Abs Val of Two A Minus B - please point flaw in the solution

[pshaikh.world]

Hi Manhattan instructors,

I need your help with respect to following question -

Is |2a - b| < 7?

(1) 2a - b < 7
(2) a = b + 3


Here is how I solved -

|2a - b| < 7 meaning -

2a - b < 7 (if 2a - b > 0) or b - 2a < 7 (if 2a - b < 0)

1) 2a - b < 7 --- not sufficient, we don't know whether 2a - b > 0 or 2a - b < 0, quiet possible 2a - b to have value 6 (where condition is met) or value -14 (where condition is violated)

2) a = b + 3 -> a - b = 3 --> a - b > 0 so a > b

as a result 2a - b > 0 but not sufficient to tell whether absolute value is less than 7 or not

Combining two, from 2nd statement 2a - b > 0, and first statement says 2a - b < 7, so sufficient to say |2a -b| < 7

So while I deduced it "C", the answer presented is E(the problem is of Manhattan's advanced quant question bank)

[pshaikh.world]

Oops realized that a > b indicates a -b > 0 but not 2a - b > 0 when a < 0.

a -b> 0
2a-b>a
2a-b>0 if a > 0 otherwise 2a-b<0

e.g. if a = -7, b = -10 (a -b = 3) then 2a = -14, and b = 10, 2a-b=-4 which is less than 0

Please mark it answered or delete it!

[tim]

no problem..