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# If a^2+b^2=41, what is the value of (a−b)2^?

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Manager
Joined: 11 Jun 2018
Posts: 98
Schools: DeGroote "22 (S)
GMAT 1: 500 Q39 V21
If a^2+b^2=41, what is the value of (a−b)2^?  [#permalink]

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Updated on: 20 Jan 2019, 09:07
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00:00

Difficulty:

35% (medium)

Question Stats:

66% (01:02) correct 34% (01:07) wrong based on 77 sessions

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If a^2+b^2=41, what is the value of (a−b)^2?

(1) a=5
(2) a⋅b=−20

Originally posted by Manat on 20 Jan 2019, 08:45.
Last edited by Manat on 20 Jan 2019, 09:07, edited 1 time in total.
Manager
Joined: 11 Jun 2018
Posts: 98
Schools: DeGroote "22 (S)
GMAT 1: 500 Q39 V21
Re: If a^2+b^2=41, what is the value of (a−b)2^?  [#permalink]

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20 Jan 2019, 08:48
Bunuel @chetan2u:-Hi experts,

Why Isn't option A sufficient?

We need to find (a-b)^2

Which is

a^2 + b^2 - 2ab
We know a^2+ b^2=41,

So we have

41-2ab
41=2ab
41/2=ab

so if we know a=5, why can't we find B?
Director
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: If a^2+b^2=41, what is the value of (a−b)2^?  [#permalink]

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20 Jan 2019, 08:57
1
Manat wrote:
If a^2+b^2=41, what is the value of (a−b)^2?

(1) a=5
(2) a⋅b=−20

Its B

a^2+b^2=41 if a = 5, then b^2 = 16, b = +/- 4

(5-4)^2 or (5+4)^2

No idea how A is sufficient here, Manat any thoughts ??

Statement B
(a−b)^2
= a^2 + b^2 - 2a*b
= 41 + 40
=81

IMO B
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
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Manager
Joined: 11 Jun 2018
Posts: 98
Schools: DeGroote "22 (S)
GMAT 1: 500 Q39 V21
Re: If a^2+b^2=41, what is the value of (a−b)2^?  [#permalink]

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20 Jan 2019, 09:00
Hi KanishkM,

I agree B is sufficient, but i think i'm missing something here,

Is the below inference wrong?

So we have

41-2ab
41=2ab
41/2=ab

so if we know a=5, why can't we find B?
Director
Joined: 09 Mar 2018
Posts: 994
Location: India
If a^2+b^2=41, what is the value of (a−b)2^?  [#permalink]

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20 Jan 2019, 09:05
Manat wrote:
Hi KanishkM,

I agree B is sufficient, but i think i'm missing something here,

Is the below inference wrong?

So we have

41-2ab
41=2ab
41/2=ab

so if we know a=5, why can't we find B?

If i want to find a value of something, how am i relating it to 0 ??

Highlighted will hold good, if question had mentioned that we can equate to 0. We can ideally manipulate the if part of the question.

a^2+b^2=41

from statement 1) a = 5, then

25 +b^2 = 41

b^2 = 16

b = +/- 4

Let me know if this helps

Is the OA correct ? is it B or D ??
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Manager
Joined: 11 Jun 2018
Posts: 98
Schools: DeGroote "22 (S)
GMAT 1: 500 Q39 V21
Re: If a^2+b^2=41, what is the value of (a−b)2^?  [#permalink]

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20 Jan 2019, 09:08
1
Perfect! Understood. OA is B, corrected it. This question is from the Economist free test.
Intern
Joined: 24 Jun 2014
Posts: 5
Re: If a^2+b^2=41, what is the value of (a−b)2^?  [#permalink]

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22 Jan 2019, 21:46
a^2+b^2 = 41

Consider Statement 1: a=5
25+b^2 = 41
b^2 = 16
b = +-4
Hence Statement 1 is insufficient

Consider Statement 2 : ab = -20
(a-b)^2 = a^2 - 2*a*b + b^2 = 41+40 = 81
Hence b is sufficent to find (a-b)^2.

Re: If a^2+b^2=41, what is the value of (a−b)2^?   [#permalink] 22 Jan 2019, 21:46
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