What is the distance between a and b on the number line?

Question

(1) |a| – |b| = 6
(2) ab > 0

WholeLottaLove · Accepted Answer

What is the distance between a and b on the number line?

(1) |a| – |b| = 6
(2) ab > 0

(1) |a| – |b| = 6

I made a stupid mistake here. I assumed that because we are dealing with absolute values here, we're dealing with just a positive number - a positive number (for example 12-6 = 6, 8-2 = 6, etc). Of course, we're looking for the distance of a and b, not the difference between |a| and |b|. For example, the difference between |-12| and |6| is (12-6=6) but on the number line they are actually 18 places apart. Therefore, we cannot determine what the distance between a and b is on the number line with #1. 
INSUFFICIENT

(2) ab > 0

This tells us nothing about the placement of a and b on the number line, only that a and b are both positive or negative.

1+2) If a and b are both positive or both negative and that |a| – |b| = 6 then we can conclude the distance is always going to be 6.
SUFFICIENT

(C)

mun23 · Answer

What is the distance between a and b on the number line?

(1) |a| – |b| = 6
(2) ab > 0

mau5 · Answer

From F.S 1, let's pick values keeping |a| – |b| = 6. For a=-12; b=6, we have |a-b| = 18, however, for a=12;b=6 we have |a-b| = 6. Insufficient.

From F.S 2, we just know that a and b are of the same sign. Insufficient.

With both taken together, either a,b>0 in which case, |a| – |b| = 6 --> a– b = 6 .

or

a,b<0 in which case, b-a = 6. Thus, the distance between the points a and b, |a-b| is the same in either case. Sufficient.

C.

Bunuel · Answer

Merging similar topics.

Bunuel · Answer

What is the distance between a and b on the number line?

We are asked to find the value of |a-b|.

(1) |a| – |b| = 6 --> if a=7 and b=1 then |a-b|=6 but if a=7 and b=-1 then |a-b|=8. Not sufficient.

(2) ab > 0 --> just says that a and b have the same sign. Not sufficient:

(1)+(2) If both a and b are positive then |a|-|b|=a-b=6 and |a-b|=6. If both a and b are negative then |a|-|b|=-a-(-b)=b-a=6, and |a-b|=6. So, in any case |a-b|=6. Sufficient.

Answer: C.

KrishnakumarKA1 · Answer

ST 1: If both are negative or both are positive, the difference will be = 6. If one of them is negative, we cannot determine the distance. INSUFFICIENT

St 2: ab>0, that means either both are negative or both are positive. But the difference is unknown. INSUFFICIENT

St 1 & St 2: the case of one of them being negative and other positive is ruled out. hence the distance will be 6. ANSWER

Option C

saurabhsavant · Answer

Hello Bunuel, Your solution is well taken. However, I have been handling mod questions on the basis of "Distance from zero on number line" concept. Can we cay that mod (a) denotes the distnace of "a" from zero? If we can then option a states that the difference of "distance of a from zero" and "difference of b from" zero is equal to 6. the distance between "a" and "b" is 6 only. As only distance is required not the actual value. so whatever be the case, the distance of a and b will be 6 only. taking an example, let the value of "a" be -67 i.e. "a" is at a distance of 67 units from zero n the number line, therefore as per the given statement (i) b can take values of -61 and -73, thereby giving two differnt values. hence SUFFICIENT. From statement (ii) we see that either both a & b are positive or negative. Clearly INSUFFICIENT. So, option A should be the answer, What am I doing wrong here?? My concept is at stake

Bunuel · Answer

How is your examples correct? If a = -67 and b =-73, then |a| – |b| = -6, not 6.

|a| – |b| = 6 (|a| = 6 + |b|) means that a is 6 units further from 0, than b is.

You are considering the case when both a and b are negative. In my solution you can see an examples giving different answers:
a=7 and b=1 then |a-b|=6 
a=7 and b=-1 then |a-b|=8.

saurabhsavant · Answer

How is your examples correct? If a = -67 and b =-73, then |a| – |b| = -6, not 6.

|a| – |b| = 6 (|a| = 6 + |b|) means that a is 6 units further from 0, than b is.

You are considering the case when both a and b are negative. In my solution you can see an examples giving different answers:
a=7 and b=1 then |a-b|=6 
a=7 and b=-1 then |a-b|=8. 
Agreed that i botched up in calculations...have been struggling with this issue....but even if we get negative 6 as an answer still the "distance" between a and b remains 6.

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Bunuel · Answer

I don't understand what you are trying to say. What is your question exactly?

saurabhsavant · Answer

Sorry to bother u..i really mean it...but here is what i gather from the question..
Ial = distance of a from zero..hope this concept is right? And ditto for b
So i guess distance between a and b would not b la-b|...rather | |a|-|b| |...
Further, if a is say 100 units from zero, then a can be at either positive 100 or negative 100.
Now, how do we placee b?
We can place b in such a manner that statement i holds good.

I.e. |b| =6+wherever a is....or gap between a and b is 6.

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saurabhsavant · Answer

One addition..|b| = wherever a is minus 6...again gap is 6

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Bunuel · Answer

The red part is where you are making an error. The distance between a and b on the number line mean |a - b|, and no way ||a| - |b||.

saurabhsavant · Answer

The red part is where you are making an error. The distance between a and b on the number line mean |a - b|, and no way ||a| - |b||. 
Well...thanx for the help...will ponder over it and hope to reconcile with the OA.

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Madhavi1990 · Answer

Made the same error : now realize its asking DISTANCE not direction. So that remains the same through C. Picked E earlier

as I kept thinking what is A and B Good one, conceptually Thank you for the explanation!

Archit3110 · Answer

#1
a & b can be either + or - insufficient
#2
ab>0
both have to be +ve or -ve ; insufficient
from 1 &2
both of same sign ; gives same value 
test with a=+/-8 and b=+/-2 ; same sign
IMO C

analytica233 · Answer

|a-b| = ?

(1) |a| – |b| = 6. a and b can be positive or negative. If a = 8 and b = 2, then |a - b| = 6; but if a = -8 and b = 2, then |a - b| = 10. INSUFFICIENT.

(2) ab > 0. There are infinite number of pairs of positive numbers or negative numbers that satisfy ab > 0. INSUFFICIENT.

(1) + (2): 
From (2) we know that a and b have the same signs
From (1) we know that |a| > |b|
--> |a| - |b| = |a - b| = 6. SUFFICIENT.

Answer: (C)

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What is the distance between a and b on the number line?

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