Last visit was: 19 Jul 2024, 04:55 It is currently 19 Jul 2024, 04:55
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
SORT BY:
Date
Tags:
Show Tags
Hide Tags
User avatar
Manager
Manager
Joined: 11 Jul 2010
Posts: 139
Own Kudos [?]: 218 [9]
Given Kudos: 20
Send PM
avatar
Manager
Manager
Joined: 30 Aug 2010
Posts: 65
Own Kudos [?]: 515 [3]
Given Kudos: 27
Location: Bangalore, India
Send PM
User avatar
Manager
Manager
Joined: 11 Jul 2010
Posts: 139
Own Kudos [?]: 218 [0]
Given Kudos: 20
Send PM
Math Expert
Joined: 02 Sep 2009
Posts: 94411
Own Kudos [?]: 642233 [2]
Given Kudos: 86282
Send PM
Re: If & represents one of the operations +, - and x. Is (a&b) + [#permalink]
1
Kudos
1
Bookmarks
Expert Reply
gmat1011 wrote:
If & represents one of the operations +, - and X
is (a & b) + (a & c) = a & (b + c) for all numbers a, b, and c ?

(1) & represents subtraction.
(2) m&2 is not equal to 2&m for some numbers m.

C/right Jeff Sackmann. Just posting it here for educational purposes.

Don't get how it can be D. Shouldn't it be E? in 2a-b-c = a-b-c, a can be 0 when there would in fact be a "Yes" answer, while it would also be possible to get "No" with other values?


The point here is that the question asks whether \((a@b)+(a@c)=a@(b+c)\) is true FOR ALL NUMBERS a, b, and c?

(1) \(@\) represents subtraction --> the question becomes is \(2a-b-c=a-b-c\), or is \(a=0\)? So \((a@b)+(a@c)=a@(b+c)\) is NOT true for all numbers a, b, and c (so the answer to the question is NO), for this expression to be true \(a\) must equal to zero (so not for all values of \(a\)). Sufficient.

(2) \(m@2\neq{2@}\) --> \(@\) represents subtraction (as it can not be addition or multiplication), so we have the the same info as above. Sufficient.

Answer: D.

Alternately you can see that \((a@b)+(a@c)=a@(b+c)\) to be true FOR ALL NUMBERS a, b, and c then \(@\) must represent multiplication as only for multiplication it's true for all numbers: \(ab+ac=ab+ac\). So the question basically ask whether \(@\) represents multiplication, both (1) and (2) give answer No toth is question.

Hope it's clear.
User avatar
Manager
Manager
Joined: 11 Jul 2010
Posts: 139
Own Kudos [?]: 218 [0]
Given Kudos: 20
Send PM
Re: If & represents one of the operations +, - and x. Is (a&b) + [#permalink]
yes - thanks Bunuel and Murali - +1 to both...

for some reason i was misinterpreting the expression "all numbers".. this makes sense - the equation is not valid for all values of a,b,c so both are in fact sufficient. thanks.
avatar
Intern
Intern
Joined: 08 Jun 2010
Posts: 41
Own Kudos [?]: 75 [0]
Given Kudos: 15
Send PM
Re: If & represents one of the operations +, - and x. Is (a&b) + [#permalink]
Statement 1- tells us exact nature of sign( subtraction). therefore,sufficient
Statement 2- 2@m not equal to m@2
take the values m=6,5. and solve and we get what the mean of sign. sufficient
so, Answer is D
Math Expert
Joined: 02 Sep 2009
Posts: 94411
Own Kudos [?]: 642233 [0]
Given Kudos: 86282
Send PM
Re: If & represents one of the operations +, - and x. Is (a&b) + [#permalink]
Expert Reply
Bunuel wrote:
gmat1011 wrote:
If & represents one of the operations +, - and X
is (a & b) + (a & c) = a & (b + c) for all numbers a, b, and c ?

(1) & represents subtraction.
(2) m&2 is not equal to 2&m for some numbers m.

C/right Jeff Sackmann. Just posting it here for educational purposes.

Don't get how it can be D. Shouldn't it be E? in 2a-b-c = a-b-c, a can be 0 when there would in fact be a "Yes" answer, while it would also be possible to get "No" with other values?


The point here is that the question asks whether \((a@b)+(a@c)=a@(b+c)\) is true FOR ALL NUMBERS a, b, and c?

(1) \(@\) represents subtraction --> the question becomes is \(2a-b-c=a-b-c\), or is \(a=0\)? So \((a@b)+(a@c)=a@(b+c)\) is NOT true for all numbers a, b, and c (so the answer to the question is NO), for this expression to be true \(a\) must equal to zero (so not for all values of \(a\)). Sufficient.

(2) \(m@2\neq{2@}\) --> \(@\) represents subtraction (as it can not be addition or multiplication), so we have the the same info as above. Sufficient.

Answer: D.

Alternately you can see that \((a@b)+(a@c)=a@(b+c)\) to be true FOR ALL NUMBERS a, b, and c then \(@\) must represent multiplication as only for multiplication it's true for all numbers: \(ab+ac=ab+ac\). So the question basically ask whether \(@\) represents multiplication, both (1) and (2) give answer No toth is question.

Hope it's clear.


Check Arithmetic Operation Functions Questions in Special Questions Directory.
Retired Moderator
Joined: 22 Aug 2013
Posts: 1181
Own Kudos [?]: 2551 [1]
Given Kudos: 459
Location: India
Send PM
Re: If & represents one of the operations +, - and x. Is (a&b) + [#permalink]
gmat1011 wrote:
If & represents one of the operations +, - and x. Is (a&b) + (a&c) = a&(b + c) for all numbers a, b, and c ?

(1) & represents subtraction.
(2) m&2 is not equal to 2&m for some numbers m.


Don't get how it can be D. Shouldn't it be E? in 2a-b-c = a-b-c, a can be 0 when there would in fact be a "Yes" answer, while it would also be possible to get "No" with other values?


Is (a&b) + (a&c) = a&(b + c) for all numbers a, b, and c ?

(1) if & represents subtraction, then LHS = (a-b) + (a-c) = 2a-b-c and RHS = a - (b+c) = a-b-c. Now obviously 2a-b-c is NOT equal to a-b-c for all numbers a, b, c. So we get our definite answer as NO for the question stem. Sufficient.

(2) m&2 is NOT equal to 2&m. Now if & is '+', then m+2 = 2+m, for all values of m. So & cannot be '+'. If & is 'x', then also mx2 = 2xm, for all values of m. So & cannot be 'x'. Thus & can only represent subtraction '-'. In which case it becomes same as first statement. Sufficient.

Hence D answer
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 34018
Own Kudos [?]: 852 [0]
Given Kudos: 0
Send PM
Re: If & represents one of the operations +, - and x. Is (a&b) + [#permalink]
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 Club Bot
Re: If & represents one of the operations +, - and x. Is (a&b) + [#permalink]
Moderator:
Math Expert
94411 posts