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555-605 (Medium)|   Algebra|      
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EBITDA
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What is the value of a^2 - 2a + b^2? Updated on: 12 Jul 2016, 09:26
Originally posted by EBITDA on 12 Jul 2016, 05:33.
Last edited by Bunuel on 12 Jul 2016, 09:26, edited 2 times in total.
Edited the question.
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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25% (medium)

Question Stats:

75% (01:29) correct 25% (01:28) wrong based on 82 sessions

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What is the value of a^2 - 2a + b^2?

1) a = 3
2) a - b = 2

Could you please explain in detail the answer to the question?

I apologize for not including the official answer, but I would like to verify it before posting it. I will add it soon.

Thank you for your understanding and help.
ShowHide Answer
Official Answer
C
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What is the value of a^2 - 2a + b^2? Updated on: 12 Jul 2016, 13:00
Originally posted by msk0657 on 12 Jul 2016, 06:11.
Last edited by msk0657 on 12 Jul 2016, 13:00, edited 1 time in total.
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EBITDA
What is the value of a^2 - 2a + b^2?

1) a = 3
2) a - b = 2

Could you please explain in detail the answer to the question?

I apologize for not including the official answer, but I would like to verify it before posting it. I will add it soon.

Thank you for your understanding and help.
Show more

Given \(a^2\) - 2a + \(b^2\)

Stat 1 : a = 3 , we don't know nothing about b ---> insufficient...we don't know a and b values..

Stat 2 : a - b = 2

Squaring both sides
\((a - b )^2\) = 4.
\(a^2\)-2ab+\(b^2\) = 4 ---> insufficient

Now both

Stat 1 + Stat 2 : take 'a' value and sub in stat 2 result.

9 - 6b + \(b^2\) = 4

We get b = 5 and 1 .

From stat 2 : a - b = 2. If this has to be correct then b has to be 1.

a = 3 and b = 1 and discarding b = 5 which doesn't fit.

Answer is C is the correct option

Re-corrected the solution...for folks who tried in the above way..

Another method given by EBITDA....
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What is the value of a^2 - 2a + b^2? 12 Jul 2016, 06:30
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EBITDA
What is the value of a^2 - 2a + b^2?

1) a = 3
2) a - b = 2

Could you please explain in detail the answer to the question?

I apologize for not including the official answer, but I would like to verify it before posting it. I will add it soon.

Thank you for your understanding and help.
Show more

What is the value of a^2 - 2ab + b^2?

Notice that a^2 - 2ab + b^2 is the square of the difference : a^2 - 2ab + b^2 = (a - b)^2

(1) a = 3. Not sufficient.

(2) a - b = 2 --> (a - b)^2 = 2^2 = 4. Sufficient.

Answer: B.
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What is the value of a^2 - 2a + b^2? 12 Jul 2016, 06:37
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Bunuel
EBITDA
What is the value of a^2 - 2a + b^2?

1) a = 3
2) a - b = 2

Could you please explain in detail the answer to the question?

I apologize for not including the official answer, but I would like to verify it before posting it. I will add it soon.

Thank you for your understanding and help.

What is the value of a^2 - 2a + b^2?

Notice that a^2 - 2a + b^2 is the square of the difference : a^2 - 2a + b^2 = (a - b)^2

(1) a = 3. Not sufficient.

(2) a - b = 2 --> (a - b)^2 = 2^2 = 4. Sufficient.

Answer: B.
Show more

Hi Bunuel,


Given \(a^2\) - 2a +\(b^2\) and \((a - b)^2\)= \(a^2\) - 2ab + \(b^2\)

How \(a^2\) - 2a + \(b^2\) = \((a - b)^2\) ? ...Can you throw some light on this how it could be ?
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What is the value of a^2 - 2a + b^2? Updated on: 12 Jul 2016, 06:48
Originally posted by nevermore on 12 Jul 2016, 06:44.
Last edited by nevermore on 12 Jul 2016, 06:48, edited 1 time in total.
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Bunuel
EBITDA
What is the value of a^2 - 2a + b^2?

1) a = 3
2) a - b = 2

Could you please explain in detail the answer to the question?

I apologize for not including the official answer, but I would like to verify it before posting it. I will add it soon.

Thank you for your understanding and help.

What is the value of a^2 - 2a + b^2?

Notice that a^2 - 2a + b^2 is the square of the difference : a^2 - 2a + b^2 = (a - b)^2

(1) a = 3. Not sufficient.

(2) a - b = 2 --> (a - b)^2 = 2^2 = 4. Sufficient.

Answer: B.
Show more

Hi Bunuel,

The question stem asks us to find the value of a^2-2a+b^2.
(a-b)^2=a^2-2ab+b^2
=(a^2-ab+b^2)-ab

We still don't know ab. I think answer should be C.
Or else, the question was not formulated correctly.
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What is the value of a^2 - 2a + b^2? 12 Jul 2016, 06:45
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Bunuel
EBITDA
What is the value of a^2 - 2a + b^2?

1) a = 3
2) a - b = 2

Could you please explain in detail the answer to the question?

I apologize for not including the official answer, but I would like to verify it before posting it. I will add it soon.

Thank you for your understanding and help.

What is the value of a^2 - 2a + b^2?

Notice that a^2 - 2a + b^2 is the square of the difference : a^2 - 2a + b^2 = (a - b)^2

(1) a = 3. Not sufficient.

(2) a - b = 2 --> (a - b)^2 = 2^2 = 4. Sufficient.

Answer: B.
Show more



a-b =2 .. and (a-b)^2= a^2 + B^2 -2ab... whereas the question says to find value of a^2 - 2a + b^2.....note its 2a and not 2ab... so how can the answer be obtained from second statement.
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What is the value of a^2 - 2a + b^2? 12 Jul 2016, 06:53
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Bunuel
EBITDA
What is the value of a^2 - 2a + b^2?

1) a = 3
2) a - b = 2

Could you please explain in detail the answer to the question?

I apologize for not including the official answer, but I would like to verify it before posting it. I will add it soon.

Thank you for your understanding and help.

What is the value of a^2 - 2a + b^2?

Notice that a^2 - 2a + b^2 is the square of the difference : a^2 - 2a + b^2 = (a - b)^2

(1) a = 3. Not sufficient.

(2) a - b = 2 --> (a - b)^2 = 2^2 = 4. Sufficient.

Answer: B.



a-b =2 .. and (a-b)^2= a^2 + B^2 -2ab... whereas the question says to find value of a^2 - 2a + b^2.....note its 2a and not 2ab... so how can the answer be obtained from second statement.
Show more

Yes, you are right I solved for a^2 - 2ab + b^2.

EBITDA, is it a^2 - 2ab + b^2 or a^2 - 2a + b^2?
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What is the value of a^2 - 2a + b^2? 12 Jul 2016, 06:59
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What is the value of a^2 - 2a + b^2?

1) a = 3
2) a - b = 2


If it is as a^2 - 2ab + b^2 then we can easily mark B as option... I guess question won't be that easy.

Bunuel, can give us solution as per the question... a^2 - 2a + b^2...
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What is the value of a^2 - 2a + b^2? 12 Jul 2016, 07:05
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What is the value of a^2 - 2a + b^2?

1) a = 3
2) a - b = 2


If it is as a^2 - 2ab + b^2 then we can easily mark B as option... I guess question won't be that easy.

Bunuel, can give us solution as per the question... a^2 - 2a + b^2...
Show more

In this case the answer is clearly C.
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What is the value of a^2 - 2a + b^2? 12 Jul 2016, 07:08
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EBITDA
What is the value of a^2 - 2a + b^2?

1) a = 3
2) a - b = 2

Could you please explain in detail the answer to the question?

I apologize for not including the official answer, but I would like to verify it before posting it. I will add it soon.

Thank you for your understanding and help.
Show more

The original question is correct.

Despite the official answer is option B, I believe that the correct answer is option C.

Could you please explain in detail your answers?

I will obtain the correct official answer in some days. As soon as I obtain it, I will let you know.
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What is the value of a^2 - 2a + b^2? 12 Jul 2016, 07:35
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What is the value of a^2 - 2a + b^2?

1) a = 3
2) a - b = 2


If it is as a^2 - 2ab + b^2 then we can easily mark B as option... I guess question won't be that easy.

Bunuel, can give us solution as per the question... a^2 - 2a + b^2...

In this case the answer is clearly C.
Show more


Hi Bunuel,

Thanks for the reply, if we club both statements then we get b = 5 and 1.

When we sub a = 3 and b = 5 / b = 1... we get two different solutions...

We always check for the unique result in DS and then I thought E will be the option...

Do we need to check that whether by substituting the values in the equation and that gives us some solutions or only unique solution ?
As requested, please post the complete solution.
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What is the value of a^2 - 2a + b^2? 12 Jul 2016, 08:28
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a^2 - 2a + b^2 ---> a * (a - 2) + b^2

1) a = 3

Substitute in the expression: 9 - 6 + b^2 ---> Not sufficient.

2) a - b = 2 ; a = 2 + b

Substitute in the expression:

(2 + b) * (2 + b - 2) + b^2 ; 2b + b^2 + b^2 ; 2b^2 + 2b ; 2b * (b + 1) ---> Not sufficient.

Combine both:

Plug a = 3, as per statement 1, into statement 2 ---> b = 1

Substitute a = 3 and b= 1 into the expression.

a^2 - 2a + b^2 = 2 ---> Sufficient ---> Option C

Can you please give your opinion on this answer?

Thank you.
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What is the value of a^2 - 2a + b^2? 12 Jul 2016, 09:25
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EBITDA
a^2 - 2a + b^2 ---> a * (a - 2) + b^2

1) a = 3

Substitute in the expression: 9 - 6 + b^2 ---> Not sufficient.

2) a - b = 2 ; a = 2 + b

Substitute in the expression:

(2 + b) * (2 + b - 2) + b^2 ; 2b + b^2 + b^2 ; 2b^2 + 2b ; 2b * (b + 1) ---> Not sufficient.

Combine both:

Plug a = 3, as per statement 1, into statement 2 ---> b = 1

Substitute a = 3 and b= 1 into the expression.

a^2 - 2a + b^2 = 2 ---> Sufficient ---> Option C

Can you please give your opinion on this answer?

Thank you.
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_____________
That's correct.
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What is the value of a^2 - 2a + b^2? 12 Jul 2016, 09:26
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msk0657
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What is the value of a^2 - 2a + b^2?

1) a = 3
2) a - b = 2


If it is as a^2 - 2ab + b^2 then we can easily mark B as option... I guess question won't be that easy.

Bunuel, can give us solution as per the question... a^2 - 2a + b^2...

In this case the answer is clearly C.


Hi Bunuel,

Thanks for the reply, if we club both statements then we get b = 5 and 1.

When we sub a = 3 and b = 5 / b = 1... we get two different solutions...

We always check for the unique result in DS and then I thought E will be the option...

Do we need to check that whether by substituting the values in the equation and that gives us some solutions or only unique solution ?
As requested, please post the complete solution.
Show more

when we combine the statements we get only one set: a=3 and b=1. So, we can get unique solution for a^2 - 2a + b^2.
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What is the value of a^2 - 2a + b^2? 12 Jul 2016, 12:25
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A.alone insufficient
B.Alone insufficient
Combined- A=3 b =1 Ans C)
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What is the value of a^2 - 2a + b^2? 12 Jul 2016, 21:14
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IMO: C)

From A) it is insufficient as we only know about (a) don't know about (b).
From B) Insufficient as well. (a-b)^2 = a^2 -2.a.b + b^2.

Combining both => Sufficient, as a is known and b is derived.
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