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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.

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[highlight]Monster collection of Verbal questions (RC, CR, and SC)[/highlight] http://gmatclub.com/forum/massive-collection-of-verbal-questions-sc-rc-and-cr-106195.html#p832142

[highlight]Massive collection of thousands of Data Sufficiency and Problem Solving questions and answers:[/highlight] http://gmatclub.com/forum/1001-ds-questions-file-106193.html#p832133

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.

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.

Answer: B.

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!
_________________

[highlight]Monster collection of Verbal questions (RC, CR, and SC)[/highlight] http://gmatclub.com/forum/massive-collection-of-verbal-questions-sc-rc-and-cr-106195.html#p832142

[highlight]Massive collection of thousands of Data Sufficiency and Problem Solving questions and answers:[/highlight] http://gmatclub.com/forum/1001-ds-questions-file-106193.html#p832133

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.

Answer: B.

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

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.

Answer: B.

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.
_________________

Pretty clear now that you explain it. Wonder why it is so troublesome for us to comprehend it?
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[highlight]Monster collection of Verbal questions (RC, CR, and SC)[/highlight] http://gmatclub.com/forum/massive-collection-of-verbal-questions-sc-rc-and-cr-106195.html#p832142

[highlight]Massive collection of thousands of Data Sufficiency and Problem Solving questions and answers:[/highlight] http://gmatclub.com/forum/1001-ds-questions-file-106193.html#p832133

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
_________________

PS: Like my approach? Please Help me with some Kudos.

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.

Answer: B.

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

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.

Answer: B.

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

Yes, your understanding is correct.
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Re: If # denotes one of the four arithmetic operations addition [#permalink]

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26 Oct 2015, 14:08

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