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If # denotes one of the four arithmetic operations addition

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If # denotes one of the four arithmetic operations addition [#permalink] New post 28 Nov 2010, 13:54
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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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Re: GMAT PREP DS, unclear answer [#permalink] New post 28 Nov 2010, 14:05
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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.

Answer: B.

Hope it's clear.
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Re: GMAT PREP DS, unclear answer [#permalink] New post 28 Nov 2010, 14:11
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.

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!

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Re: GMAT PREP DS, unclear answer [#permalink] New post 28 Nov 2010, 14:49
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.

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
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Re: GMAT PREP DS, unclear answer [#permalink] New post 28 Nov 2010, 14:55
Expert's post
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.

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.
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Re: GMAT PREP DS, unclear answer [#permalink] New post 28 Nov 2010, 15:04
Pretty clear now that you explain it. Wonder why it is so troublesome for us to comprehend it?
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Re: GMAT PREP DS, unclear answer [#permalink] New post 13 Aug 2011, 06:53
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 [#permalink] New post 21 Jun 2013, 01:50
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Re: If # denotes one of the four arithmetic operations addition [#permalink] New post 22 Jun 2013, 02:32
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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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Re: GMAT PREP DS, unclear answer [#permalink] New post 25 Apr 2014, 05:09
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.

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!
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Re: GMAT PREP DS, unclear answer [#permalink] New post 06 May 2014, 08:00
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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.

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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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: GMAT PREP DS, unclear answer   [#permalink] 06 May 2014, 08:00
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