Is ab < 0 ? (1) a = b - 6 (2) b < 0

For simplicity, assuming ab>0 and it's only possible if either a<0 or b<0.

Statement 1 says a = b - 6. Here nothing is said about b. thus NOT sufficient.
Statement 1 says b < 0. But no information about a.
If a <0, then ab>0 and if a> 0, then ab<0. multiple answers. thus statement (2) alone is NOT sufficient.

Combining 1 & 2, we get b<0 and a = [neg value]-6 i.e. a <0.
Here we get a single answer : ab>0
So, option (c) wins.

Is ab < 0 ?

(1) a = b - 6
(2) b < 0

___________________________________

The question asks if a and b are opposite signs.
ST 1: a = b - 6
b = 7 a = 1 No
b = 4 a = -2 Yes
This statement is not sufficient

ST 2: b<0
a can be less than or greater than zero. Again, not sufficient.

ST 1 + 2
b is negative
and a =b - 6
If b is negative, a will always be negative.
This means that ab will be positive. A definite NO.

Therefore, C is sufficient

Can be represented on number line:
STATEMENT1:
------------a---------(a is 6 less thn b)--------b------------
Alone NS
STATEMENT2:
b<0 Alone NS

Combining 1 & 2
b<0
=> a<0
=>ab>0
Therefore 'C'

Statement I : a= b- 6
if, b<0, then a<0 . ab becomes > 0 . Answer to the question : NO
if, b=0 , then a=6. ab becomes 0. Answer to the question : NO
if, 0<b<6, then a<0. ab becomes < 0 . Answer to the question : YES
No unique answer. NOT SUFFICIENT.

Statement II: b<0
if, a< 0, ab becomes > 0, Answer to the question : NO
if, a>0, ab becomes < 0, Answer to the question : YES
No unique answer. NOT SUFFICIENT.


Both Statement I & II,
As, b<0 and a is 6 less than b
So, a<0
ab<0. Answer to the question : YES
Only one unique answer. SUFFICIENT.

There are 2 variables (a and b) in the original condition. In order to match the number of variables and the number of equations, we need 2 equations. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that C is the correct answer. Using both the condition 1) and the condition 2), we get a=b-6<0 and b<0. Since ab>0, the answer is no and the conditions are not sufficient. Thus, the correct answer is C.




l For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.