Last visit was: 18 Nov 2025, 22:20 It is currently 18 Nov 2025, 22:20
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
Sub 505 Level|   Functions and Custom Characters|               
User avatar
nsp007
User avatar
Joined: 19 Nov 2009
Last visit: 15 Dec 2010
Posts: 162
Own Kudos:
315
 [9]
Given Kudos: 44
Posts: 162
Kudos: 315
 [9]
The symbol ▽ represents one of the following operations... 01 Jul 2010, 00:52
1
Kudos
Add Kudos
8
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

5% (low)

Question Stats:

86% (00:43) correct 14% (00:39) wrong based on 1115 sessions

History

Date
Time
Result
Not Attempted Yet
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
ShowHide Answer
Official Answer
A
User avatar
skovinsky
User avatar
Kaplan GMAT Instructor
Joined: 21 Jun 2010
Last visit: 17 Dec 2019
Posts: 129
Own Kudos:
626
 [1]
Location: Toronto
Posts: 129
Kudos: 626
 [1]
The symbol ▽ represents one of the following operations... 01 Jul 2010, 01:22
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
nsp007
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

Show more

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!
avatar
hothihongcam
avatar
Joined: 17 May 2010
Last visit: 13 Oct 2010
Posts: 3
Own Kudos:
4
Posts: 3
Kudos: 4
The symbol ▽ represents one of the following operations... 08 Jul 2010, 00:48
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Can we assume in every case that a v b = a -/+/* b
User avatar
skovinsky
User avatar
Kaplan GMAT Instructor
Joined: 21 Jun 2010
Last visit: 17 Dec 2019
Posts: 129
Own Kudos:
626
Location: Toronto
Posts: 129
Kudos: 626
The symbol ▽ represents one of the following operations... 08 Jul 2010, 01:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
hothihongcam
Can we assume in every case that a v b = a -/+/* b
Show more

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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,103
Given Kudos: 99,964
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,355
Kudos: 778,103
The symbol ▽ represents one of the following operations... 11 Oct 2013, 18:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,103
Given Kudos: 99,964
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,355
Kudos: 778,103
The symbol ▽ represents one of the following operations... 11 Oct 2013, 18:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Show more

Similar questions to practice:
if-represents-one-of-the-operations-and-x-is-k-l-m-144138.html
if-denotes-one-of-two-arithmetic-operations-addition-or-50178.html
if-the-symbol-represents-either-addition-or-multiplication-104600.html
if-the-operation-is-one-of-the-four-arithmetic-operations-101283.html
if-the-operation-is-one-of-the-four-arithmetic-operations-93966.html
if-denotes-one-of-the-four-arithmetic-operations-addition-105472.html
the-symbol-represents-one-of-the-four-arithmetic-operation-107575.html
if-the-symbol-represents-either-addition-subtraction-101741.html
if-the-symbol-represents-either-addition-or-multiplication-104600.html
if-represents-one-of-the-operations-and-is-a-101337.html
the-operation-x-n-for-all-positive-integers-greater-than-99064.html
if-represents-one-of-the-operations-and-x-is-k-l-m-144138.html
if-the-symbol-represents-one-of-the-following-operations-161138.html

Hope it helps.
User avatar
Qoofi
User avatar
Joined: 18 Dec 2012
Last visit: 23 Feb 2024
Posts: 64
Own Kudos:
191
Given Kudos: 56
Location: India
Concentration: General Management, Strategy
GMAT 1: 530 Q37 V25
GMAT 2: 660 Q49 V32
GPA: 3.32
WE:Manufacturing and Production (Manufacturing)
GMAT 2: 660 Q49 V32
Posts: 64
Kudos: 191
The symbol ▽ represents one of the following operations... 11 Oct 2013, 20:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
jlgdr
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
Show more

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

Cheers
Qoofi
User avatar
KrishnakumarKA1
User avatar
Joined: 05 Jan 2017
Last visit: 13 Oct 2020
Posts: 403
Own Kudos:
310
Given Kudos: 15
Location: India
Posts: 403
Kudos: 310
The symbol ▽ represents one of the following operations... 15 Mar 2017, 02:24
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
User avatar
EatMyDosa
User avatar
Joined: 06 Jan 2017
Last visit: 01 Dec 2022
Posts: 85
Own Kudos:
114
Given Kudos: 283
Location: India
Concentration: General Management, Finance
GPA: 3.33
Products:
My Reviews
Posts: 85
Kudos: 114
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.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Show more

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?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,103
Given Kudos: 99,964
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,355
Kudos: 778,103
The symbol ▽ represents one of the following operations... 11 Sep 2020, 00:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EatMyDosa
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?
Show more

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.
User avatar
EatMyDosa
User avatar
Joined: 06 Jan 2017
Last visit: 01 Dec 2022
Posts: 85
Own Kudos:
114
Given Kudos: 283
Location: India
Concentration: General Management, Finance
GPA: 3.33
Products:
My Reviews
Posts: 85
Kudos: 114
The symbol ▽ represents one of the following operations... 11 Sep 2020, 00:23
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
EatMyDosa
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.
Show more

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?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,103
Given Kudos: 99,964
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,355
Kudos: 778,103
The symbol ▽ represents one of the following operations... 11 Sep 2020, 00:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EatMyDosa
Bunuel
EatMyDosa
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?
Show more

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?
User avatar
EatMyDosa
User avatar
Joined: 06 Jan 2017
Last visit: 01 Dec 2022
Posts: 85
Own Kudos:
114
Given Kudos: 283
Location: India
Concentration: General Management, Finance
GPA: 3.33
Products:
My Reviews
Posts: 85
Kudos: 114
The symbol ▽ represents one of the following operations... 11 Sep 2020, 00:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
EatMyDosa
Bunuel
EatMyDosa
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?
Show more

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.
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 18 Nov 2025
Posts: 21,712
Own Kudos:
26,991
Given Kudos: 300
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 21,712
Kudos: 26,991
The symbol ▽ represents one of the following operations... 06 Dec 2020, 10:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EatMyDosa
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, 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?
Show more

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.
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 18 Nov 2025
Posts: 6,836
Own Kudos:
16,349
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
My Reviews
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,836
Kudos: 16,349
The symbol ▽ represents one of the following operations... 23 Mar 2025, 02:04
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Question: Value of 3 ▽ 2 = ?

Statement 1: 0▽1 = 1
0+1 = 1
0-1 ≠ 1
0x1 ≠ 1
0÷1 ≠ 1

i.e ▽ is Addition sign
hence, 3 ▽ 2 = 3 + 2 = 5
SUFFICIENT

Statement 2: 1▽0 = 1
1+0 = 1
1 - 0 = 1
0x1 ≠ 1
0÷1 ≠ 1

i.e ▽ may be Addition sign or Subtraction sign
hence, 3 ▽ 2 = 3 + 2 = 5 OR 3 ▽ 2 = 3 - 2 = 1
NOT SUFFICIENT

Answer: Option A

Related Video:




nsp007
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
Show more
Moderators:
Bunuel
Math Expert
105355 posts
kingbucky
496 posts