|s – t| ||s| - |t||?

Question

|s – t| > ||s| - |t||?

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

chetan2u · Accepted Answer

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

Izzyjolly · Answer

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. Answer B.

chetan2u · Answer

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

rohit8865 · Answer

Chetan

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

rohit8865 · Answer

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

malavika1 · Answer

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.

Probus · Answer

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

Jsound996 · Answer

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

Pranavsawant · Answer

A nice way to see this is that this is basically the reverse triangle inequality but with a strict inequality. Now equality in the reverse triangle inequality occurs iff s = t
Can s=t in (1)? Yes, therefore we can't say
Can s=t in (2)? No, therefore we must have the strict triangle inequality and B is sufficient.

20 second question

fattty

|s – t| > ||s| - |t||?

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

|s – t| > ||s| - |t||?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

|s – t| > ||s| - |t||?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards