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# If (a – b)2c = 0, then which of the following must be true?

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Manager
Joined: 15 Mar 2012
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If (a – b)2c = 0, then which of the following must be true? [#permalink]

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Updated on: 30 Mar 2013, 10:32
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If ((a – b)^2)c = 0, then which of the following must be true?

I. a = b
II. (a – b) c = 0
III. c = 0

A. II only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III

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MV
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Originally posted by marcovg4 on 30 Mar 2013, 10:18.
Last edited by marcovg4 on 30 Mar 2013, 10:32, edited 1 time in total.
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Re: If (a – b)2c = 0, then which of the following must be true? [#permalink]

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30 Mar 2013, 10:28
2
$$c(a-b)^2=0$$

In this case we have 2 options
$$c=0$$ or $$(a-b)^2=0, a-b=0$$

I.a = b a-b=0
This can be false, if c = 0

II. (a – b) c = 0
We know that one (or both) between $$c$$ and $$a-b$$ equals 0, so when you multiply a 0 by any number you obtain 0. This must be true

III.c = 0
This can be false if a-b=0
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Manager
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Re: If (a – b)2c = 0, then which of the following must be true? [#permalink]

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30 Mar 2013, 10:34
Zarrolou,

I forgot to write the answer choice. Try again please.
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MV
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Re: If (a – b)2c = 0, then which of the following must be true? [#permalink]

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30 Mar 2013, 10:39
Can you explain why? I thought III option is true, since it is saying that c = 0, hence (a-b)^2 * c = 0
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MV
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Re: If (a – b)2c = 0, then which of the following must be true? [#permalink]

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30 Mar 2013, 10:47
marcovg4 wrote:
Can you explain why? I thought III option is true, since it is saying that c = 0, hence (a-b)^2 * c = 0

Option III says that, given $$(a-b)^2 * c = 0$$, c must be =0.
Try with numbers : $$(5-5)^2 * 1000 = 0$$; in this (a-b)^2 * c = 0 but c = 1000, not 0. So III can be false as you see.
It's the same reason why you exclude option I. We know that one term (c, or a-b) must be =0, but we don't know which one. Option I and III exclude the other term saying respectively that a-b=0 and c=0, on the other hand option II is correct because makes no assumption: c(a-b)=0 => we know that at least one of those therms is 0 (and the option doesn't specify which one, that's the point) , so 0*(a-b)=0 or c*(0)=0 => always TRUE.

Hope it's clear
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Manager
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Re: If (a – b)2c = 0, then which of the following must be true? [#permalink]

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30 Mar 2013, 11:06
Zarrolou wrote:
marcovg4 wrote:
Can you explain why? I thought III option is true, since it is saying that c = 0, hence (a-b)^2 * c = 0

Option III says that, given $$(a-b)^2 * c = 0$$, c must be =0.
Try with numbers : $$(5-5)^2 * 1000 = 0$$; in this (a-b)^2 * c = 0 but c = 1000, not 0. So III can be false as you see.
It's the same reason why you exclude option I. We know that one term (c, or a-b) must be =0, but we don't know which one. Option I and III exclude the other term saying respectively that a-b=0 and c=0, on the other hand option II is correct because makes no assumption: c(a-b)=0 => we know that at least one of those therms is 0 (and the option doesn't specify which one, that's the point) , so 0*(a-b)=0 or c*(0)=0 => always TRUE.

Hope it's clear

I agree with you, I have to understand the "right" approach to this kind of questions
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MV
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Re: If (a – b)2c = 0, then which of the following must be true? [#permalink]

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30 Mar 2013, 12:26
marcovg4 wrote:
Zarrolou wrote:
marcovg4 wrote:
Can you explain why? I thought III option is true, since it is saying that c = 0, hence (a-b)^2 * c = 0

Option III says that, given $$(a-b)^2 * c = 0$$, c must be =0.
Try with numbers : $$(5-5)^2 * 1000 = 0$$; in this (a-b)^2 * c = 0 but c = 1000, not 0. So III can be false as you see.
It's the same reason why you exclude option I. We know that one term (c, or a-b) must be =0, but we don't know which one. Option I and III exclude the other term saying respectively that a-b=0 and c=0, on the other hand option II is correct because makes no assumption: c(a-b)=0 => we know that at least one of those therms is 0 (and the option doesn't specify which one, that's the point) , so 0*(a-b)=0 or c*(0)=0 => always TRUE.

Hope it's clear

I agree with you, I have to understand the "right" approach to this kind of questions

basically what Zarrolou says, is that in I and III you have not sufficient information to answer the question (remember is a MUST be true question, not a maybe question)

In fact rephrasing the question you have (a-b)*c=0. you have to have all the elements to say for sure that the equation is equal to zero.

Only the II one works.
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Re: If (a – b)2c = 0, then which of the following must be true? [#permalink]

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08 Jul 2015, 03:38
marcovg4 wrote:
If ((a – b)^2)c = 0, then which of the following must be true?

I. a = b
II. (a – b) c = 0
III. c = 0

A. II only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III

i'm wrong again

i thought C is the answer. but it can't be true while C=0. if it is then equation will be 0. So a=b is only solution
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If (a – b)2c = 0, then which of the following must be true? [#permalink]

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08 Jul 2015, 23:42
2
If ((a – b)^2)c = 0, then which of the following must be true?

This would be zero if a = b or if c = 0 (or both of these cases). We can't say that a must be equal to b because c could be zero. Eliminate B, C, and E. Since the remaining choices both have II evaluate III. c need not be zero since a can equal b. Eliminate D.
I. a = b
II. (a – b) c = 0
III. c = 0

A. II only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III
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Re: If (a – b)2c = 0, then which of the following must be true? [#permalink]

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10 Sep 2017, 10:42
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Re: If (a – b)2c = 0, then which of the following must be true?   [#permalink] 10 Sep 2017, 10:42
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# If (a – b)2c = 0, then which of the following must be true?

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