Is |a−b|

Question

Is |a−b| < |a| + |b| ?

Statement 1: ab<0
Statement 2:  a^b<0

kumarparitosh123 · Answer

The question is basically asking whether A and B are of opposite signs??

Statement 1: A and B are of opposite sign.
Sufficient
Statement 2: A is negative and B is odd number.
So sufficient.

Thus answer is D.

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ccooley · Answer

The second one actually isn't sufficient - A and B could both be negative! For instance, if A = -1 and B = -3 (which is odd), the answer to the question is 'yes'. If A = -1 and B = 3, the answer to the question is 'no' (since |a-b| = |a| + |b|).

kumarparitosh123 · Answer

Thanks a ton Sir for correcting me !! +1 for you .

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brandon7 · Answer

can you explain how you rephrased the question?

Archit3110 · Answer

for given info |a−b| < |a| + |b|
#1
ab<0
we have two cases ; either a is -ve or b is +ve integers or vice versa
case 1 ; a is -ve and b +ve integer then |a−b| < |a| + |b| ; (-5,2) ;7=7 ; no
case 2 ; when a + ve and b -ve then |a−b| = |a| + |b| ; (5,-2) ; 7=7 ; no 
sufficient
#2
 a^b<0 
is insufficient as we can have either b to be odd and a -ve or both a &b are -ve so insufficient

IMO A

varmashreekanth · Answer

Hi,
I have taken the following approach to solve this question. Please correct me if I am wrong.

Since it is a DS question, first we will have to simplify the question statement.

Is\( |a-b| < |a|+|b| ?\)
Squaring both sides, we will get.
Is \((|a-b|^2)<(|a|+|b|)^2 ?\)
Is \((a^2 - 2ab +b^2)<(a^2+2|a||b|+b^2)?\)

Since \(a^2\) and \(b^2\) will always be greater than equal to 0, so it will now affect the inequality sign. We can eliminate \(a^2\) and \(b^2\).

Is \((-2ab)<2|a||b| ?\)
On further simplification, we will get

Is \((-ab) < |a||b| ?\)

Now we know that \(|a||b| \)will always be positive or zero, .i.e

\(|a||b| >= 0\). i.e 0 would be the minimum possible value. So now we can replace \(|a||b|\) with 0 in the above equation. So now the question stem becomes :-

Is \((-ab) < 0?\)

Multiplying with -1 on both sides, the inequality sign will be reversed.

Is \(ab > 0 ?\)

So we have to check whether ab>0 or not or in other ways we have to check whether both a and b are of the same sign or not.

Now considering the statements.

Statement 1:- \(ab<0\)
So a and b are of opposite signs.
So from this statement, we are getting a definite answer to the question Is \(ab > 0?\)
This statement is sufficient.
We can eliminate options B, C, and E

Statement 2:- \(a^b < 0\)
This implies a is negative.
But don't know about the orientation of b.
If b is negative, then \(ab > 0\) and if b is positive, then \(ab < 0\).
So we are not getting a definite answer to the question Is \(ab < 0?\) from this statement.
This statement is insufficient. We can eliminate option D.

So IMO option A is the correct answer.

bumpbot · Answer

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Is |a−b| < |a| + |b| ?

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GMAT Data Sufficiency (DS) Questions

Is |a−b| < |a| + |b| ?

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