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|s – t| > ||s| - |t||?

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|s – t| > ||s| - |t||? [#permalink]

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New post 13 Jan 2016, 22:39
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|s – t| > ||s| - |t||?

(1) s + t < 0
(2) st < 0
[Reveal] Spoiler: OA
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Re: ㅣs – tㅣ > ㅣㅣsㅣ - ㅣtㅣㅣ? [#permalink]

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New post 13 Jan 2016, 22:57
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fattty wrote:
ㅣs – tㅣ > ㅣㅣsㅣ - ㅣtㅣㅣ?
1) s + t < 0
2) st < 0



Hi..
when we look at the equation, what stands out is-
1) If both s and t are of same sign, the answer to the Q is NO, as both will be equal.. and suff
2) If both have different signs, answer is YES... SUff..

lets see the choices..
1) s + t < 0
both s and t can be negative.. or both can be of different sign.. insuff

2) st < 0
both s and t are of different sign .. suff as per the condition 20 mentioned above..

B
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


BANGALORE/-

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Re: |s – t| > ||s| - |t||? [#permalink]

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New post 25 Jan 2016, 04:43
chetan2u wrote:
fattty wrote:
ㅣs – tㅣ > ㅣㅣsㅣ - ㅣtㅣㅣ?
1) s + t < 0
2) st < 0



Hi..
when we look at the equation, what stands out is-
1) If both s and t are of same sign, the answer to the Q is NO, as both will be equal.. and suff
2) If both have different signs, answer is YES... SUff..

lets see the choices..
1) s + t < 0
both s and t can be negative.. or both can be of different sign.. insuff

2) st < 0
both s and t are of different sign .. suff as per the condition 20 mentioned above..

B


Chetan

could you please elaborate it for me ...??
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Posts: 5662
|s – t| > ||s| - |t||? [#permalink]

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New post 25 Jan 2016, 05:35
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rohit8865 wrote:
chetan2u wrote:
fattty wrote:
ㅣs – tㅣ > ㅣㅣsㅣ - ㅣtㅣㅣ?
1) s + t < 0
2) st < 0



Hi..
when we look at the equation, what stands out is-
1) If both s and t are of same sign, the answer to the Q is NO, as both will be equal.. and suff
2) If both have different signs, answer is YES... SUff..

lets see the choices..
1) s + t < 0
both s and t can be negative.. or both can be of different sign.. insuff

2) st < 0
both s and t are of different sign .. suff as per the condition 20 mentioned above..

B


Chetan

could you please elaborate it for me ...??


Hi Rohit,

lets see what the statement tells us..
ㅣs – tㅣ > ㅣㅣsㅣ - ㅣtㅣㅣ...

1) If both s and t are of same sign, the answer to the Q is NO, as both will be equal.. and suff
lets take s as 4 and t as 5..
|4-5|>||4|-|5||..
|-1|>|-1|... 1>1.. NO
lets take them -ive now s=-4 and t=-5..
|-4-(-5)|>||-4|-|-5||..
|1|>|-1|... 1>1.. NO

so whatever values we take for s and t, if they both are of same sign, the two sides will be equal..
so our answer for [b]ㅣs – tㅣ > ㅣㅣsㅣ - ㅣtㅣㅣ
is NO.. and thus suff..[/b]

2) If both have different signs, answer is YES... SUff..
say s=4 and t=-5..
|4-(-5)|>||4|-|-5||..
|9|>|-1|... 9>1.. yes..
you can take any values for s and t but of different signs , you will always get YES for ㅣs – tㅣ > ㅣㅣsㅣ - ㅣtㅣㅣ..

so what do we require to know, just that the signs of s and t is same or different and we will be able to answer for is ㅣs – tㅣ > ㅣㅣsㅣ - ㅣtㅣㅣ?

now lets see the statements..

1) s + t < 0
We cannot say anything about signs
both s and t can be negative.. or both can be of different sign.. insuff

2) st < 0
both s and t are of different sign, then only the product will be <0..
-a*-b= +ab
+a*+b=+ab, but -a*+b=-ab
.. suff as per the condition (2) mentioned above..
I hope it helps
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


BANGALORE/-

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Director
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Joined: 05 Mar 2015
Posts: 962
Re: |s – t| > ||s| - |t||? [#permalink]

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New post 25 Jan 2016, 07:19
Hi Rohit,
lets see what the statement tells us..
ㅣs – tㅣ > ㅣㅣsㅣ - ㅣtㅣㅣ...
1) If both s and t are of same sign, the answer to the Q is NO, as both will be equal.. and suff
lets take s as 4 and t as 5..
|4-5|>||4|-|5||..
|-1|>|-1|... 1>1.. NO
lets take them -ive now s=-4 and t=-5..
|-4-(-5)|>||-4|-|-5||..
|1|>|-1|... 1>1.. NO

so whatever values we take for s and t, if they both are of same sign, the two sides will be equal..
so our answer for ㅣs – tㅣ > ㅣㅣsㅣ - ㅣtㅣㅣ is NO.. and thus suff..
2) If both have different signs, answer is YES... SUff..
say s=4 and t=-5..
|4-(-5)|>||4|-|-5||..
|9|>|-1|... 9>1.. yes..
you can take any values for s and t but of different signs , you will always get YES for ㅣs – tㅣ > ㅣㅣsㅣ - ㅣtㅣㅣ..

so what do we require to know, just that the signs of s and t is same or different and we will be able to answer for is ㅣs – tㅣ > ㅣㅣsㅣ - ㅣtㅣㅣ?

now lets see the statements..
1) s + t < 0
We cannot say anything about signs
both s and t can be negative.. or both can be of different sign.. insuff

2) st < 0
both s and t are of different sign, then only the product will be <0..
-a*-b= +ab
+a*+b=+ab, but -a*+b=-ab
.. suff as per the condition (2) mentioned above..
I hope it helps[/quote]

tanks a lot...+1
Intern
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Joined: 18 Jan 2017
Posts: 36
|s – t| > ||s| - |t||? [#permalink]

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New post 15 Mar 2017, 03:30
Even one absolute (modulus) is a tricky thing; here we have two consecutive ones! Will take me at least 5 minutes on the exam day, to get anywhere near to the solution here.

I guess value substitution is the only way to solve it.
|s – t| > ||s| - |t||?   [#permalink] 15 Mar 2017, 03:30
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