If a and b are nonzero numbers on the number line, is 0 between a and

Question

If a and b are nonzero numbers on the number line, is 0 between a and b ?

(1) The distance between 0 and a is greater than the distance between 0 and b.
(2) The sum of the distances between 0 and a and between 0 and b is greater than the distance between 0 and the sum a + b.

lacktutor · Answer

a,b — nonzero numbers in the number line.
Is 0 between a and b?
—> a<0 and b>0???

(Statement1):
the distance of 0a > the distance of 0b
—> a= 5, b= 3 —> 5>3 (No)
—> a=—3, b= 2 —> 0a=3, 0b=2 —> 0a> 0b (Yes)
Insufficient

(Statement2):
—> the sum of 0a and 0b > 0(a+b)

If a=3 and b=5, then 0a+0b> 0(a+b)
—> 5+3> 8 —> it does not get an exact match for (stat2)

If a=—3 and b=—5, then 0a+0b> 0(a+b)—> 3+5> 8 ( it is the same thing) if a and b both are negative as you mentioned then 0 is not between them. either a or B has to be -ve and other +ve

If a=—3 and b= 5, then 0a+0b> 0(a+b) —> 3+5> —3+5
8> 2 ( correct)
—> a< 0 and b>0 ( always Yes)
Sufficient

The answer is B

I don't think answer is B for sure, statement 2 is more like |a| + |b| > a+b

Posted from my mobile device

navya27 · Answer

lacktutor · Answer

vanya27

The first two cases in Statement2, both of them do not get an exact match for statement2. 
—> If both a and b are positive or negative, 0(zero) will not be between them. Also, you already mentioned it too.

Case3:
Well, In order statement2 to hold true, a should be negative and b should be positive. (a<0, b>0) 
—> Is 0(zero) between a and b?— this is what a question is asking. 
( Always Yes) 
The answer should be B.

Roosh18 · Answer

How to solve this using a number line drawing?

TheNightKing · Answer

I got this wrong but here is the deal.

For sum of distances between ( 0 and a) and (0 and b) to be greater than the distance between (0 and a+b) the 0 has to be in between a and b. If both a and b are on either side of the 0 then the the distances will be equal and not biased.

Hope that makes sense.!

JoeAl · Answer

This can be solved using absolute values.

statement 1 : |0-a| > |0-b|
Not sufficient

statemtent 2:

==> |a|+|b| > |a+b| 
Condition true only when a and b are of opposite sign
Hence sufficient

Kimberly77 · Answer

Great explanatioin  lacktutor . One question not quite sure this part of why 5>3 is No? Could you clarify? Thanks

—> a= 5, b= 3 —> 5>3 (No)

Rishab2409 · Answer

To determine if 0 is between a and b on the number line, we need to find out if a and b have opposite signs (one positive and one negative).

Statement (1): In distance terms: |a| > |b|, this tells us about their magnitude, but nothing about their signs.  Example:  If a = -3 and b = 1, 0 is between them. But if a = 3 and b = 1, 0 is not between them. Statement (1) alone is NOT sufficient.

Statement (2): In distance terms: |a| + |b| > |a + b|. According to the triangle inequality rule, |a| + |b| = |a + b| when a and b have the same sign, but |a| + |b| > |a + b| when a and b have opposite signs. Because |a| + |b| > |a + b|, a and b must have opposite signs. Since one is positive and the other is negative, 0 is definitely between a and b. Statement (2) alone IS sufficient.

If a and b are nonzero numbers on the number line, is 0 between a and

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