GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 13 Aug 2018, 23:39

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.

Close

Request Expert Reply

Confirm Cancel

If # represents one of the operations +,- and *, is a #

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
avatar
Joined: 16 Feb 2010
Posts: 189
If # represents one of the operations +,- and *, is a #  [#permalink]

Show Tags

New post Updated on: 19 Sep 2010, 16:09
7
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

69% (01:05) correct 31% (01:29) wrong based on 418 sessions

HideShow timer Statistics

If # represents one of the operations +,- and *, is a # (b-c) = (a#b) – (a#c) for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a

(2) # represents subtraction

Originally posted by zisis on 19 Sep 2010, 15:49.
Last edited by zisis on 19 Sep 2010, 16:09, edited 1 time in total.
Manager
Manager
avatar
Joined: 20 Jul 2010
Posts: 228
GMAT ToolKit User Reviews Badge
Re: If # represents one of the operations +,- and *, is a #  [#permalink]

Show Tags

New post 19 Sep 2010, 15:58
I converted question to 3 euqations where # can be +, - or *

So
I) When # = *
ab-ac = ab-ac (true for all values)

II) When # = +
Is a+b-c=b-c

III) When #=-
Is a-b+c = -b-c?

With option A we know # is not * as 1*a is always equal to a*1. So given equation is not equal
With option B , equation is not equal.

So answer choice D
_________________

If you like my post, consider giving me some KUDOS !!!!! Like you I need them

Manager
Manager
avatar
Joined: 23 Sep 2009
Posts: 135
Re: If # represents one of the operations +,- and *, is a #  [#permalink]

Show Tags

New post 19 Sep 2010, 16:50
1
zisis wrote:
If # represents one of the operations +,- and *, is a # (b-c) = (a#b) – (a#c) for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a

(2) # represents subtraction



Mods, please to DS section...posted by mistake in PS - apologies


1. From choice 1 it is clear that # is subtraction. coz a+1=1+1, a*1=1*a but a-1!=(not equal) 1-a.
2. Choice 2 says directly that it is subtraction.

Hence answer is D
_________________

Thanks,
VP

Intern
Intern
User avatar
Joined: 27 Jul 2010
Posts: 16
Location: Bangalore
Re: If # represents one of the operations +,- and *, is a #  [#permalink]

Show Tags

New post 19 Sep 2010, 19:38
vigneshpandi wrote:
zisis wrote:
If # represents one of the operations +,- and *, is a # (b-c) = (a#b) – (a#c) for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a

(2) # represents subtraction



Mods, please to DS section...posted by mistake in PS - apologies


1. From choice 1 it is clear that # is subtraction. coz a+1=1+1, a*1=1*a but a-1!=(not equal) 1-a.
2. Choice 2 says directly that it is subtraction.

Hence answer is D



IMO, it cannot be "not equal" always.

If # is subtraction,

a#(b-c)=a-(b-c)=a-b+c

(a#b)-(a#c)=(a-b)-(a-c)=a-b-a+c=-b+c

a-b+c=-b+c when a=0 and not equal for other values.. So both are insufficient.. Am I missing something here?
_________________

Nothing is free.. You 've to earn it!!!

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47871
Re: If # represents one of the operations +,- and *, is a #  [#permalink]

Show Tags

New post 20 Sep 2010, 00:14
BalakumaranP wrote:
IMO, it cannot be "not equal" always.

If # is subtraction,

a#(b-c)=a-(b-c)=a-b+c

(a#b)-(a#c)=(a-b)-(a-c)=a-b-a+c=-b+c

a-b+c=-b+c when a=0 and not equal for other values.. So both are insufficient.. Am I missing something here?


If # represents one of the operations +, - and *, is \(a#(b-c)=(a#b)-(a#c)\) for all numbers \(a\), \(b\) and \(c\).

(1) \(a#1\) is not equal to \(1#a\) for some numbers \(a\).

\(#\) is neither addition (as \(a+1=1+a\)) not multiplication (as \(a*1=1*a\)), so \(#\) is a subtraction. Then \(LHS=a#(b-c)=a-b+c\) and \(RHS=(a#b)-(a#c)=(a-b)-(a-c)=c-b\), so the question becomes "is \(a-b+c=c-b\) for all numbers \(a\), \(b\) and \(c\)?" --> "is \(a=0\)". So when \(a=0\) (and \(#\) is a subtraction) then \(a#(b-c)=(a#b)-(a#c)\) holds true but not for other values of \(a\), so not for all numbers \(a\), \(b\) and \(c\). Answer to the question is NO. Sufficient.

(2) \(#\) represents subtraction --> the same as above. Sufficient.

Answer: D.

Hope it's clear.
_________________

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
User avatar
Joined: 27 Jul 2010
Posts: 16
Location: Bangalore
Re: If # represents one of the operations +,- and *, is a #  [#permalink]

Show Tags

New post 20 Sep 2010, 03:09
Okay.. I read the question wrong...
_________________

Nothing is free.. You 've to earn it!!!

Manager
Manager
avatar
Joined: 04 Aug 2010
Posts: 116
Re: If # represents one of the operations +,- and *, is a #  [#permalink]

Show Tags

New post 20 Sep 2010, 19:10
1
(1) a#1 is not equal to 1#a for some numbers a

a + 1 = 1 + a for all a
a*1 = 1*a for all a

a - 1 != 1 - a

Statement (1) implies # is a minus sign, so it has same meaning as (2).

Ans D
Manager
Manager
avatar
Joined: 06 Aug 2010
Posts: 190
Location: Boston
Re: If # represents one of the operations +,- and *, is a #  [#permalink]

Show Tags

New post 21 Sep 2010, 10:55
zisis wrote:
If # represents one of the operations +,- and *, is a # (b-c) = (a#b) – (a#c) for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a

(2) # represents subtraction



Mods, please to DS section...posted by mistake in PS - apologies


You're told that "#" is either addition, subtraction, or multiplication, and then asked if "#" satisfies the distributive property. Of these three, distribution only holds for multiplication, so if "#" is "*", it holds, and if "#" isn't "*", then it does not hold.

All we really need to know is what operation "#" really is.

(1) This is only true of subtraction, so # is subtraction and the distributive property does not hold. Sufficient.
(2) Same as above. Sufficient.

(D)
Retired Moderator
avatar
Joined: 29 Apr 2015
Posts: 862
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
GMAT ToolKit User Premium Member
Re: If # represents one of the operations +,- and *, is a #  [#permalink]

Show Tags

New post 03 Jun 2015, 08:54
zisis wrote:
If # represents one of the operations +,- and *, is a # (b-c) = (a#b) – (a#c) for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a

(2) # represents subtraction


Could someone edit this question so it will be an actual question? There is no proper question stem.
_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47871
Re: If # represents one of the operations +,- and *, is a #  [#permalink]

Show Tags

New post 03 Jun 2015, 08:58
reto wrote:
zisis wrote:
If # represents one of the operations +,- and *, is a # (b-c) = (a#b) – (a#c) for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a

(2) # represents subtraction


Could someone edit this question so it will be an actual question? There is no proper question stem.


What do you mean? Everything is correct there. Similar questions: Operations/functions defining algebraic/arithmetic expressions

Check functions related questions in our Special Questions Directory.

Symbols Representing Arithmetic Operation
Rounding Functions
Various Functions
_________________

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Retired Moderator
avatar
Joined: 29 Apr 2015
Posts: 862
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
GMAT ToolKit User Premium Member
Re: If # represents one of the operations +,- and *, is a #  [#permalink]

Show Tags

New post 03 Jun 2015, 09:07
Bunuel wrote:
reto wrote:
zisis wrote:
If # represents one of the operations +,- and *, is a # (b-c) = (a#b) – (a#c) for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a

(2) # represents subtraction


Could someone edit this question so it will be an actual question? There is no proper question stem.


What do you mean? Everything is correct there. Similar questions: Operations/functions defining algebraic/arithmetic expressions

Check functions related questions in our Special Questions Directory.

Symbols Representing Arithmetic Operation
Rounding Functions
Various Functions



The question mark is missing in the question stem.
_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Senior Manager
Senior Manager
User avatar
S
Status: love the club...
Joined: 24 Mar 2015
Posts: 278
Re: If # represents one of the operations +,- and *, is a #  [#permalink]

Show Tags

New post 17 Aug 2017, 19:22
Bunuel wrote:
BalakumaranP wrote:
IMO, it cannot be "not equal" always.

If # is subtraction,

a#(b-c)=a-(b-c)=a-b+c

(a#b)-(a#c)=(a-b)-(a-c)=a-b-a+c=-b+c

a-b+c=-b+c when a=0 and not equal for other values.. So both are insufficient.. Am I missing something here?


If # represents one of the operations +, - and *, is \(a#(b-c)=(a#b)-(a#c)\) for all numbers \(a\), \(b\) and \(c\).

(1) \(a#1\) is not equal to \(1#a\) for some numbers \(a\).

\(#\) is neither addition (as \(a+1=1+a\)) not multiplication (as \(a*1=1*a\)), so \(#\) is a subtraction. Then \(LHS=a#(b-c)=a-b+c\) and \(RHS=(a#b)-(a#c)=(a-b)-(a-c)=c-b\), so the question becomes "is \(a-b+c=c-b\) for all numbers \(a\), \(b\) and \(c\)?" --> "is \(a=0\)". So when \(a=0\) (and \(#\) is a subtraction) then \(a#(b-c)=(a#b)-(a#c)\) holds true but not for other values of \(a\), so not for all numbers \(a\), \(b\) and \(c\). Answer to the question is NO. Sufficient.

(2) \(#\) represents subtraction --> the same as above. Sufficient.

Answer: D.

Hope it's clear.


I don't understand why the answer is not E. if a = 0, then yes, if a is not equal to 0, then no. So not sufficient, as nothing can be said conclusively ...
anybody out there to help me ....?

thanks
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47871
Re: If # represents one of the operations +,- and *, is a #  [#permalink]

Show Tags

New post 17 Aug 2017, 21:24
gmatcracker2017 wrote:
Bunuel wrote:
BalakumaranP wrote:
IMO, it cannot be "not equal" always.

If # is subtraction,

a#(b-c)=a-(b-c)=a-b+c

(a#b)-(a#c)=(a-b)-(a-c)=a-b-a+c=-b+c

a-b+c=-b+c when a=0 and not equal for other values.. So both are insufficient.. Am I missing something here?


If # represents one of the operations +, - and *, is \(a#(b-c)=(a#b)-(a#c)\) for all numbers \(a\), \(b\) and \(c\).

(1) \(a#1\) is not equal to \(1#a\) for some numbers \(a\).

\(#\) is neither addition (as \(a+1=1+a\)) not multiplication (as \(a*1=1*a\)), so \(#\) is a subtraction. Then \(LHS=a#(b-c)=a-b+c\) and \(RHS=(a#b)-(a#c)=(a-b)-(a-c)=c-b\), so the question becomes "is \(a-b+c=c-b\) for all numbers \(a\), \(b\) and \(c\)?" --> "is \(a=0\)". So when \(a=0\) (and \(#\) is a subtraction) then \(a#(b-c)=(a#b)-(a#c)\) holds true but not for other values of \(a\), so not for all numbers \(a\), \(b\) and \(c\). Answer to the question is NO. Sufficient.

(2) \(#\) represents subtraction --> the same as above. Sufficient.

Answer: D.

Hope it's clear.


I don't understand why the answer is not E. if a = 0, then yes, if a is not equal to 0, then no. So not sufficient, as nothing can be said conclusively ...
anybody out there to help me ....?

thanks


The question asks: is \(a#(b-c)=(a#b)-(a#c)\) for all numbers \(a\), \(b\) and \(c\)? From each statement we got a deinite NO answer - NO the equation doe NOT hold true for all numbers, it's true if a = 0 but not true if a is not 0.
_________________

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
User avatar
S
Status: love the club...
Joined: 24 Mar 2015
Posts: 278
Re: If # represents one of the operations +,- and *, is a #  [#permalink]

Show Tags

New post 17 Aug 2017, 22:01
gmatcracker2017 wrote:
Bunuel wrote:
BalakumaranP wrote:
IMO, it cannot be "not equal" always.

If # is subtraction,

a#(b-c)=a-(b-c)=a-b+c

(a#b)-(a#c)=(a-b)-(a-c)=a-b-a+c=-b+c

a-b+c=-b+c when a=0 and not equal for other values.. So both are insufficient.. Am I missing something here?


If # represents one of the operations +, - and *, is \(a#(b-c)=(a#b)-(a#c)\) for all numbers \(a\), \(b\) and \(c\).

(1) \(a#1\) is not equal to \(1#a\) for some numbers \(a\).

\(#\) is neither addition (as \(a+1=1+a\)) not multiplication (as \(a*1=1*a\)), so \(#\) is a subtraction. Then \(LHS=a#(b-c)=a-b+c\) and \(RHS=(a#b)-(a#c)=(a-b)-(a-c)=c-b\), so the question becomes "is \(a-b+c=c-b\) for all numbers \(a\), \(b\) and \(c\)?" --> "is \(a=0\)". So when \(a=0\) (and \(#\) is a subtraction) then \(a#(b-c)=(a#b)-(a#c)\) holds true but not for other values of \(a\), so not for all numbers \(a\), \(b\) and \(c\). Answer to the question is NO. Sufficient.

(2) \(#\) represents subtraction --> the same as above. Sufficient.

Answer: D.

Hope it's clear.


I don't understand why the answer is not E. if a = 0, then yes, if a is not equal to 0, then no. So not sufficient, as nothing can be said conclusively ...
anybody out there to help me ....?

thanks


Thanks Bunuel, you are soooo... great .... :clap:
Senior Manager
Senior Manager
avatar
S
Joined: 15 Jan 2017
Posts: 367
CAT Tests
Re: If # represents one of the operations +,- and *, is a #  [#permalink]

Show Tags

New post 14 Sep 2017, 15:09
Key word in A --> 'not equal to' -- thus the only time a#1 not 1#a is when # = minus
Really need to read questions properly!
Senior Manager
Senior Manager
avatar
S
Joined: 15 Jan 2017
Posts: 367
CAT Tests
Re: If # represents one of the operations +,- and *, is a #  [#permalink]

Show Tags

New post 14 Sep 2017, 15:10
Key word in A --> 'not equal to' -- thus the only time a#1 not 1#a is when # = minus
Really need to read questions properly!
Re: If # represents one of the operations +,- and *, is a # &nbs [#permalink] 14 Sep 2017, 15:10
Display posts from previous: Sort by

If # represents one of the operations +,- and *, is a #

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.