Abominable ABs

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parul9: Master | Next Rank: 500 Posts; Posts: 197; Joined: Thu Sep 15, 2011 10:22 amFollowed by: 2 members; Thanked: 6 times

by parul9 » Mon Oct 10, 2011 5:36 am

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

(1) a < 0

(2) ab >= 0

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

Last edited by parul9 on Mon Oct 10, 2011 7:11 am, edited 1 time in total.

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Source: Beat The GMAT — Data Sufficiency | Mon Oct 10, 2011 5:36 am

n@resh: Senior | Next Rank: 100 Posts; Posts: 61; Joined: Tue Apr 13, 2010 3:29 am; Thanked: 8 times

by n@resh » Mon Oct 10, 2011 6:36 am

parul9 wrote:If a and b are integers, and |a| > |b|, is a Â· |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!

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parul9: Master | Next Rank: 500 Posts; Posts: 197; Joined: Thu Sep 15, 2011 10:22 amFollowed by: 2 members; Thanked: 6 times

by parul9 » Mon Oct 10, 2011 7:10 am

n@resh wrote:
parul9 wrote:If a and b are integers, and |a| > |b|, is a Â· |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!

Like this post

nandy1984: Master | Next Rank: 500 Posts; Posts: 105; Joined: Fri Nov 05, 2010 8:29 pm; Thanked: 4 times

by nandy1984 » Mon Oct 10, 2011 7:44 am

parul9 wrote:
n@resh wrote:
parul9 wrote:If a and b are integers, and |a| > |b|, is a Â· |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

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n@resh: Senior | Next Rank: 100 Posts; Posts: 61; Joined: Tue Apr 13, 2010 3:29 am; Thanked: 8 times

by n@resh » Mon Oct 10, 2011 8:23 am

nandy1984 wrote:
parul9 wrote:
n@resh wrote:
parul9 wrote:If a and b are integers, and |a| > |b|, is a Â· |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|!

Like this post

nandy1984: Master | Next Rank: 500 Posts; Posts: 105; Joined: Fri Nov 05, 2010 8:29 pm; Thanked: 4 times

by nandy1984 » Wed Oct 12, 2011 8:21 am

n@resh wrote:
nandy1984 wrote:
parul9 wrote:
n@resh wrote:
parul9 wrote:If a and b are integers, and |a| > |b|, is a Â· |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....

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nandy1984: Master | Next Rank: 500 Posts; Posts: 105; Joined: Fri Nov 05, 2010 8:29 pm; Thanked: 4 times

by nandy1984 » Wed Oct 12, 2011 8:22 am

n@resh wrote:
nandy1984 wrote:
parul9 wrote:
n@resh wrote:
parul9 wrote:If a and b are integers, and |a| > |b|, is a Â· |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....

Like this post

nandy1984: Master | Next Rank: 500 Posts; Posts: 105; Joined: Fri Nov 05, 2010 8:29 pm; Thanked: 4 times

by nandy1984 » Wed Oct 12, 2011 8:23 am

n@resh wrote:
nandy1984 wrote:
parul9 wrote:
n@resh wrote:
parul9 wrote:If a and b are integers, and |a| > |b|, is a Â· |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....

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