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|s – t| > ||s| - |t||?

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Intern
Joined: 29 Nov 2015
Posts: 11
|s – t| > ||s| - |t||?  [#permalink]

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13 Jan 2016, 22:39
2
1
16
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Difficulty:

75% (hard)

Question Stats:

53% (01:53) correct 47% (02:13) wrong based on 317 sessions

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|s – t| > ||s| - |t||?

(1) s + t < 0
(2) st < 0
Math Expert
Joined: 02 Aug 2009
Posts: 7107
|s – t| > ||s| - |t||?  [#permalink]

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25 Jan 2016, 05:35
4
2
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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

General Discussion
Math Expert
Joined: 02 Aug 2009
Posts: 7107
Re: ㅣs – tㅣ > ㅣㅣsㅣ - ㅣtㅣㅣ?  [#permalink]

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13 Jan 2016, 22:57
2
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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

VP
Joined: 05 Mar 2015
Posts: 1004
Re: |s – t| > ||s| - |t||?  [#permalink]

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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 ...??
VP
Joined: 05 Mar 2015
Posts: 1004
Re: |s – t| > ||s| - |t||?  [#permalink]

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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
Joined: 18 Jan 2017
Posts: 36
|s – t| > ||s| - |t||?  [#permalink]

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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.
Manager
Joined: 10 Apr 2018
Posts: 180
|s – t| > ||s| - |t||?  [#permalink]

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17 Sep 2018, 08:05
Hi,

Well there is blog (written by VeritasKarishma, and it has been neatly composed into a link by Bunuel, ) on absolute values which discusses several important properties.

https://gmatclub.com/forum/properties-o ... 91317.html.

This question can be solved in 30 secs if we know them. There are several questions on these properties. So i guess its worth spending 10 mins on them.

PS: I am not the author of the Blog, so in case you liked the blog, hit Kudos for the author of blog not me .

Probus
Manager
Joined: 06 Nov 2016
Posts: 62
Location: Viet Nam
GPA: 3.54
Re: |s – t| > ||s| - |t||?  [#permalink]

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17 Sep 2018, 08:29
2
Is |s – t| > | |s| - |t| | ? --> Is ($$s-t)^2 > (|s| - |t|)^2$$ ? --> Is $$s^2 - 2st + t^2 > s^2 - 2|st| + t^2$$ ? --> Is st < |st| ? --> Is st < 0 ?

(1) s + t < 0. If both s and t are negative --> No. If s and t have different signs --> Yes. --> Not sufficient.
(2) st < 0. --> Sufficient.

fattty wrote:
|s – t| > ||s| - |t||?

(1) s + t < 0
(2) st < 0

_________________
Re: |s – t| > ||s| - |t||? &nbs [#permalink] 17 Sep 2018, 08:29
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