Abominable ABs

[parul9]

If a and b are integers, and |a| > |b|, is a · |b| < a - b?

(1) a < 0

(2) ab >= 0

OA : [spoiler]E Can someone please explain??[/spoiler]

[n@resh]

If a and b are integers, and |a| > |b|, is a · |b| < a - b?

(1) a < 0

(2) ab 0

OA : [spoiler]E Can someone please explain??[/spoiler]

From stat1: a < 0,
plug-in numbers: a = -1, b = 0 ; 0 < -1 ( FALSE)
a = -2, b = 1 ; -2 < -3 (FALSE)
a = -2, b = -1 ; -2 < -1 ( TRUE)
clearly, not sufficient.

From stat2: ab 0; it seems expression missing it's relation sign!
well, if we consider <, > then obviously it's not sufficient!
but if we have ab = 0; to satisfy |a| > |b|, then a must be non-zero (but it can be < 0 or >0), so b should be 0!
e.g: a = -2, b = 0; 0 < -2 ( FALSE)
a = 2, b = 0; 0 < 2 ( TRUE)

Hence, it's not sufficient!

NOTE: if i consider, ab = 0 and a < 0 ; then the statement can be solved by using these both statements!
However, as 2nd statement isn't clear then i'll go for not sufficient. E!

[parul9]

If a and b are integers, and |a| > |b|, is a · |b| < a - b?

(1) a < 0

(2) ab 0

OA : [spoiler]E Can someone please explain??[/spoiler]

From stat1: a < 0,
plug-in numbers: a = -1, b = 0 ; 0 < -1 ( FALSE)
a = -2, b = 1 ; -2 < -3 (FALSE)
a = -2, b = -1 ; -2 < -1 ( TRUE)
clearly, not sufficient.

From stat2: ab 0; it seems expression missing it's relation sign!
well, if we consider <, > then obviously it's not sufficient!
but if we have ab = 0; to satisfy |a| > |b|, then a must be non-zero (but it can be < 0 or >0), so b should be 0!
e.g: a = -2, b = 0; 0 < -2 ( FALSE)
a = 2, b = 0; 0 < 2 ( TRUE)

Hence, it's not sufficient!

NOTE: if i consider, ab = 0 and a < 0 ; then the statement can be solved by using these both statements!
However, as 2nd statement isn't clear then i'll go for not sufficient. E!

The second statement is ab >= 0. I will edit the main post too!

[nandy1984]

If a and b are integers, and |a| > |b|, is a · |b| < a - b?

(1) a < 0

(2) ab 0

OA : [spoiler]E Can someone please explain??[/spoiler]

From stat1: a < 0,
plug-in numbers: a = -1, b = 0 ; 0 < -1 ( FALSE)
a = -2, b = 1 ; -2 < -3 (FALSE)
a = -2, b = -1 ; -2 < -1 ( TRUE)
clearly, not sufficient.

From stat2: ab 0; it seems expression missing it's relation sign!
well, if we consider <, > then obviously it's not sufficient!
but if we have ab = 0; to satisfy |a| > |b|, then a must be non-zero (but it can be < 0 or >0), so b should be 0!
e.g: a = -2, b = 0; 0 < -2 ( FALSE)
a = 2, b = 0; 0 < 2 ( TRUE)

Hence, it's not sufficient!

NOTE: if i consider, ab = 0 and a < 0 ; then the statement can be solved by using these both statements!
However, as 2nd statement isn't clear then i'll go for not sufficient. E!

The second statement is ab >= 0. I will edit the main post too!

Naresh has explained the statement 1...Coming to Statement 2 following the same procedure

Statement 2 : ab>= 0
There are several conditions like
i) a>0,b>0,ab>0
ii) a<0,b<0,ab>0
iii) a>0,b=0,ab=0
iv) a<0,b=0,ab=0
v) a=0,b<0,ab=0 ---> a*|b|=0 ---> a-b>0 ---> b>0 correct
v)a=0, b>0, ab=0 ---> a*|b|=0 ---> -b>0 which is wrong
No need to solve all the combinations above just the last two combinations have two different results so we can say its INSUFFICIENT.

Combining Statement 1) and 2) we get combinations
(ii)a<0,b<0,ab>0 ----> a*|b|<0 ---> a-b either positive or negative depending on values of "a" and "b" if a=-2,b=-3 then a-b> a*|b| correct...1>-6 ; if a=-3,b=-2 then a-b =-1, a*|b| = -3*2=-6 -1>-6 correct.
(iv)a<0,b=0,ab=0 ----> a=-3 ---> -3>0 wrong...
so from the two combinations we get different answers so its INSUFFICIENT...Ans:E

If anyone can explain this in a more simplistic way you are welcome. I tried my best ...if i am wrong CORRECT ME...Thanks

[n@resh]

If a and b are integers, and |a| > |b|, is a · |b| < a - b?

(1) a < 0

(2) ab 0

OA : [spoiler]E Can someone please explain??[/spoiler]

From stat1: a < 0,
plug-in numbers: a = -1, b = 0 ; 0 < -1 ( FALSE)
a = -2, b = 1 ; -2 < -3 (FALSE)
a = -2, b = -1 ; -2 < -1 ( TRUE)
clearly, not sufficient.

From stat2: ab 0; it seems expression missing it's relation sign!
well, if we consider <, > then obviously it's not sufficient!
but if we have ab = 0; to satisfy |a| > |b|, then a must be non-zero (but it can be < 0 or >0), so b should be 0!
e.g: a = -2, b = 0; 0 < -2 ( FALSE)
a = 2, b = 0; 0 < 2 ( TRUE)

Hence, it's not sufficient!

NOTE: if i consider, ab = 0 and a < 0 ; then the statement can be solved by using these both statements!
However, as 2nd statement isn't clear then i'll go for not sufficient. E!

The second statement is ab >= 0. I will edit the main post too!

Naresh has explained the statement 1...Coming to Statement 2 following the same procedure

Statement 2 : ab>= 0
There are several conditions like
i) a>0,b>0,ab>0
ii) a<0,b<0,ab>0
iii) a>0,b=0,ab=0
iv) a<0,b=0,ab=0
v) a=0,b<0,ab=0 ---> a*|b|=0 ---> a-b>0 ---> b>0 correct
v)a=0, b>0, ab=0 ---> a*|b|=0 ---> -b>0 which is wrongNo need to solve all the combinations above just the last two combinations have two different results so we can say its INSUFFICIENT.

Combining Statement 1) and 2) we get combinations
(ii)a<0,b<0,ab>0 ----> a*|b|<0 ---> a-b either positive or negative depending on values of "a" and "b" if a=-2,b=-3 then a-b> a*|b| correct...1>-6 ; if a=-3,b=-2 then a-b =-1, a*|b| = -3*2=-6 -1>-6 correct.
(iv)a<0,b=0,ab=0 ----> a=-3 ---> -3>0 wrong...
so from the two combinations we get different answers so its INSUFFICIENT...Ans:E

If anyone can explain this in a more simplistic way you are welcome. I tried my best ...if i am wrong CORRECT ME...Thanks

Answer will be still: E! nevertheless, a can't be zero as per |a| > |b|!

[nandy1984]

If a and b are integers, and |a| > |b|, is a · |b| < a - b?

(1) a < 0

(2) ab 0

OA : [spoiler]E Can someone please explain??[/spoiler]

From stat1: a < 0,
plug-in numbers: a = -1, b = 0 ; 0 < -1 ( FALSE)
a = -2, b = 1 ; -2 < -3 (FALSE)
a = -2, b = -1 ; -2 < -1 ( TRUE)
clearly, not sufficient.

From stat2: ab 0; it seems expression missing it's relation sign!
well, if we consider <, > then obviously it's not sufficient!
but if we have ab = 0; to satisfy |a| > |b|, then a must be non-zero (but it can be < 0 or >0), so b should be 0!
e.g: a = -2, b = 0; 0 < -2 ( FALSE)
a = 2, b = 0; 0 < 2 ( TRUE)

Hence, it's not sufficient!

NOTE: if i consider, ab = 0 and a < 0 ; then the statement can be solved by using these both statements!
However, as 2nd statement isn't clear then i'll go for not sufficient. E!

The second statement is ab >= 0. I will edit the main post too!

Naresh has explained the statement 1...Coming to Statement 2 following the same procedure

Statement 2 : ab>= 0
There are several conditions like
i) a>0,b>0,ab>0
ii) a<0,b<0,ab>0
iii) a>0,b=0,ab=0
iv) a<0,b=0,ab=0
v) a=0,b<0,ab=0 ---> a*|b|=0 ---> a-b>0 ---> b>0 correct
v)a=0, b>0, ab=0 ---> a*|b|=0 ---> -b>0 which is wrongNo need to solve all the combinations above just the last two combinations have two different results so we can say its INSUFFICIENT.

Combining Statement 1) and 2) we get combinations
(ii)a<0,b<0,ab>0 ----> a*|b|<0 ---> a-b either positive or negative depending on values of "a" and "b" if a=-2,b=-3 then a-b> a*|b| correct...1>-6 ; if a=-3,b=-2 then a-b =-1, a*|b| = -3*2=-6 -1>-6 correct.
(iv)a<0,b=0,ab=0 ----> a=-3 ---> -3>0 wrong...
so from the two combinations we get different answers so its INSUFFICIENT...Ans:E

If anyone can explain this in a more simplistic way you are welcome. I tried my best ...if i am wrong CORRECT ME...Thanks

Answer will be still: E! nevertheless, a can't be zero as per |a| > |b|!

HELLO nARESH THIS IS A WONDERFUL POINT I HAVE NOT THOUGHT ABOUT THAT....a can't be zero as per |a| > |b|!...tHANK YOU....

[nandy1984]

If a and b are integers, and |a| > |b|, is a · |b| < a - b?

(1) a < 0

(2) ab 0

OA : [spoiler]E Can someone please explain??[/spoiler]

From stat1: a < 0,
plug-in numbers: a = -1, b = 0 ; 0 < -1 ( FALSE)
a = -2, b = 1 ; -2 < -3 (FALSE)
a = -2, b = -1 ; -2 < -1 ( TRUE)
clearly, not sufficient.

From stat2: ab 0; it seems expression missing it's relation sign!
well, if we consider <, > then obviously it's not sufficient!
but if we have ab = 0; to satisfy |a| > |b|, then a must be non-zero (but it can be < 0 or >0), so b should be 0!
e.g: a = -2, b = 0; 0 < -2 ( FALSE)
a = 2, b = 0; 0 < 2 ( TRUE)

Hence, it's not sufficient!

NOTE: if i consider, ab = 0 and a < 0 ; then the statement can be solved by using these both statements!
However, as 2nd statement isn't clear then i'll go for not sufficient. E!

The second statement is ab >= 0. I will edit the main post too!

Naresh has explained the statement 1...Coming to Statement 2 following the same procedure

Statement 2 : ab>= 0
There are several conditions like
i) a>0,b>0,ab>0
ii) a<0,b<0,ab>0
iii) a>0,b=0,ab=0
iv) a<0,b=0,ab=0
v) a=0,b<0,ab=0 ---> a*|b|=0 ---> a-b>0 ---> b>0 correct
v)a=0, b>0, ab=0 ---> a*|b|=0 ---> -b>0 which is wrongNo need to solve all the combinations above just the last two combinations have two different results so we can say its INSUFFICIENT.

Combining Statement 1) and 2) we get combinations
(ii)a<0,b<0,ab>0 ----> a*|b|<0 ---> a-b either positive or negative depending on values of "a" and "b" if a=-2,b=-3 then a-b> a*|b| correct...1>-6 ; if a=-3,b=-2 then a-b =-1, a*|b| = -3*2=-6 -1>-6 correct.
(iv)a<0,b=0,ab=0 ----> a=-3 ---> -3>0 wrong...
so from the two combinations we get different answers so its INSUFFICIENT...Ans:E

If anyone can explain this in a more simplistic way you are welcome. I tried my best ...if i am wrong CORRECT ME...Thanks

Answer will be still: E! nevertheless, a can't be zero as per |a| > |b|!

HELLO nARESH THIS IS A WONDERFUL POINT I HAVE NOT THOUGHT ABOUT THAT....a can't be zero as per |a| > |b|!...tHANK YOU....

[nandy1984]

If a and b are integers, and |a| > |b|, is a · |b| < a - b?

(1) a < 0

(2) ab 0

OA : [spoiler]E Can someone please explain??[/spoiler]

From stat1: a < 0,
plug-in numbers: a = -1, b = 0 ; 0 < -1 ( FALSE)
a = -2, b = 1 ; -2 < -3 (FALSE)
a = -2, b = -1 ; -2 < -1 ( TRUE)
clearly, not sufficient.

From stat2: ab 0; it seems expression missing it's relation sign!
well, if we consider <, > then obviously it's not sufficient!
but if we have ab = 0; to satisfy |a| > |b|, then a must be non-zero (but it can be < 0 or >0), so b should be 0!
e.g: a = -2, b = 0; 0 < -2 ( FALSE)
a = 2, b = 0; 0 < 2 ( TRUE)

Hence, it's not sufficient!

NOTE: if i consider, ab = 0 and a < 0 ; then the statement can be solved by using these both statements!
However, as 2nd statement isn't clear then i'll go for not sufficient. E!

The second statement is ab >= 0. I will edit the main post too!

Naresh has explained the statement 1...Coming to Statement 2 following the same procedure

Statement 2 : ab>= 0
There are several conditions like
i) a>0,b>0,ab>0
ii) a<0,b<0,ab>0
iii) a>0,b=0,ab=0
iv) a<0,b=0,ab=0
v) a=0,b<0,ab=0 ---> a*|b|=0 ---> a-b>0 ---> b>0 correct
v)a=0, b>0, ab=0 ---> a*|b|=0 ---> -b>0 which is wrongNo need to solve all the combinations above just the last two combinations have two different results so we can say its INSUFFICIENT.

Combining Statement 1) and 2) we get combinations
(ii)a<0,b<0,ab>0 ----> a*|b|<0 ---> a-b either positive or negative depending on values of "a" and "b" if a=-2,b=-3 then a-b> a*|b| correct...1>-6 ; if a=-3,b=-2 then a-b =-1, a*|b| = -3*2=-6 -1>-6 correct.
(iv)a<0,b=0,ab=0 ----> a=-3 ---> -3>0 wrong...
so from the two combinations we get different answers so its INSUFFICIENT...Ans:E

If anyone can explain this in a more simplistic way you are welcome. I tried my best ...if i am wrong CORRECT ME...Thanks

Answer will be still: E! nevertheless, a can't be zero as per |a| > |b|!

HELLO nARESH THIS IS A WONDERFUL POINT I HAVE NOT THOUGHT ABOUT THAT....a can't be zero as per |a| > |b|!...tHANK YOU....