euro wrote:If 'a' and 'b' are integers, and |a| > |b|, is a*|b| < a-b ?
(1) a < b
(2) a*b >= 0
The answer is really "E"... let´s look into a more "analytical/technical approach" taking into account one of my 'golden rules' for Data Sufficiency: "
simplify the question stem and/or the statements whenever possible". This is particularly useful here, because inequalities and modulus are (in general) difficult to deal with, especially when he have little info on the signs of each individual parameter/variable!!
vaibhavtripathi wrote:
'|a|>|b|' also means that '|a|>0', since minimum value for |b| can be 0 and |a| has to be greater than that.
Excellent, therefore we know, for sure, that
a is non-zero!
Now let us simplify the question stem dividing in two cases:
(*) If
b is null, the question is equivalent to: is "
a positive?" (verify that)!
(**) If
b is NOT null, the question is equivalent to (verify that!):
> "Is
b less than
a.(1-
b) ?" If
b is positive ;
> "Is
b less than
a.(1+
b) ?" If
b is negative ;
That´s all we need to work pretty quick from here... have a look:
(1) a< b
BIFURCATES, therefore insufficient:
> Take
b null , then
a is certainly negative (why?), therefore from equivalence (*) we answer in the NEGATIVE ;
Practical example:
b = 0 and
a = -1.
> Take
b negative, then (from |a|> |b|) we are sure (think geometrically on the number line) that
a <
b < 0, therefore the equivalence (**) is certainly satisfied (answering in the POSITIVE), because the LHS is negative and the RHS is positive or null (null only when
b is equal to -1, do not forget that
a and
b are integers!).
Practical example:
b = -1 and
a = -2.
(2) ab is non-negative
BIFURCATES with exactly the same cases explored in statement (1)!
(1+2) BIFURCATES immediately (why?), therefore "E".
Best Regards,
Fabio.
