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Manager  Joined: 16 Feb 2010
Posts: 158
If # represents one of the operations +,- and *, is a #  [#permalink]

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13 00:00

Difficulty:   35% (medium)

Question Stats: 70% (01:33) correct 30% (02:01) wrong based on 494 sessions

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If # represents one of the operations +,- and *, is a # (b-c) = (a#b) – (a#c) for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a

(2) # represents subtraction

Originally posted by zisis on 19 Sep 2010, 15:49.
Last edited by zisis on 19 Sep 2010, 16:09, edited 1 time in total.
Manager  Joined: 23 Sep 2009
Posts: 94
Re: If # represents one of the operations +,- and *, is a #  [#permalink]

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1
zisis wrote:
If # represents one of the operations +,- and *, is a # (b-c) = (a#b) – (a#c) for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a

(2) # represents subtraction

Mods, please to DS section...posted by mistake in PS - apologies

1. From choice 1 it is clear that # is subtraction. coz a+1=1+1, a*1=1*a but a-1!=(not equal) 1-a.
2. Choice 2 says directly that it is subtraction.

Manager  Joined: 04 Aug 2010
Posts: 71
Re: If # represents one of the operations +,- and *, is a #  [#permalink]

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1
(1) a#1 is not equal to 1#a for some numbers a

a + 1 = 1 + a for all a
a*1 = 1*a for all a

a - 1 != 1 - a

Statement (1) implies # is a minus sign, so it has same meaning as (2).

Ans D
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If # represents one of the operations +,- and *, is a #  [#permalink]

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1

If a = zero, LHS = RHS , and ans to main Q stem is YES
If a$$\neq{0}$$ zero, LHS$$\neq{0}$$ RHS, ans to main q stem is NO.
How is St 1 suff?
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Re: If # represents one of the operations +,- and *, is a #  [#permalink]

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1

If a = zero, LHS = RHS , and ans to main Q stem is YES
If a$$\neq{0}$$ zero, LHS$$\neq{0}$$ RHS, ans to main q stem is NO.
How is St 1 suff?

From (1) we get that the equation is NOT true for ALL numbers. It's true only if a = 0 (so not for ALL numbers).
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If # represents one of the operations +,- and *, is a #  [#permalink]

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1

If a = zero, LHS = RHS , and ans to main Q stem is YES
If a$$\neq{0}$$ zero, LHS$$\neq{0}$$ RHS, ans to main q stem is NO.
How is St 1 suff?

This question actually has a built-in 'design flaw' which makes the information in the two Facts irrelevant. The way that the question is phrased, there are only 3 possibilities and they ALL lead to a "Sufficient" answer. There are a lot of details in the wording that make the prompt 'complicated looking' - so instead, here's a much simpler question that is based on the same design flaw:

"Is this lightbulb always on?"

IF... the lightbulb is ALWAYS on... then we have a definitive/Sufficient answer to the question that is asked (Sufficient YES).
IF... the lightbulb is NEVER on... then we also have a definitive/Sufficient answer to the question that is asked (Sufficient NO).
IF... the lightbulb is SOMETIMES on... then we still have a definitive/Sufficient answer to the question that is asked (Sufficient NO).

From the date on this post, we can clearly see that this is an old question (and it's likely that whoever wrote it didn't even recognize the flaw in it). While you'll likely see at least one Symbolism question on Test Day - and you'll certainly have to work through lots of little Arithmetic steps during the Exam - it's incredibly unlikely that you will face any flawed questions on the Official GMAT. This is all meant to say that you should ignore this question.

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Manager  Joined: 20 Jul 2010
Posts: 174
Re: If # represents one of the operations +,- and *, is a #  [#permalink]

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I converted question to 3 euqations where # can be +, - or *

So
I) When # = *
ab-ac = ab-ac (true for all values)

II) When # = +
Is a+b-c=b-c

III) When #=-
Is a-b+c = -b-c?

With option A we know # is not * as 1*a is always equal to a*1. So given equation is not equal
With option B , equation is not equal.

Intern  Joined: 27 Jul 2010
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Re: If # represents one of the operations +,- and *, is a #  [#permalink]

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vigneshpandi wrote:
zisis wrote:
If # represents one of the operations +,- and *, is a # (b-c) = (a#b) – (a#c) for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a

(2) # represents subtraction

Mods, please to DS section...posted by mistake in PS - apologies

1. From choice 1 it is clear that # is subtraction. coz a+1=1+1, a*1=1*a but a-1!=(not equal) 1-a.
2. Choice 2 says directly that it is subtraction.

IMO, it cannot be "not equal" always.

If # is subtraction,

a#(b-c)=a-(b-c)=a-b+c

(a#b)-(a#c)=(a-b)-(a-c)=a-b-a+c=-b+c

a-b+c=-b+c when a=0 and not equal for other values.. So both are insufficient.. Am I missing something here?
Math Expert V
Joined: 02 Sep 2009
Posts: 59721
If # represents one of the operations +,- and *, is a #  [#permalink]

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BalakumaranP wrote:
IMO, it cannot be "not equal" always.

If # is subtraction,

a#(b-c)=a-(b-c)=a-b+c

(a#b)-(a#c)=(a-b)-(a-c)=a-b-a+c=-b+c

a-b+c=-b+c when a=0 and not equal for other values.. So both are insufficient.. Am I missing something here?

If # represents one of the operations +, - and *, is $$a#(b-c)=(a#b)-(a#c)$$ for all numbers $$a$$, $$b$$ and $$c$$.

(1) $$a#1$$ is not equal to $$1#a$$ for some numbers $$a$$.

$$#$$ is neither addition (as $$a+1=1+a$$) not multiplication (as $$a*1=1*a$$), so $$#$$ is a subtraction. Then $$LHS=a#(b-c)=a-b+c$$ and $$RHS=(a#b)-(a#c)=(a-b)-(a-c)=c-b$$, so the question becomes "is $$a-b+c=c-b$$ for all numbers $$a$$, $$b$$ and $$c$$?" --> "is $$a=0$$". So when $$a=0$$ (and $$#$$ is a subtraction) then $$a#(b-c)=(a#b)-(a#c)$$ holds true but not for other values of $$a$$, so not for all numbers $$a$$, $$b$$ and $$c$$. Answer to the question is NO. Sufficient.

(2) $$#$$ represents subtraction --> the same as above. Sufficient.

Hope it's clear.
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Re: If # represents one of the operations +,- and *, is a #  [#permalink]

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Okay.. I read the question wrong...
Manager  Joined: 06 Aug 2010
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Re: If # represents one of the operations +,- and *, is a #  [#permalink]

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zisis wrote:
If # represents one of the operations +,- and *, is a # (b-c) = (a#b) – (a#c) for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a

(2) # represents subtraction

Mods, please to DS section...posted by mistake in PS - apologies

You're told that "#" is either addition, subtraction, or multiplication, and then asked if "#" satisfies the distributive property. Of these three, distribution only holds for multiplication, so if "#" is "*", it holds, and if "#" isn't "*", then it does not hold.

All we really need to know is what operation "#" really is.

(1) This is only true of subtraction, so # is subtraction and the distributive property does not hold. Sufficient.
(2) Same as above. Sufficient.

(D)
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Re: If # represents one of the operations +,- and *, is a #  [#permalink]

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zisis wrote:
If # represents one of the operations +,- and *, is a # (b-c) = (a#b) – (a#c) for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a

(2) # represents subtraction

Could someone edit this question so it will be an actual question? There is no proper question stem.
Math Expert V
Joined: 02 Sep 2009
Posts: 59721
Re: If # represents one of the operations +,- and *, is a #  [#permalink]

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reto wrote:
zisis wrote:
If # represents one of the operations +,- and *, is a # (b-c) = (a#b) – (a#c) for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a

(2) # represents subtraction

Could someone edit this question so it will be an actual question? There is no proper question stem.

What do you mean? Everything is correct there. Similar questions: Operations/functions defining algebraic/arithmetic expressions

Check functions related questions in our Special Questions Directory.

Symbols Representing Arithmetic Operation
Rounding Functions
Various Functions
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Re: If # represents one of the operations +,- and *, is a #  [#permalink]

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Bunuel wrote:
reto wrote:
zisis wrote:
If # represents one of the operations +,- and *, is a # (b-c) = (a#b) – (a#c) for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a

(2) # represents subtraction

Could someone edit this question so it will be an actual question? There is no proper question stem.

What do you mean? Everything is correct there. Similar questions: Operations/functions defining algebraic/arithmetic expressions

Check functions related questions in our Special Questions Directory.

Symbols Representing Arithmetic Operation
Rounding Functions
Various Functions

The question mark is missing in the question stem.
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Re: If # represents one of the operations +,- and *, is a #  [#permalink]

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Bunuel wrote:
BalakumaranP wrote:
IMO, it cannot be "not equal" always.

If # is subtraction,

a#(b-c)=a-(b-c)=a-b+c

(a#b)-(a#c)=(a-b)-(a-c)=a-b-a+c=-b+c

a-b+c=-b+c when a=0 and not equal for other values.. So both are insufficient.. Am I missing something here?

If # represents one of the operations +, - and *, is $$a#(b-c)=(a#b)-(a#c)$$ for all numbers $$a$$, $$b$$ and $$c$$.

(1) $$a#1$$ is not equal to $$1#a$$ for some numbers $$a$$.

$$#$$ is neither addition (as $$a+1=1+a$$) not multiplication (as $$a*1=1*a$$), so $$#$$ is a subtraction. Then $$LHS=a#(b-c)=a-b+c$$ and $$RHS=(a#b)-(a#c)=(a-b)-(a-c)=c-b$$, so the question becomes "is $$a-b+c=c-b$$ for all numbers $$a$$, $$b$$ and $$c$$?" --> "is $$a=0$$". So when $$a=0$$ (and $$#$$ is a subtraction) then $$a#(b-c)=(a#b)-(a#c)$$ holds true but not for other values of $$a$$, so not for all numbers $$a$$, $$b$$ and $$c$$. Answer to the question is NO. Sufficient.

(2) $$#$$ represents subtraction --> the same as above. Sufficient.

Hope it's clear.

I don't understand why the answer is not E. if a = 0, then yes, if a is not equal to 0, then no. So not sufficient, as nothing can be said conclusively ...
anybody out there to help me ....?

thanks
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Re: If # represents one of the operations +,- and *, is a #  [#permalink]

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gmatcracker2017 wrote:
Bunuel wrote:
BalakumaranP wrote:
IMO, it cannot be "not equal" always.

If # is subtraction,

a#(b-c)=a-(b-c)=a-b+c

(a#b)-(a#c)=(a-b)-(a-c)=a-b-a+c=-b+c

a-b+c=-b+c when a=0 and not equal for other values.. So both are insufficient.. Am I missing something here?

If # represents one of the operations +, - and *, is $$a#(b-c)=(a#b)-(a#c)$$ for all numbers $$a$$, $$b$$ and $$c$$.

(1) $$a#1$$ is not equal to $$1#a$$ for some numbers $$a$$.

$$#$$ is neither addition (as $$a+1=1+a$$) not multiplication (as $$a*1=1*a$$), so $$#$$ is a subtraction. Then $$LHS=a#(b-c)=a-b+c$$ and $$RHS=(a#b)-(a#c)=(a-b)-(a-c)=c-b$$, so the question becomes "is $$a-b+c=c-b$$ for all numbers $$a$$, $$b$$ and $$c$$?" --> "is $$a=0$$". So when $$a=0$$ (and $$#$$ is a subtraction) then $$a#(b-c)=(a#b)-(a#c)$$ holds true but not for other values of $$a$$, so not for all numbers $$a$$, $$b$$ and $$c$$. Answer to the question is NO. Sufficient.

(2) $$#$$ represents subtraction --> the same as above. Sufficient.

Hope it's clear.

I don't understand why the answer is not E. if a = 0, then yes, if a is not equal to 0, then no. So not sufficient, as nothing can be said conclusively ...
anybody out there to help me ....?

thanks

The question asks: is $$a#(b-c)=(a#b)-(a#c)$$ for all numbers $$a$$, $$b$$ and $$c$$? From each statement we got a deinite NO answer - NO the equation doe NOT hold true for all numbers, it's true if a = 0 but not true if a is not 0.
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Re: If # represents one of the operations +,- and *, is a #  [#permalink]

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gmatcracker2017 wrote:
Bunuel wrote:
BalakumaranP wrote:
IMO, it cannot be "not equal" always.

If # is subtraction,

a#(b-c)=a-(b-c)=a-b+c

(a#b)-(a#c)=(a-b)-(a-c)=a-b-a+c=-b+c

a-b+c=-b+c when a=0 and not equal for other values.. So both are insufficient.. Am I missing something here?

If # represents one of the operations +, - and *, is $$a#(b-c)=(a#b)-(a#c)$$ for all numbers $$a$$, $$b$$ and $$c$$.

(1) $$a#1$$ is not equal to $$1#a$$ for some numbers $$a$$.

$$#$$ is neither addition (as $$a+1=1+a$$) not multiplication (as $$a*1=1*a$$), so $$#$$ is a subtraction. Then $$LHS=a#(b-c)=a-b+c$$ and $$RHS=(a#b)-(a#c)=(a-b)-(a-c)=c-b$$, so the question becomes "is $$a-b+c=c-b$$ for all numbers $$a$$, $$b$$ and $$c$$?" --> "is $$a=0$$". So when $$a=0$$ (and $$#$$ is a subtraction) then $$a#(b-c)=(a#b)-(a#c)$$ holds true but not for other values of $$a$$, so not for all numbers $$a$$, $$b$$ and $$c$$. Answer to the question is NO. Sufficient.

(2) $$#$$ represents subtraction --> the same as above. Sufficient.

Hope it's clear.

I don't understand why the answer is not E. if a = 0, then yes, if a is not equal to 0, then no. So not sufficient, as nothing can be said conclusively ...
anybody out there to help me ....?

thanks

Thanks Bunuel, you are soooo... great .... Senior Manager  S
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Re: If # represents one of the operations +,- and *, is a #  [#permalink]

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Key word in A --> 'not equal to' -- thus the only time a#1 not 1#a is when # = minus
Really need to read questions properly!
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Posts: 332
Re: If # represents one of the operations +,- and *, is a #  [#permalink]

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Key word in A --> 'not equal to' -- thus the only time a#1 not 1#a is when # = minus
Really need to read questions properly!
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Re: If # represents one of the operations +,- and *, is a #  [#permalink]

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zisis wrote:
If # represents one of the operations +,- and *, is a # (b-c) = (a#b) – (a#c) for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a

(2) # represents subtraction

Given: # represents one of the operations +,- and *

Asked: Is a # (b-c) = (a#b) – (a#c) for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a
a+1 = 1+a
a*1 = 1*a
$$a-1 \neq 1-a$$
# = -
a#(b-c) = a-b+c
(a#b) – (a#c) = (a-b) - (a-c) = c -b
a # (b-c)$$\neq$$ (a#b) – (a#c)
SUFFICIENT

(2) # represents subtraction
# = -
a#(b-c) = a-b+c
(a#b) – (a#c) = (a-b) - (a-c) = c -b
a # (b-c)$$\neq$$ (a#b) – (a#c)
SUFFICIENT

IMO D Re: If # represents one of the operations +,- and *, is a #   [#permalink] 09 Sep 2019, 04:53
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