February 24, 2019 February 24, 2019 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. February 23, 2019 February 23, 2019 07:00 AM PST 09:00 AM PST Learn reading strategies that can help even nonvoracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 174

If @ represents one of the operations +, , and x, is k@(l+m
[#permalink]
Show Tags
14 Dec 2012, 06:13
Question Stats:
73% (01:42) correct 27% (01:57) wrong based on 1329 sessions
HideShow timer Statistics
If @ represents one of the operations +, , and x, is k@(l+m)=(k@l)+(k@m) for all numbers k, l,and m? (1) k@1 is not equal to 1@k for some numbers k. (2) @ represents subtraction.
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 53066

Re: If @ represents one of the operations +, , and x, is k@(l+m
[#permalink]
Show Tags
09 Aug 2013, 01:35
Qoofi wrote: The answer could Option E
If we take k=l=m=0 & k=1, l=2, m=3, from statement 1 we will get both "yes" or "no". Similarly Statement 2 also gives the same result.
The question doesn't specify anything about k,l,m
Could you explain? From (1) we got that @ is subtraction. So, the question becomes: is k(l+m)=(kl)+(km) for ALL NUMBERS k, l,and m? This equation holds if k=0. Therefore the equation does NOT hold true for ALL NUMBERS (it holds if k=0). The same applies to the second statement. Similar questions to practice: ifrepresentsoneoftheoperationsandxisklm144138.htmlifdenotesoneoftwoarithmeticoperationsadditionor50178.htmlifthesymbolrepresentseitheradditionormultiplication104600.htmliftheoperationisoneofthefourarithmeticoperations101283.htmliftheoperationisoneofthefourarithmeticoperations93966.htmlifdenotesoneofthefourarithmeticoperationsaddition105472.htmlthesymbolrepresentsoneofthefourarithmeticoperation107575.htmlifthesymbolrepresentseitheradditionsubtraction101741.htmlifthesymbolrepresentseitheradditionormultiplication104600.htmlifrepresentsoneoftheoperationsandisa101337.htmltheoperationxnforallpositiveintegersgreaterthan99064.htmlHope it helps.
_________________
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




Math Expert
Joined: 02 Sep 2009
Posts: 53066

Re: If @ represents one of the operations +, , and x, is k@(l+m
[#permalink]
Show Tags
14 Dec 2012, 06:27
If @ represents one of the operations +, , and x, is k@(l+m)=(k@l)+(k@m) for all numbers k, l,and m?(1) k@1 is not equal to 1@k for some numbers k. @ is neither addition (as \(k+1=1+k\)) nor multiplication (as \(k*1=1*k\)), thus @ represents subtraction. Knowing that we can determine whether \(k(l+m)=(kl)+(km)\) for all numbers k, l,and m. Sufficient. (2) @ represents subtraction. The same here. Sufficient. Answer: D.
_________________
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: 16 Apr 2009
Posts: 14

Re: If @ represents one of the operations +, , and x, is k@(l+m
[#permalink]
Show Tags
16 Dec 2012, 11:04
Bunuel wrote: If @ represents one of the operations +, , and x, is k@(l+m)=(k@l)+(k@m) for all numbers k, l,and m?
(1) k@1 is not equal to 1@k for some numbers k. @ is neither addition (as \(k+1=1+k\)) nor multiplication (as \(k*1=1*k\)), thus @ represents subtraction. Knowing that we can determine whether \(k(l+m)=(kl)+(km)\) for all numbers k, l,and m. Sufficient.
(2) @ represents subtraction. The same here. Sufficient.
Answer: D. Dear Bunnel, I would like to understand the above question first.. If we take the @ as subtraction from statement 1 and 2 then the equation stands as \(klm=2klm\), which is not equal in both the side. I was wondering whether the question asks about the operation of the @ sign, which makes the equation of k@(l+m)=(k@l)+(k@m) okay from both end. Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 53066

Re: If @ represents one of the operations +, , and x, is k@(l+m
[#permalink]
Show Tags
16 Dec 2012, 23:07
Drik wrote: Bunuel wrote: If @ represents one of the operations +, , and x, is k@(l+m)=(k@l)+(k@m) for all numbers k, l,and m?
(1) k@1 is not equal to 1@k for some numbers k. @ is neither addition (as \(k+1=1+k\)) nor multiplication (as \(k*1=1*k\)), thus @ represents subtraction. Knowing that we can determine whether \(k(l+m)=(kl)+(km)\) for all numbers k, l,and m. Sufficient.
(2) @ represents subtraction. The same here. Sufficient.
Answer: D. Dear Bunnel, I would like to understand the above question first.. If we take the @ as subtraction from statement 1 and 2 then the equation stands as \(klm=2klm\), which is not equal in both the side. I was wondering whether the question asks about the operation of the @ sign, which makes the equation of k@(l+m)=(k@l)+(k@m) okay from both end. Thanks No, the question asks: "is k@(l+m)=(k@l)+(k@m) for ALL numbers k, l,and m", where @ represents one of the operations +, , and x.
_________________
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



Manager
Joined: 18 Dec 2012
Posts: 96
Location: India
Concentration: General Management, Strategy
GMAT 1: 660 Q49 V32 GMAT 2: 530 Q37 V25
GPA: 3.32
WE: Manufacturing and Production (Manufacturing)

Re: If @ represents one of the operations +, , and x, is k@(l+m
[#permalink]
Show Tags
01 Aug 2013, 09:31
The answer could Option E If we take k=l=m=0 & k=1, l=2, m=3, from statement 1 we will get both "yes" or "no". Similarly Statement 2 also gives the same result. The question doesn't specify anything about k,l,m Could you explain?
_________________
I'm telling this because you don't get it. You think you get it which is not the same as actually getting it. Get it?



Intern
Joined: 09 Sep 2013
Posts: 16

Re: If @ represents one of the operations +, , and x, is k@(l+m
[#permalink]
Show Tags
12 Oct 2013, 11:20
The way I approached this question was basically "is @ multiplication"?
That is the only symbol that will make the equation in the question stem equal.
The first statement tells us indeed that @ is not multiplication or even addition. The only other option is subtraction...so we have our answer and it is not multiplication. Sufficient.
The second statement tells us @ is subtraction. Ok so we know it is not multiplication. Sufficient.



Intern
Joined: 17 Jun 2013
Posts: 1
Concentration: International Business, Technology
GMAT Date: 03192014

Re: If @ represents one of the operations +, , and x, is k@(l+m
[#permalink]
Show Tags
16 Nov 2013, 20:37
The way i see the question, k o (l +m) = (k o l) + (k o m) is only true where o is x(multiplication) for o = + and o = , it's not true.
1. k o 1 not equal to 1 o k. This statement is true only when o is subtraction (). But we know that the above statement is valid only for multiplication. So this option is SUFFICIENT. 2. o represents subtraction . This statement is SUFFICIENT , as we know that the question is valid only for multiplication.



Intern
Joined: 23 Apr 2012
Posts: 48

Re: If @ represents one of the operations +, , and x, is k@(l+m
[#permalink]
Show Tags
16 Nov 2013, 22:24
If @ represents one of the operations +, , and x, is k@(l+m)=(k@l)+(k@m) for all numbers k, l,and m?
(1) k@1 is not equal to 1@k for some numbers k. (2) @ represents subtraction.
The answer to this question could be a yes or a no. If we can somehow say for sure  yes or no, then we know the option is sufficient. 2) clearly says @ is subtractn. Therefore, the equation in the question is NOT true for all nos. k,l,m. SUFFICIENT.
1)k@1 != 1@k implies that @ s not x . This could be + since if k is neg, k+1 is not equal to 1(k) This could be  since k1 != 1k. substituting in the question, for +: is k+(l+m)=(k+l) + (k+m). NO. for  : is k(lm)= (kl) + (km) . NO.
There the equation is NOT true for all nos. SUFFICIENT.
D it is!



Intern
Joined: 09 Feb 2013
Posts: 24

Re: If represents one of the operations +, , and x, is k(l+m
[#permalink]
Show Tags
13 Jul 2015, 08:07
St1 : @ is substraction
if we take K=5, l=3, m=2 Then 0 is not equal to 5....as per question stem answer is NO.
If we take K=0,l=1,m= 2
Then 3= 3....so answer is YES
Since we get yes and no both....shouldn't this statement be insufficient ?
Where am I doing the mistake ?



Director
Affiliations: GMATQuantum
Joined: 19 Apr 2009
Posts: 612

If represents one of the operations +, , and x, is k(l+m
[#permalink]
Show Tags
22 Aug 2015, 23:23
This is a tricky question that troubles a lot of students.
Based on statement 1, the symbol {o} has to be equal to subtraction, because in the case of addition and multiplication the operation k{o}1 is equal to 1{o}k for all all numbers. So the conclusion from statement 1 is that the symbol stands for only subtraction.
Now if we go back to the original question in the main stem, which asks if Does k{o}(l+m) = (k{o}l) + (k{o}m) for all numbers k, l, and m? meaning is the answer to this question a definite Yes or No. If the {o} stands for subtraction then the condition k{l+m} is not equal to (kl) + (km) for all numbers. It may hold true for k=l=m=0, but we need to answer the question if it holds true for all possible values of k, l, and m, and the answer to that is a definite No, which makes it sufficient.
Cheers, Dabral



NonHuman User
Joined: 09 Sep 2013
Posts: 9892

Re: If @ represents one of the operations +, , and x, is k@(l+m
[#permalink]
Show Tags
17 Oct 2018, 03:16
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If @ represents one of the operations +, , and x, is k@(l+m
[#permalink]
17 Oct 2018, 03:16






