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

Question

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

Bunuel · Accepted Answer

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.

gettinit · Answer

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

Bunuel · Answer

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.

MisterEko · Answer

Pretty clear now that you explain it. Wonder why it is so troublesome for us to comprehend it?

petrifiedbutstanding · Answer

Bunuel! It was the most obvious thing that we missed!

Thank you!!!

kpali · Answer

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

SD007 · Answer

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

ENGRTOMBA2018 · Answer

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.

robu · Answer

why the option D is not the answer. please explain. I think in stmt 1 the operation can be addition?

Bunuel · Answer

It can be addition as well as subtraction. So, 1 # 2 can be 1 + 2 = 3 as well as 1 - 2 = -1.

dabaobao · Answer

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.

ANSWER: B

ManifestDreamMBA · Answer

# denotes one of the four arithmetic operations addition, subtraction, multiplication and division
1 # 2 = ?

Statement 1 
n # 0 = n
n + 0 = n  ✅ 
n - 0 = n  ✅ 
n * 0 = n  ❌ 
n / 0 = n  ❌ 
 # can be addition or subtraction 
 1 # 2 = 3 or -1 
 Insufficient

Statement 2  
 n # n = 0 
 n + n = 0 ❌
n - n = 0  ✅ 
n * n = 0 ❌
n / n = 0 ❌ 
 # represents subtraction
1 # 2 = -1 
 Sufficient

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

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