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# From Grockit: If # represents +, -, *, or /, then does

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From Grockit: If # represents +, -, *, or /, then does [#permalink]  29 Nov 2010, 21:09
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35% (medium)

Question Stats:

66% (01:57) correct 34% (01:02) wrong based on 41 sessions
From Grockit:

If # represents +, -, *, or /, then does (a+b)#c = (a#c) + (b#c) for all numbers a, b, and c?

1. 1#c = c#1

2. # represents +
[Reveal] Spoiler: OA

Last edited by JenniferClopton on 30 Nov 2010, 06:55, edited 1 time in total.
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Re: DS Problem: Associative and Distributive Properties [#permalink]  29 Nov 2010, 21:21
I initially chose D. Working quickly, I reasoned that both + and * would satisfy the distributive equation for all a, b, and c. But, when you write it out, this is obviously not the case...

(a+b)+c ≠ (a+c) + (b+c)

(a+b)*c = (a*c) + (b*c)
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Re: DS Problem: Associative and Distributive Properties [#permalink]  29 Nov 2010, 22:41
From Statement (1)

# could be

# = + ( for any c )

# = - ( for c = 1)

# = * ( for any c )

# = / ( for c = 1, -1 )

Therefore, # could be + or *

+ doesn't satisfy the equation (a+b)#c = (a#b) + (b#c)

It will satisfy only if b =0

* also doesn't satisfy the equation (a+b)#c = (a#b) + (b#c)

It will satisfy only if a = 0 or b = c

From Statement (2)

# = +

Even after combining the (1) and (2), we can't say that equation will be satisfied for all the values of a,b, and c.

Did I miss something?
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Re: DS Problem: Associative and Distributive Properties [#permalink]  29 Nov 2010, 22:55
From both the options we can not say that equation will be satisfied for all the values of a,b, and c...
BUT we can say that equation will NOT be satisfied for all the values of a,b, and c.

IMO D
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Respect,
Vaibhav

PS: Correct me if I am wrong.

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Re: DS Problem: Associative and Distributive Properties [#permalink]  29 Nov 2010, 23:16
Jennifer is this question write or it is (a+b)#c = (a#c) + (b#c)

Because if it is (a+b)#c = (a#b) + (b#c) as u have mentioned in the question then..
Statement 1 does not satisfy the condition in any way. Therefore (a+b)#c = (a#b) + (b#c) does not stand and this statement gives us the answer that condition is not possible.

Statement 2 also provide that (a+b)#c = (a#b) + (b#c) does not stand and this statement again gives us answer that condition is not possible.

And therefore answer will be "D"

But OA is "B" ... and for that the condition should be (a+b)#c = (a#c) + (b#c) and not as u mentioned in the question.
In this Statement 1 will satisfy in * and / conditions and will not in + and - conditions
But statement 2 will satisfy the condition and the answer will be "B"

Plz recheck ur question.
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Re: DS Problem: Associative and Distributive Properties [#permalink]  29 Nov 2010, 23:49
JenniferClopton wrote:
From Grockit:

If # represents +, -, *, or /, then does (a+b)#c = (a#c) + (b#c) for all numbers a, b, and c?

1. 1#c = c#1

2. # represents +

I think the correct question ought to be as above

Statement 1 : 1#c=c#1 ... means # is either + or * ... If it is +, the answer is "no" ... If it is *, the answer is "yes"
Statement 2 : Sufficient to answer "no"

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Re: DS Problem: Associative and Distributive Properties [#permalink]  29 Nov 2010, 23:50
Expert's post
JenniferClopton wrote:
From Grockit:

If # represents +, -, *, or /, then does (a+b)#c = (a#b) + (b#c) for all numbers a, b, and c?

1. 1#c = c#1

2. # represents +

It should be: (a+b)#c = (a#c) + (b#c) instead of (a+b)#c = (a#b) + (b#c)

(1) 1#c = c#1 --> # can be either addition or multiplication: 1*c=c*1 and 1+c=c+1 (true for ALL numbers of a, b, and c). Now, if it's addition then we'll have: a+b+c\neq{a+c+b+c } (so it's doesn't hold true for ALL numbers a, b, and c, it holds true when c=0) and if it's multiplication then we'll have: ac+bc={ac+bc } (so it's holds true for ALL numbers of a, b, and c). Not sufficient.

(2) # represents + --> if # represents addition then given equation doesn't hold true for all numbers a, b, and c, it holds true when c=0. So we have the answer No to the question. Sufficient.

Similar questions:
operations-101337.html
jeff-sackmann-extreme-challenge-q-105352.html

Hope it helps.
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Re: DS Problem: Associative and Distributive Properties [#permalink]  30 Nov 2010, 06:57
Bunuel wrote:
It should be: (a+b)#c = (a#c) + (b#c) instead of (a+b)#c = (a#b) + (b#c)

I have corrected the error in the initial post. Apologies. This question has fooled me twice!
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Re: DS Problem: Associative and Distributive Properties [#permalink]  30 Nov 2010, 07:05
BTW WHT'S THE CORRECT ANSWER TO THIS QUESTION I CHOSE

OA-(b)
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Re: DS Problem: Associative and Distributive Properties [#permalink]  30 Nov 2010, 07:43
3
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Guys consider giving me KUDOS..... i have corrected a question. come on be sporty...
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Re: From Grockit: If # represents +, -, *, or /, then does [#permalink]  08 Jan 2014, 18:32
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Re: From Grockit: If # represents +, -, *, or /, then does   [#permalink] 08 Jan 2014, 18:32
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