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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]

10 Nov 2010, 03:56

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94% (01:41) correct

5% (01:23) wrong

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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: Addition or multiplication [#permalink]

10 Nov 2010, 04:23

zerotoinfinite2006 wrote:

[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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Re: Addition or multiplication [#permalink] 10 Nov 2010, 04:23

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If the symbol @ represents either addition or multiplication

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If the symbol @ represents either addition or multiplication

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