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

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VP
Joined: 30 Jun 2008
Posts: 1022
If a and b are nonzero numbers on the number line, is 0 [#permalink]

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10 Oct 2008, 01:17
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67% (01:11) correct 33% (02:50) wrong based on 19 sessions

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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 of a + b
_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

Manager
Joined: 10 Aug 2008
Posts: 73
Re: PS : GMATPrep - Number Line [#permalink]

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10 Oct 2008, 01:31
For me 2nd statement alone is sufficient. hence Ans is B.

Amit whts the officilal answer ?
Manager
Joined: 27 Sep 2008
Posts: 76
Re: PS : GMATPrep - Number Line [#permalink]

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10 Oct 2008, 01:31
is (a+b)/2 = 0 ?

statement 1

|a|>|b|

a > b or -a > -b = a < b

insufficient

statement 2

|a|+|b| > |a+b|

a+b > a+b or -a-b > -a-b

meaning either a is negative and b is positive or the other way around !

sufficient

VP
Joined: 30 Jun 2008
Posts: 1022
Re: PS : GMATPrep - Number Line [#permalink]

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10 Oct 2008, 04:12
Greenberg wrote:
is (a+b)/2 = 0 ?

statement 1

|a|>|b|

a > b or -a > -b = a < b

insufficient

statement 2

|a|+|b| > |a+b|

a+b > a+b or -a-b > -a-b

meaning either a is negative and b is positive or the other way around !

sufficient

OA is B. Greenberg I don't understand how you conclude from a+b> a+b that one has to be +ve or -ve

Thanks
_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

Manager
Joined: 27 Sep 2008
Posts: 76
Re: PS : GMATPrep - Number Line [#permalink]

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10 Oct 2008, 04:39
3
KUDOS
amitdgr wrote:
Greenberg wrote:
is (a+b)/2 = 0 ?

statement 1

|a|>|b|

a > b or -a > -b = a < b

insufficient

statement 2

|a|+|b| > |a+b|

a+b > a+b or -a-b > -a-b

meaning either a is negative and b is positive or the other way around !

sufficient

OA is B. Greenberg I don't understand how you conclude from a+b> a+b that one has to be +ve or -ve

Thanks

A quote from the attached paper "At first glance, one might consider writing out the different scenarios for the absolute value expressions in this equation, however, that would be a mistake. A conceptual approach is much better. Let's use the "guarantee of positive" to think about the equation /x/ + /y/ = /x + y/. The left side of the equation takes the variables x and y and makes them positive before they are added. The right side of the equation adds the variables first and then makes the result positive.

What must be true about x and y for the two sides of the equation to be equal? If x and y are both positive (x = 2, y = 3), both sides of the equation equal 5. If x and y are both negative (x = -2, y = -3), both sides of the equation still equal 5. If, however, one value is positive and the other is negative (x = -2, y = 3), the left side of the equation is 5, but the right side of the equation is 1. We see that for the two sides of the equation to be equal, x and y must have the same sign".

Now re-think about it when |x|+|y| > |x+y| and you will figure it out.

Attachments

ABSOLUTE value and Inequality.doc [74.5 KiB]

VP
Joined: 30 Jun 2008
Posts: 1022
Re: PS : GMATPrep - Number Line [#permalink]

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10 Oct 2008, 05:28
Greenberg wrote:
amitdgr wrote:
Greenberg wrote:
is (a+b)/2 = 0 ?

statement 1

|a|>|b|

a > b or -a > -b = a < b

insufficient

statement 2

|a|+|b| > |a+b|

a+b > a+b or -a-b > -a-b

meaning either a is negative and b is positive or the other way around !

sufficient

OA is B. Greenberg I don't understand how you conclude from a+b> a+b that one has to be +ve or -ve

Thanks

A quote from the attached paper "At first glance, one might consider writing out the different scenarios for the absolute value expressions in this equation, however, that would be a mistake. A conceptual approach is much better. Let's use the "guarantee of positive" to think about the equation /x/ + /y/ = /x + y/. The left side of the equation takes the variables x and y and makes them positive before they are added. The right side of the equation adds the variables first and then makes the result positive.

What must be true about x and y for the two sides of the equation to be equal? If x and y are both positive (x = 2, y = 3), both sides of the equation equal 5. If x and y are both negative (x = -2, y = -3), both sides of the equation still equal 5. If, however, one value is positive and the other is negative (x = -2, y = 3), the left side of the equation is 5, but the right side of the equation is 1. We see that for the two sides of the equation to be equal, x and y must have the same sign".

Now re-think about it when |x|+|y| > |x+y| and you will figure it out.

Thank you +1
_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

Senior Manager
Joined: 21 Apr 2008
Posts: 265
Location: Motortown
Re: PS : GMATPrep - Number Line [#permalink]

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31 Oct 2008, 18:07
Thankyou Greenberg
I learnt good concepts today
+1 for you
Re: PS : GMATPrep - Number Line   [#permalink] 31 Oct 2008, 18:07
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