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The symbol ▽ represents one of the following operations... 01 Jul 2010, 00:52
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The symbol ▽ represents one of the following operations: addition, subtraction, multiplication, or division. What is the value of 3 ▽ 2?

(1) 0▽1 = 1
(2) 1▽0 = 1
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The symbol ▽ represents one of the following operations... 01 Jul 2010, 01:22
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The symbol ▽ represents one of the following operations: addition, subtraction, multiplication, or division. What is the value of 3 ▽ 2?
(1) 0▽1 = 1
(2) 1▽0 = 1


Since 3 ▽ 2 will have a different value for each of the 4 operations, we need to know which operation ▽ represents to answer the question.

(1) 0▽1 = 1

\(0*1 = 0\)
\(0+1 = 1\)
\(0 / 1 = 0\)
\(0-1 = -1\)

Since only addition makes (1) true, "▽" must represent addition: sufficient (eliminate B, C, E).

(2) 1▽0 = 1

\(1*0 = 0\)
\(1+0 = 1\)
\(1/0 = undefined\)
\(1-0 = 1\)

Both addition and subtraction make (2) true. Accordingly, "▽" could represent either addition or subtraction. Since:

\(3-2\)

and

\(3+2\)

don't have the same value, (2) is insufficient (eliminate D).

Choose A!
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The symbol ▽ represents one of the following operations... 08 Jul 2010, 00:48
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Can we assume in every case that a v b = a -/+/* b
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The symbol ▽ represents one of the following operations... 08 Jul 2010, 01:34
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hothihongcam
Can we assume in every case that a v b = a -/+/* b

No - the ▽ operation is one that's made up for this question - it's not a "real" mathematical term.

On the GMAT, we sometimes see symbolism questions (which are really just another form of function questions) - when those definitions appear on a question, they're only for the purpose of that particular question.

Don't worry, you didn't sleep through the class in high school in which your teacher covered "▽". :-D
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The symbol ▽ represents one of the following operations... 11 Oct 2013, 18:08
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The symbol ▽ represents one of the following operations: addition, subtraction, multiplication, or division. What is the value of 3 ▽ 2?

(1) 0▽1 = 1. The symbol can only be addition. Thus 3 ▽ 2 = 3 + 2 = 5. Sufficient.

(2) 1▽0 = 1. The symbol is either addition or subtraction. Thus 3 ▽ 2 = 3 + 2 = 5 or 3 ▽ 2 = 3 - 2 = 1. Not sufficient.

Answer: A.
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The symbol ▽ represents one of the following operations... 11 Oct 2013, 18:08
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The symbol ▽ represents one of the following operations: addition, subtraction, multiplication, or division. What is the value of 3 ▽ 2?

(1) 0▽1 = 1. The symbol can only be addition. Thus 3 ▽ 2 = 3 + 2 = 5. Sufficient.

(2) 1▽0 = 1. The symbol is either addition or subtraction. Thus 3 ▽ 2 = 3 + 2 = 5 or 3 ▽ 2 = 3 - 2 = 1. Not sufficient.

Answer: A.

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The symbol ▽ represents one of the following operations... 11 Oct 2013, 20:29
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The symbol ▽ represents one of the following operations: addition, subtraction, multiplication, or division. What is the value of 3 ▽ 2?

(1) 0▽1 = 1
(2) 1▽0 = 1

Statement 1 : Only operation that could give the value 1 for the given eqn is "addition". Sufficient

Statement 2 : Both "addition & subtraction" can give the value 1 for the given eqn. Hence insufficient.

Option A

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The symbol ▽ represents one of the following operations... 15 Mar 2017, 02:24
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St 1:For the four mentioned operators, the value will be 1,-1,0 and 0 respectively. therefore the operator is addition. hence the value will be 3+2 = 5. ANSWER
St 2: For the four mentioned operators, the value will be 1,1,0 and not defined respectively. therefore the operator can be addition or subtraction .INSUFFIUCIENT

Option A
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The symbol ▽ represents one of the following operations... Updated on: 11 Sep 2020, 00:26
Originally posted by EatMyDosa on 11 Sep 2020, 00:12.
Last edited by EatMyDosa on 11 Sep 2020, 00:26, edited 1 time in total.
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The symbol ▽ represents one of the following operations: addition, subtraction, multiplication, or division. What is the value of 3 ▽ 2?

(1) 0▽1 = 1. The symbol can only be addition. Thus 3 ▽ 2 = 3 + 2 = 5. Sufficient.

(2) 1▽0 = 1. The symbol is either addition or subtraction. Thus 3 ▽ 2 = 3 + 2 = 5 or 3 ▽ 2 = 3 - 2 = 1. Not sufficient.

Answer: A.

Hi Bunuel, ScottTargetTestPrep, VeritasKarishma, BrentGMATPrepNow

(1) Why can't symbol ▽ be subtraction? We can have --> a ▽ b = b-a also, right? There is no order of operation given in the question, so don;t we have to consider all possibilities?
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The symbol ▽ represents one of the following operations... 11 Sep 2020, 00:18
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Bunuel
The symbol ▽ represents one of the following operations: addition, subtraction, multiplication, or division. What is the value of 3 ▽ 2?

(1) 0▽1 = 1. The symbol can only be addition. Thus 3 ▽ 2 = 3 + 2 = 5. Sufficient.

(2) 1▽0 = 1. The symbol is either addition or subtraction. Thus 3 ▽ 2 = 3 + 2 = 5 or 3 ▽ 2 = 3 - 2 = 1. Not sufficient.

Answer: A.

Hi Bunuel, ScottTargetTestPrep, VeritasKarishma, @BranGmatPrepNow

(1) Why can't symbol ▽ be subtraction? We can have --> a ▽ b = b-a also, right? There is no order of operation given in the question, so don;t we have to consider all possibilities?

We are told that ▽ represents one of the following operations: addition, subtraction, multiplication, or division. So, when you replace ▽ with addition, subtraction, multiplication, or division in 0▽1 = 1, the equation must be true. 0 - 1 does not equal to 1, so ▽ is not a subtraction.
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The symbol ▽ represents one of the following operations... 11 Sep 2020, 00:23
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Bunuel
The symbol ▽ represents one of the following operations: addition, subtraction, multiplication, or division. What is the value of 3 ▽ 2?

(1) 0▽1 = 1. The symbol can only be addition. Thus 3 ▽ 2 = 3 + 2 = 5. Sufficient.

(2) 1▽0 = 1. The symbol is either addition or subtraction. Thus 3 ▽ 2 = 3 + 2 = 5 or 3 ▽ 2 = 3 - 2 = 1. Not sufficient.

Answer: A.

Hi Bunuel, ScottTargetTestPrep, VeritasKarishma, @BranGmatPrepNow

(1) Why can't symbol ▽ be subtraction? We can have --> a ▽ b = b-a also, right? There is no order of operation given in the question, so don;t we have to consider all possibilities?

We are told that ▽ represents one of the following operations: addition, subtraction, multiplication, or division. So, when you replace ▽ with addition, subtraction, multiplication, or division in 0▽1 = 1, the equation must be true. 0 - 1 does not equal to 1, so ▽ is not a subtraction.

Bunuel,

Right, but then why are be taking the order of subtraction in 0▽1 = 1 as 0 -1? It can also be 1-0, right? We are NOT given in the question that we have to subtract the 2nd number from the 1st number. It could very well be vice-versa.

Am I missing some rule (PEMDAS or else) here?
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The symbol ▽ represents one of the following operations... 11 Sep 2020, 00:30
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Bunuel
The symbol ▽ represents one of the following operations: addition, subtraction, multiplication, or division. What is the value of 3 ▽ 2?

(1) 0▽1 = 1. The symbol can only be addition. Thus 3 ▽ 2 = 3 + 2 = 5. Sufficient.

(2) 1▽0 = 1. The symbol is either addition or subtraction. Thus 3 ▽ 2 = 3 + 2 = 5 or 3 ▽ 2 = 3 - 2 = 1. Not sufficient.

Answer: A.

Hi Bunuel, ScottTargetTestPrep, VeritasKarishma, @BranGmatPrepNow

(1) Why can't symbol ▽ be subtraction? We can have --> a ▽ b = b-a also, right? There is no order of operation given in the question, so don;t we have to consider all possibilities?

We are told that ▽ represents one of the following operations: addition, subtraction, multiplication, or division. So, when you replace ▽ with addition, subtraction, multiplication, or division in 0▽1 = 1, the equation must be true. 0 - 1 does not equal to 1, so ▽ is not a subtraction.

Bunuel,

Right, but then why are be taking the order of subtraction in 0▽1 = 1 as 0 -1? It can also be 1-0, right? We are NOT given in the question that we have to subtract the 2nd number from the 1st number. It could very well be vice-versa.

Am I missing some rule (PEMDAS or else) here?

Imagine this, I write a + b and cover + sign with ▽. Then I ask to guess what sign is covered by ▽ by giving some clues. Why would you consider a▽b to mean b▽a, when it's clearly written a▽b?
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The symbol ▽ represents one of the following operations... 11 Sep 2020, 00:43
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Bunuel
The symbol ▽ represents one of the following operations: addition, subtraction, multiplication, or division. What is the value of 3 ▽ 2?

(1) 0▽1 = 1. The symbol can only be addition. Thus 3 ▽ 2 = 3 + 2 = 5. Sufficient.

(2) 1▽0 = 1. The symbol is either addition or subtraction. Thus 3 ▽ 2 = 3 + 2 = 5 or 3 ▽ 2 = 3 - 2 = 1. Not sufficient.

Answer: A.

Hi Bunuel, ScottTargetTestPrep, VeritasKarishma, @BranGmatPrepNow

(1) Why can't symbol ▽ be subtraction? We can have --> a ▽ b = b-a also, right? There is no order of operation given in the question, so don;t we have to consider all possibilities?

We are told that ▽ represents one of the following operations: addition, subtraction, multiplication, or division. So, when you replace ▽ with addition, subtraction, multiplication, or division in 0▽1 = 1, the equation must be true. 0 - 1 does not equal to 1, so ▽ is not a subtraction.

Bunuel,

Right, but then why are be taking the order of subtraction in 0▽1 = 1 as 0 -1? It can also be 1-0, right? We are NOT given in the question that we have to subtract the 2nd number from the 1st number. It could very well be vice-versa.

Am I missing some rule (PEMDAS or else) here?

Imagine this, I write a + b and cover + sign with ▽. Then I ask to guess what sign is covered by ▽ by giving some clues. Why would you consider a▽b to mean b▽a, when it's clearly written a▽b?

Bunuel,

Yes, that's a fair point. Thanks for your response.

My source of confusion was/is that what if the definition of operator is ▽ --> (2nd no.) --- operation (defined by operator ▽) --- (1st no.).

In many operator based questions, we are usually given a definition or direction regarding the order of operations of a particular operator. Here, we are not given any such directions, so I didn't see any reason to not consider both possibilities.
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The symbol ▽ represents one of the following operations... 06 Dec 2020, 10:56
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The symbol ▽ represents one of the following operations: addition, subtraction, multiplication, or division. What is the value of 3 ▽ 2?

(1) 0▽1 = 1. The symbol can only be addition. Thus 3 ▽ 2 = 3 + 2 = 5. Sufficient.

(2) 1▽0 = 1. The symbol is either addition or subtraction. Thus 3 ▽ 2 = 3 + 2 = 5 or 3 ▽ 2 = 3 - 2 = 1. Not sufficient.

Answer: A.

Hi Bunuel, ScottTargetTestPrep, VeritasKarishma, BrentGMATPrepNow

(1) Why can't symbol ▽ be subtraction? We can have --> a ▽ b = b-a also, right? There is no order of operation given in the question, so don;t we have to consider all possibilities?

Explanation:

The exact sentence is “the symbol ▽ represents one of the following operations: addition, subtraction, ...” If ▽ represents subtraction, then we should be able to replace the ▽ sign with the “ - “ sign and get an equality. In other words, if ▽ represents subtraction, then a ▽ b can only equal a - b. If we define ▽ as a ▽ b = b - a, then we can no longer claim that ▽ represents subtraction. It is true that b - a is also an operation which involves a, b and the minus sign; but if a ▽ b is b - a, then ▽ is doing something more than subtraction; it is also changing the order of terms.
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The symbol ▽ represents one of the following operations... 27 Dec 2023, 23:33
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