gmatrant wrote:I was reading the Manhattan "Equations and Inequalities" book where in it stated that if two inequalities are given
i) a > b
ii) c > d

the we can combine the two inequalities to state positively that a+c > b+d.

But this does not hold true with the below problem

Example DS problem

Is p+q > r+s ?
i) p > r+s
ii) q > r+s

Now this is true as long as p, q are positive values.
If p is -4 , r is -3 , s is -3 then p > r+s
If q is -5 r is -3 , s is -3 then q > r+s
Combining the inequality
p+q > 2(r+s) so it means but p+q is greater than (r+s) as well but
with the above values p+q < r+s since p+q = -9 and r+s =-6.

Can experts please help as to when can inequalities be combined to conclude a solution and when we cannot combine.

OA is E

pemdas wrote:he's not making any *assumptions*
he simply forgot to add r+s from the right hand side of the first inequality to the right hand side of the second inequality. Together they will make r+s + r+s and translated into his example -3-3 -3-3=-12 and this will hold true for -9>-12 always. So one can safely combine the inequalities provided the sign is the same.

pemdas wrote:he's not making any *assumptions*
he simply forgot to add r+s from the right hand side of the first inequality to the right hand side of the second inequality. Together they will make r+s + r+s and translated into his example -3-3 -3-3=-12 and this will hold true for -9>-12 always. So one can safely combine the inequalities provided the sign is the same.