MGMAT Adv Quant - workout set 10, problem 98

[aboinpally]

MGMAT Adv Quant - workout set 10, problem 98

Q) What is the value of |a+b| ?
1) (a+b+c+d)(a+b-c-d) = 16
2) c+d = 3

solving option 1 you can get
(a+b)^2 = (c+d)^2 + 16
Is this statement not sufficient because only value that is possible for (a+b) = 5 ? (25 = 16 + 9, where c+d = 3)
OR I am missing another set of numbers that satisfy the equation

P.S - I searched for this question before posting but could not find it. If its already been discussed, can you please point me to the right post.

[LazyNK]

Hi Aboinpally,
The statement is not sufficient. There is no constraint on a+b and c+d to be integers, in fact, no c constraint for both a+b and c+d to even be rational. Thus there can be infinite no. of values of a+b and c+d for which statement one can be true. One example is when c+d=1, a+b=√24 , which is allowed because no constraint is given that a+b and c+d have to be integers.
Hence not sufficient.
-NK

[aboinpally]

Thanks NK - i tend to assume that given variables are integers !

[jnelson0612]

Many thanks LazyNK!