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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # The symbol ∆ denotes one of the four arithmetic operations:addition,su

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Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10780
Location: Pune, India
Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

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jabhatta@umail.iu.edu wrote:

As a test taker -- how are we supposed to know that ∆ should represent BOTH division AND subtraction

I assumed, the conditions applied individually (subtraction OR division) and thus opted for E

It's clear one or the other works

Since the question says 6∆3=<3
6/3 = 2
OR
6-3 = 3

--------------

∆ will represent one operation only - either division or subtraction. Which one it actually represents, we do not know. So whichever statement MUST BE TRUE should be the one in which ∆ could represent either operation, it would hold.

I. 2∆2 = 0
Is true if ∆ is subtraction but not if it is division.

II. 2∆2 = 1
Is true if ∆ is division but not if it is subtraction.

III. 4∆2 = 2
4 - 2 = 2
4/2 = 2
So this will hold irrespective of whether ∆ is subtraction or division. So this statement will definitely be true.
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Karishma
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Joined: 15 Dec 2016
Posts: 253
Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

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jabhatta@umail.iu.edu wrote:

As a test taker -- how are we supposed to know that ∆ should represent BOTH division AND subtraction

I assumed, the conditions applied individually (subtraction OR division) and thus opted for E

It's clear one or the other works

Since the question says 6∆3=<3
6/3 = 2
OR
6-3 = 3

--------------

∆ will represent one operation only - either division or subtraction. Which one it actually represents, we do not know. So whichever statement MUST BE TRUE should be the one in which ∆ could represent either operation, it would hold.

I. 2∆2 = 0
Is true if ∆ is subtraction but not if it is division.

II. 2∆2 = 1
Is true if ∆ is division but not if it is subtraction.

III. 4∆2 = 2
4 - 2 = 2
4/2 = 2
So this will hold irrespective of whether ∆ is subtraction or division. So this statement will definitely be true.

Thank you VeritasKarishma for following up!

If I understand correctly it's the MUST BE TRUE that tells the test maker to test both subtraction and division

If the question stem had" may be true".. Do you think E would be accurate in that case ?

Thank you

Posted from my mobile device
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10780
Location: Pune, India
Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

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jabhatta@umail.iu.edu wrote:
jabhatta@umail.iu.edu wrote:

As a test taker -- how are we supposed to know that ∆ should represent BOTH division AND subtraction

I assumed, the conditions applied individually (subtraction OR division) and thus opted for E

It's clear one or the other works

Since the question says 6∆3=<3
6/3 = 2
OR
6-3 = 3

--------------

∆ will represent one operation only - either division or subtraction. Which one it actually represents, we do not know. So whichever statement MUST BE TRUE should be the one in which ∆ could represent either operation, it would hold.

I. 2∆2 = 0
Is true if ∆ is subtraction but not if it is division.

II. 2∆2 = 1
Is true if ∆ is division but not if it is subtraction.

III. 4∆2 = 2
4 - 2 = 2
4/2 = 2
So this will hold irrespective of whether ∆ is subtraction or division. So this statement will definitely be true.

Thank you VeritasKarishma for following up!

If I understand correctly it's the MUST BE TRUE that tells the test maker to test both subtraction and division

If the question stem had" may be true".. Do you think E would be accurate in that case ?

Thank you

Posted from my mobile device

Yes, absolutely correct!
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Karishma
Veritas Prep GMAT Instructor

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Joined: 03 Jun 2019
Posts: 3339
Location: India
GMAT 1: 690 Q50 V34 WE: Engineering (Transportation)
Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

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AbdurRakib wrote:
The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?

I. 2∆2 = 0
II. 2∆2 = 1
III. 4∆2 = 2

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?

Since 6∆3≤ 3
6*3 = 18 >3
6+3=9>3
6/3 = 2 <=3
6-3 =3 <=3
Therefore, operator ∆ denotes / or - operations

I. 2∆2 = 0
2/2=1
2-2=0
NOT NECESSARILY TRUE

II. 2∆2 = 1
2/2=1
2-2=0
NOT NECESSARILY TRUE

III. 4∆2 = 2
4/2=2
4-2=2
4∆2 = 2 regardless of the operator / or -
MUST BE TRUE

IMO C
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Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
Intern  B
Joined: 12 May 2020
Posts: 2
Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

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Hi all,

Could any experts help me to confirm with my following calculation is correct or not. I think it will solve most quickly than others.

Given: 6#3<=3 ---> The same: 2x3#3<=3, so only III: 4#2=2 ---> 2x2#2 = 2 <=3: Satisfied. Others is not
Only care about formulas to find the answer soonest, no need to calculate one by one.

Thanks!
Intern  B
Joined: 08 Jun 2020
Posts: 1
Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

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1
Hello, I have a query regarding the answer. The question states that the the symbol denoted in the question stem must be any ONE of the four operations and though I too agree that given the example the answer choice should hodl true in subtraction AND division, I dont understand how it could be two operations even though its mentioned it should be any ONE. Thank you.
EMPOWERgmat Instructor V
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GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

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Hi sam12rawat,

When a Quant question asks "which of the following MUST be true?", what it's really asking is "which of the following is ALWAYS true no matter how many different examples we can come up with?"

In the case of this Roman Numeral question, we have to consider whether each of those 3 equations is ALWAYS true or not. Even though the 'symbol' might be subtraction or division (we can never actually define which one), only Roman Numeral 3 is ALWAYS true (whether the symbol is subtraction or division).

GMAT assassins aren't born, they're made,
Rich
_________________ Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su   [#permalink] 06 Jul 2020, 16:50

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