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If the symbol @ represents either addition or multiplication

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If the symbol @ represents either addition or multiplication [#permalink] New post 10 Nov 2010, 02:56
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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
[Reveal] Spoiler: OA

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Re: If the symbol @ represents either addition or multiplication [#permalink] New post 22 Jun 2013, 02:28
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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

Answer : B
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Re: Addition or multiplication [#permalink] New post 10 Nov 2010, 03:23
Expert's post
zerotoinfinite2006 wrote:
Image

[Reveal] Spoiler:
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)

Answer: B.

Similar problems:
symbols-89562.html?hilit=represents%20addition
operations-101337.html?hilit=addition%20multiplication
symbol-problem-101741.html?hilit=symbol#p788840
ds-question-100955.html?hilit=symbol
just-800-level-question-99064.html?hilit=symbol

Hope it helps.
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Expert Post
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Re: If the symbol @ represents either addition or multiplication [#permalink] New post 21 Jun 2013, 01:50
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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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

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Re: If the symbol @ represents either addition or multiplication   [#permalink] 21 Jun 2013, 01:50
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