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# |s – t| > ||s| - |t||?

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Re: ㅣs – tㅣ > ㅣㅣsㅣ - ㅣtㅣㅣ? [#permalink]
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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
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Re: |s – t| > ||s| - |t||? [#permalink]
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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Re: |s – t| > ||s| - |t||? [#permalink]
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
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|s – t| > ||s| - |t||? [#permalink]
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.
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|s – t| > ||s| - |t||? [#permalink]
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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 .

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

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

This is a "Yes/No" type DS question, so we need to figure out if the statements can or can't give a definite Yes or No.
The only scenarios when |s – t| > ||s| - |t|| is true, is when s>0 and t<0, or s<0 and t>0. (One of the values have to be positive, while the other is negative).
So we are trying to find if S and T have opposite signs.

1.) s + t < 0
s and t can both be negative, or one can be positive or negative.
Statement 1 is insufficient!

2.) st <0
This means that one of the variables is negative, while the other is positive.
It directly answers the question, which |s – t| > ||s| - |t|| will always be true!
Statement 2 is sufficient!

Answer is B
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Re: |s t| > ||s| - |t||? [#permalink]
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Re: |s t| > ||s| - |t||? [#permalink]
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