Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 16 Feb 2010
Posts: 201

If # represents one of the operations +, and *, is a # [#permalink]
Show Tags
Updated on: 19 Sep 2010, 16:09
7
This post was BOOKMARKED
Question Stats:
71% (01:03) correct 29% (01:26) wrong based on 376 sessions
HideShow timer Statistics
If # represents one of the operations +, and *, is a # (bc) = (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
Official Answer and Stats are available only to registered users. Register/ Login.
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
Joined: 20 Jul 2010
Posts: 236

Re: If # represents one of the operations +, and *, is a # [#permalink]
Show Tags
19 Sep 2010, 15:58
I converted question to 3 euqations where # can be +,  or * So I) When # = * abac = abac (true for all values) II) When # = + Is a+bc=bc III) When #= Is ab+c = bc? 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
Joined: 23 Sep 2009
Posts: 143

Re: If # represents one of the operations +, and *, is a # [#permalink]
Show Tags
19 Sep 2010, 16:50
1
This post received KUDOS
zisis wrote: If # represents one of the operations +, and *, is a # (bc) = (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 a1!=(not equal) 1a. 2. Choice 2 says directly that it is subtraction. Hence answer is D
_________________
Thanks, VP



Intern
Joined: 27 Jul 2010
Posts: 17
Location: Bangalore

Re: If # represents one of the operations +, and *, is a # [#permalink]
Show Tags
19 Sep 2010, 19:38
vigneshpandi wrote: zisis wrote: If # represents one of the operations +, and *, is a # (bc) = (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 a1!=(not equal) 1a. 2. Choice 2 says directly that it is subtraction. Hence answer is D IMO, it cannot be "not equal" always. If # is subtraction, a#(bc)=a(bc)=ab+c (a#b)(a#c)=(ab)(ac)=aba+c=b+c ab+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
Joined: 02 Sep 2009
Posts: 44592

Re: If # represents one of the operations +, and *, is a # [#permalink]
Show Tags
20 Sep 2010, 00:14
BalakumaranP wrote: IMO, it cannot be "not equal" always.
If # is subtraction,
a#(bc)=a(bc)=ab+c
(a#b)(a#c)=(ab)(ac)=aba+c=b+c
ab+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 \(a#(bc)=(a#b)(a#c)\) 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 \(LHS=a#(bc)=ab+c\) and \(RHS=(a#b)(a#c)=(ab)(ac)=cb\), so the question becomes "is \(ab+c=cb\) for all numbers \(a\), \(b\) and \(c\)?" > "is \(a=0\)". So when \(a=0\) (and \(#\) is a subtraction) then \(a#(bc)=(a#b)(a#c)\) 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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 27 Jul 2010
Posts: 17
Location: Bangalore

Re: If # represents one of the operations +, and *, is a # [#permalink]
Show Tags
20 Sep 2010, 03:09
Okay.. I read the question wrong...
_________________
Nothing is free.. You 've to earn it!!!



Manager
Joined: 04 Aug 2010
Posts: 127

Re: If # represents one of the operations +, and *, is a # [#permalink]
Show Tags
20 Sep 2010, 19:10
1
This post received KUDOS
(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
Joined: 06 Aug 2010
Posts: 194
Location: Boston

Re: If # represents one of the operations +, and *, is a # [#permalink]
Show Tags
21 Sep 2010, 10:55
zisis wrote: If # represents one of the operations +, and *, is a # (bc) = (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
Joined: 29 Apr 2015
Posts: 874
Location: Switzerland
Concentration: Economics, Finance
WE: Asset Management (Investment Banking)

Re: If # represents one of the operations +, and *, is a # [#permalink]
Show Tags
03 Jun 2015, 08:54
zisis wrote: If # represents one of the operations +, and *, is a # (bc) = (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
Joined: 02 Sep 2009
Posts: 44592

Re: If # represents one of the operations +, and *, is a # [#permalink]
Show Tags
03 Jun 2015, 08:58



Retired Moderator
Joined: 29 Apr 2015
Posts: 874
Location: Switzerland
Concentration: Economics, Finance
WE: Asset Management (Investment Banking)

Re: If # represents one of the operations +, and *, is a # [#permalink]
Show Tags
03 Jun 2015, 09:07
Bunuel wrote: reto wrote: zisis wrote: If # represents one of the operations +, and *, is a # (bc) = (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 expressionsCheck functions related questions in our Special Questions Directory. Symbols Representing Arithmetic OperationRounding FunctionsVarious FunctionsThe 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
Status: love the club...
Joined: 24 Mar 2015
Posts: 276

Re: If # represents one of the operations +, and *, is a # [#permalink]
Show Tags
17 Aug 2017, 19:22
Bunuel wrote: BalakumaranP wrote: IMO, it cannot be "not equal" always.
If # is subtraction,
a#(bc)=a(bc)=ab+c
(a#b)(a#c)=(ab)(ac)=aba+c=b+c
ab+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 \(a#(bc)=(a#b)(a#c)\) 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 \(LHS=a#(bc)=ab+c\) and \(RHS=(a#b)(a#c)=(ab)(ac)=cb\), so the question becomes "is \(ab+c=cb\) for all numbers \(a\), \(b\) and \(c\)?" > "is \(a=0\)". So when \(a=0\) (and \(#\) is a subtraction) then \(a#(bc)=(a#b)(a#c)\) 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
Joined: 02 Sep 2009
Posts: 44592

Re: If # represents one of the operations +, and *, is a # [#permalink]
Show Tags
17 Aug 2017, 21:24
gmatcracker2017 wrote: Bunuel wrote: BalakumaranP wrote: IMO, it cannot be "not equal" always.
If # is subtraction,
a#(bc)=a(bc)=ab+c
(a#b)(a#c)=(ab)(ac)=aba+c=b+c
ab+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 \(a#(bc)=(a#b)(a#c)\) 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 \(LHS=a#(bc)=ab+c\) and \(RHS=(a#b)(a#c)=(ab)(ac)=cb\), so the question becomes "is \(ab+c=cb\) for all numbers \(a\), \(b\) and \(c\)?" > "is \(a=0\)". So when \(a=0\) (and \(#\) is a subtraction) then \(a#(bc)=(a#b)(a#c)\) 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 \(a#(bc)=(a#b)(a#c)\) 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? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 276

Re: If # represents one of the operations +, and *, is a # [#permalink]
Show Tags
17 Aug 2017, 22:01
gmatcracker2017 wrote: Bunuel wrote: BalakumaranP wrote: IMO, it cannot be "not equal" always.
If # is subtraction,
a#(bc)=a(bc)=ab+c
(a#b)(a#c)=(ab)(ac)=aba+c=b+c
ab+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 \(a#(bc)=(a#b)(a#c)\) 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 \(LHS=a#(bc)=ab+c\) and \(RHS=(a#b)(a#c)=(ab)(ac)=cb\), so the question becomes "is \(ab+c=cb\) for all numbers \(a\), \(b\) and \(c\)?" > "is \(a=0\)". So when \(a=0\) (and \(#\) is a subtraction) then \(a#(bc)=(a#b)(a#c)\) 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 ....



Senior Manager
Joined: 15 Jan 2017
Posts: 361

Re: If # represents one of the operations +, and *, is a # [#permalink]
Show Tags
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
Joined: 15 Jan 2017
Posts: 361

Re: If # represents one of the operations +, and *, is a # [#permalink]
Show Tags
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 #
[#permalink]
14 Sep 2017, 15:10






