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Intern  Joined: 22 Jun 2010
Posts: 33
Yesterday Diana spent a total of 240 minutes attending a  [#permalink]

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7 00:00

Difficulty:   35% (medium)

Question Stats: 76% (02:00) correct 24% (02:04) wrong based on 275 sessions

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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.
Math Expert V
Joined: 02 Sep 2009
Posts: 55670

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mehdiov wrote:
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.

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Intern  Joined: 02 Jul 2013
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Bunuel wrote:
mehdiov wrote:
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?
Math Expert V
Joined: 02 Sep 2009
Posts: 55670

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bulletpoint wrote:
Bunuel wrote:
mehdiov wrote:
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?

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Re: Yesterday Diana spent a total of 240 minutes attending a  [#permalink]

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mehdiov wrote:
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.

Let T denotes the time spent attending a training class.
Let E denotes the time spent responding to E-mails.
Let P denotes the time spent talking on the phone.

T +E + P = 240

DS: Find P ?

Statement 1 : T = 0.9 E .......(i)
Also, T +E + P = 240
0.9 E + E + P = 240
1.9 E + P = 240 .........(ii)

NOT SUFFICIENT

Statement 2:
T = 0.6 (E+P) ........(iii)
Also, T +E + P = 240
T + T /0.6 = 240 ..........(iv)
OR
(0.6+1) (E+P) = 240.......(v)
we can find T but not P.

NOT SUFFICIENT

Combined : From i & iii
0.9 E = 0.6 (E+P)
0.3 E = 0.6 P
E = 2P

From (v) 1.6 (2P+P) = 240
P = 240 / 4.8 = 50

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Re: Yesterday Diana spent a total of 240 minutes attending a  [#permalink]

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For statement 1, isn't P the same as 240-1.9 E, which then again would be 240 ? I.e. 1.9E + (240 - 1.9E) = 240 ?

I am confused

Best, gota900
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A kudo a day... Re: Yesterday Diana spent a total of 240 minutes attending a   [#permalink] 30 Dec 2018, 05:48
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