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03 Apr 2023, 01:30
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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)!
Difficulty:
35%
(medium)
Question Stats:
65% (01:15) correct
35%
(01:39)
wrong
based on 141
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Not Attempted Yet
If a and b are positive, what is the value of a − b?
(1) \(a^2 + 2ab + b^2 = 36\)
(2) \(a^2 − b^2 = 12\)
(1) \(a^2 + 2ab + b^2 = 36\)
(2) \(a^2 − b^2 = 12\)
03 Apr 2023, 06:59
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Bunuel
Solution:
Pre Analysis:
- Given \(a,b>0\)
- We are asked the value of \(a-b\)
Statement 1: \(a^2 + 2ab + b^2 = 36\)
- According to this statement, \((a+b)^2=36\)
- From this we can infer \(a+b=6\). Since \(a,b>0\) we are ignoring \(a+b=-6\)
- We do not get the value of \(a-b\) from this
- Thus, statement 1 alone is not sufficient and we can eliminate options A and D
Statement 2: \(a^2 − b^2 = 12\)
- According to this statement, \((a+b)(a-b)=12\)
- We do not get the value of \(a-b\) from this
- Thus, statement 2 alone is also not sufficient and we can eliminate option B
Combining:
- Statement 1: \(a+b=6\)
- Statement 2: \((a+b)(a-b)=12\)
- Upon combining, we can easily say \(a-b=2\)
Hence the right answer is Option C
General Discussion
13 Apr 2023, 19:35
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Since both a and b are positive, from second option we can infer that
If (a+b)(a-b)=12
12 can have factors as 12*1, 6*2, 4*3 only.
From above 3 pairs only 6*2 is a possible factor which can satisfy equation (a+b)(a-b).
Hence a-b = 2
Option B is the answer
Whats wrong in this logic!! Plz correct.
Posted from my mobile device
If (a+b)(a-b)=12
12 can have factors as 12*1, 6*2, 4*3 only.
From above 3 pairs only 6*2 is a possible factor which can satisfy equation (a+b)(a-b).
Hence a-b = 2
Option B is the answer
Whats wrong in this logic!! Plz correct.
Posted from my mobile device
