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# If # denotes one of the four arithmetic operations addition

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28 Nov 2010, 14:54
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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

[Reveal] Spoiler:
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.
[Reveal] Spoiler: OA

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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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28 Nov 2010, 15:11
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.

So, when it is said for all N integers rule applies to all the integers and it is the same for 0, 322, and 856,909? I guess one has to pay attention to the wording such as all... Thanks a lot!

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

Thank you!!!
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petrifiedbutstanding

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

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21 Jun 2013, 02:50
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Re: If # denotes one of the four arithmetic operations addition [#permalink]

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22 Jun 2013, 03:32
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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

[Reveal] Spoiler:
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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25 Apr 2014, 06:09
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.

On second statement, I fell on the zero trap, thinking well what if n=0 then could be either multiplication, subtraction, or sum.

I'm trying to guess that what you meant is that since 'n' must be a variable it should be able to take different values and still give =0. In that case, only subtraction works

Am I understanding you correctly?

Thanks
Cheers!
J
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Joined: 02 Sep 2009
Posts: 39728

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06 May 2014, 09:00
jlgdr 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.

On second statement, I fell on the zero trap, thinking well what if n=0 then could be either multiplication, subtraction, or sum.

I'm trying to guess that what you meant is that since 'n' must be a variable it should be able to take different values and still give =0. In that case, only subtraction works

Am I understanding you correctly?

Thanks
Cheers!
J

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

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26 Oct 2015, 15:08
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Re: If # denotes one of the four arithmetic operations addition [#permalink]

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20 May 2017, 16:20
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If # denotes one of the four arithmetic operations addition   [#permalink] 20 May 2017, 16:20
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