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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]

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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: OA
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Re: GMAT Prep Problem on arithmetic operation [#permalink]

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New post 04 Feb 2010, 04:12
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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 #.

So the answer is B.

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

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New post 29 Oct 2015, 15:01
Bunuel wrote:
MrEasy wrote:
Though if n=0 it can denote addition and multiplication as well but one value of n can not determine #.

So the answer is B.

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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New post 29 Oct 2015, 15:10
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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 #.

So the answer is B.

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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New post 17 Mar 2016, 03:30
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 #.

So the answer is B.

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 [#permalink]

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New post 17 Mar 2016, 03:50
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 #.

So the answer is B.

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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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

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Re: If # denotes one of the four arithmetic operations addition   [#permalink] 03 Apr 2017, 03:44
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