010, 16:04
Pretty clear now that you explain it. Wonder why it is so troublesome for us to comprehend it?
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Re: If # denotes one of the four arithmetic operations addition, subtracti  [#permalink]

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13 Aug 2011, 07:53
Bunuel! It was the most obvious thing that we missed!

Thank you!!!
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Re: If # denotes one of the four arithmetic operations addition, subtracti  [#permalink]

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22 Jun 2013, 03:32
1
MisterEko wrote:
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

Not sure how the answer is B?

If N is 0 (which is a possibility, isn't it?), then the operation can be either +,- or x, which would yield different results for the stated operation.

Appreciate the help, and sorry if this has been posted before, it was hard to search for the question since the operation sign is weird.

Question, we need not calculate 1#2, but just find out the operator for #=?

1) n # 0 = n for all integers n

This is valid for the operators +, - => Cant narrow to one =>Not Suff

(2) n # n = 0 for all integers n

This is valid for - operator => Sufficient.

B
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Re: If # denotes one of the four arithmetic operations addition, subtracti  [#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, subtracti  [#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, subtracti  [#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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Re: If # denotes one of the four arithmetic operations addition, subtracti  [#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, subtracti  [#permalink]

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16 Sep 2019, 04:25
MrEasy wrote:
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

If +, 1+2 = 3
If - , 1 -2 = -1
If *, 1 * 2 = 2
If /, 1/2 = 1/2

1) # could be + or -. Not Sufficient
2) # has to be -. Sufficient.

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

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22 Oct 2019, 07:57
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Re: If # denotes one of the four arithmetic operations addition, subtracti   [#permalink] 22 Oct 2019, 07:57
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