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

 It is currently 13 Dec 2018, 05:19

Join School Specific Chat Rooms  |  Stanford Chat (Calls Started)  |  Wharton Chat  (Calls Expected Soon)  |  Fuqua Chat (Calls Expected Soon)

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

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

Events & Promotions

Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• The winning strategy for 700+ on the GMAT

December 13, 2018

December 13, 2018

08:00 AM PST

09:00 AM PST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
• GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

December 14, 2018

December 14, 2018

09:00 AM PST

10:00 AM PST

10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.

If the symbol @ represents either addition or multiplication

Author Message
TAGS:

Hide Tags

Manager
Joined: 17 Aug 2010
Posts: 51

Show Tags

10 Nov 2010, 02:56
4
13
00:00

Difficulty:

5% (low)

Question Stats:

81% (01:10) correct 19% (01:22) wrong based on 710 sessions

HideShow timer Statistics

If the symbol @ represents either addition or multiplication, which operation does it represent?

(1) a@b=b@a for all numbers a and b
(2) a@(b–c)=(a@b)–(a@c) for all numbers a, b, and c

_________________

I don't want kudos.. I want to see smile on your face if I am able to help you.. which is priceless.

Math Expert
Joined: 02 Sep 2009
Posts: 51184

Show Tags

10 Nov 2010, 03:23
4
5
zerotoinfinite2006 wrote:

OA is "B", I am confused.

How come
a + ( b -c ) = (a + b) - (a + c) ?
and why not

a + b = b + a

If the symbol @ represents either addition or multiplication, which operation does it represent?

(1) a@b=b@a for all numbers a and b --> @ can be addition (a+b=b+a) as well as multiplication (a*b=b*a). Not sufficient.

(2) a@(b–c)=(a@b)–(a@c) for all numbers a, b, and c --> if @ represents addition we will have $$a@(b-c)=a+b-c$$ which is not equal to $$(a@b)-(a@c)=(a+b)-(a+c)=b-c$$, so @ must be multiplication. Sufficient. (Just to check: $$a@(b-c)=a*(b-c)=ab-ac$$ which is equal to $$(a@b)-(a@c)=ab-ac$$)

Similar problems:
symbol-problem-101741.html?hilit=symbol#p788840
ds-question-100955.html?hilit=symbol
just-800-level-question-99064.html?hilit=symbol

Hope it helps.
_________________
General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 51184

Show Tags

21 Jun 2013, 01:50
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

All DS Functions and Custom Characters questions: search.php?search_id=tag&tag_id=40
All PS Functions and Custom Characters questions: search.php?search_id=tag&tag_id=61

_________________
Intern
Joined: 22 May 2013
Posts: 46
Concentration: General Management, Technology
GPA: 3.9
WE: Information Technology (Computer Software)

Show Tags

22 Jun 2013, 02:28
3
zerotoinfinite2006 wrote:
If the symbol @ represents either addition or multiplication, which operation does it represent?

(1) a@b=b@a for all numbers a and b
(2) a@(b–c)=(a@b)–(a@c) for all numbers a, b, and c

Question: what is the operation @ ?
@ = + or *

As soon as you look at the questions, you will be reminded of the number properties Commutative and Distributive.

statement 1:
(1) a@b=b@a
Commutative property =>valid for both, + as well as *, =>cant say, Not Suff
(2) a@(b–c)=(a@b)–(a@c)
Distributive property=> Always valid for * -> Sufficient

_________________

Senior Manager
Joined: 19 Oct 2012
Posts: 323
Location: India
Concentration: General Management, Operations
GMAT 1: 660 Q47 V35
GMAT 2: 710 Q50 V38
GPA: 3.81
WE: Information Technology (Computer Software)

Show Tags

21 Nov 2015, 01:33
in statement B.. Why dont we consider the case of 0 where both +, x will work there by yielding E as answer? Is it because the Question says a,b,c are Numbers and hence we dont consider the case of 0? Which implies to consider 0 only when the it is mentioned to consider all integers/ or just integers. Therefore, if question mentions numbers it will be false to assume integers?

_________________

Citius, Altius, Fortius

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6629
GMAT 1: 760 Q51 V42
GPA: 3.82

Show Tags

22 Nov 2015, 01:29
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If the symbol @ represents either addition or multiplication, which operation does it represent?

(1) a@b=b@a for all numbers a and b
(2) a@(b–c)=(a@b)–(a@c) for all numbers a, b, and c

There is one variable (@) and 2 equations are given by the 2 conditions, so there is high chance (D) will be our answer.
For condition 1, @=*,+ , so this is insufficient.
For condition 2, @=*. This is sufficient, so the answer becomes (B).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Joined: 02 Jun 2015
Posts: 22
Location: United States

Show Tags

01 Sep 2018, 12:49
1
The symbol $$\triangle$$ can be + or *

1) a $$\triangle$$ b = b $$\triangle$$ a for all numbers a and b

If a=1 and b=1
1+1 = 1+1 = 2
1*1 = 1*1 = 1

If a=2 and b=1
2+1 = 1+2 = 3
2*1 = 1*2 = 2

These give us 2 different answers + or *
INSUFFICIENT

2) a $$\triangle$$ (b-c) = (a $$\triangle$$ b) - (a $$\triangle$$ c) for all numbers a, b, and c.

If a=1 b=1 c=1

1 + (1 - 1) = (1+1) - (1+1)
1 + 0 = 2 - 2
1=0
It can not be addition +

1 * (1 - 1) = (1*1) - (1*1)
1* 0 = 1 - 1
0 = 0
It has to be multiplication * Only one answer. SUFFICIENT

Hope it helps!
Thanks, Alecita
Re: If the symbol @ represents either addition or multiplication &nbs [#permalink] 01 Sep 2018, 12:49
Display posts from previous: Sort by