sign of duration

CFA Level III
#1

this is from practice exam vol1 exam2 afternoon Q40

a company issued fixed rate bond, its duration is now 4. then using receiver swap, reduce the duration. swap fixed sidw duration is 3.75 and floating side is 0.5.

then in my understanding, pay is negative while receice is positive so overall duration is -4 + 3.75 - 0.5 = -0.75 while the answer says it is positive. why?

#2

Looks like an error. Check the errata.

#3

Didn’t read the question. But in that context, using a receiver swap by shorting it . Why you implied that using means just buying?