Yesterday Diana spent a total of 240 minutes attending a training class, responding to E-
mails, and talking on the phone. If she did no two of these three activities at the same
time, how much time did she spend talking on the phone?
(1) Yesterday the amount of time that Diana spent attending the training class was
90 percent of the amount of time that she spent responding to E-mails.
(2) Yesterday the amount of time that Diana spent attending the training class was
60 percent of the total amount of time that she spent responding to E-mails and
talking on the phone.
Given: \(C+E+P=240\), where C is th time she spent on training class, E is the time she spent on E-mail and P is the time she spent on phone. Question: \(P=?\)
(1) \(C=0.9E\) --> \(C+E+P=0.9E+E+P=1.9E+P=240\). Not sufficient to calculate \(P\) (one equation, two variables).
(2) \(C=0.6(E+P)\) --> \(C+E+P=0.6(E+P)+E+P=1.6E+1.6P=240\). Not sufficient to calculate \(P\) (one equation, two variables).
(1)+(2) \(1.9E+P=240\) and \(1.6E+1.6P=240\) --> we have two distinct linear equations with two variables hence we can calculate each of them. Sufficient.
Bunuel, for statement 2 we can rearrange to get E+P=240/1.6. If we have E+P, cant we plug this into C+E+P=240, which gives us C+(240/1.6)=240, which gives us C=240-(240/1.6)? Hence 2 would be sufficient as you rearrange to get P?