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09 Jan 2023, 02:30
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A
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:
64% (01:33) correct
36%
(01:49)
wrong
based on 67
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Is \(|a - b| - (a - b) > 0\) ?
(1) \(a < b\)
(2) \(a > 0\) and \(b > 0\)
(1) \(a < b\)
(2) \(a > 0\) and \(b > 0\)
09 Jan 2023, 03:21
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Bunuel
A good question that we can solve quite seamlessly using basic concept of modulus and absolute value.
Is \(|a - b| - (a - b) > 0\) ?
\(|a - b| > (a - b) \)
Inference: Is the distance between a and b greater than the difference in value of a and b ?
Note: The distance between two points is always non negative.
Statement 1
\(a < b\)
If the value of a is less than that of b, the difference between a and b is always negative. This is regardless of the position of a and of b on the number line.
Hence we can infer that the statement tells us that a - b is negative.
Is \(|a - b| - (a - b) > 0\) -- Well Yes ! as |a-b| is non negative.
This statement is sufficient, and we can eliminate B, C and E.
Statement 2
\(a > 0\) and \(b > 0\)
This statement tells us that both a and b lie to the left of 0 on a number line.
Let's see what the possible combination can be
-------- 0 -------- a -------- b ----
This situation is similar to that of Statement 1 in which a < b. We already know if this were the case, \(|a - b| - (a - b) > 0\)
-------- 0 -------- b -------- a ----
However if a > b, the distance between a and b is same as the difference between their values.
Is \(|a - b| - (a - b) > 0\) -- No, LHS = RHS
Hence the statement is not sufficient.
Option A
13 Jan 2023, 14:39
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Is my approach correct?
Thank you
|a-b| -(a-b)>0
|a-b| is always +ve
Then I translate the question to:
-(a-b)>0
b-a>0
Is b>a ?
1) a< b suff
2) i need to know more info
Answ: A
Posted from my mobile device
Thank you
|a-b| -(a-b)>0
|a-b| is always +ve
Then I translate the question to:
-(a-b)>0
b-a>0
Is b>a ?
1) a< b suff
2) i need to know more info
Answ: A
Posted from my mobile device
