Working together but independently, Scott and Eric can addre

Could someone please explain how Statement 1 is sufficient? I went through the responses already here but could not understand as they are rather unclear. Thank you.

Edit 1: I managed to solve it this way, could anyone confirm that this is in fact correct?

S = Rate of Scott
E = Rate of Eric

\(S + E =\frac{x}{18}\) X being the amount of work done, and 18 being the time taken, thus X/18 given the rate for the two together

1. In M minutes, Scott addresses three times as many envelopes as Eric addresses in M minutes.

\(Eric = EM\)
\(Scott = 3EM\)

\(3EM + EM = \frac{x}{18}\)
\(4EM = \frac{x}{18}\)
\(x = 72EM\)

x = 72EM which means it would take Eric 72 hours to complete X amount of work, and since Scott can address three times as many envelopes as Eric, he can complete X amount of work in 24 hours.

The formula for the statement in question is (S+E)*18=X. The questions is S*?=X
1.The first statement gives us ratio of Scott's rate of work to Eric's. The ratios is S/E=3r/1r
(3r+1r)*18=X; 72r=X; r=X/72; S=3X/72=X/24. It takes Scott 24 hours to address X envelopes. This statement is sufficient.
2. The second statement gives us Eric's rate: E=X/72; (S+E)*18=72E; 18S=54E; 1S=3E; It takes Eric three times as much time to address X enveloped as it takes Scott. Since Eric can do the work in 72 hours, Scott can do it in 72/3=24 hours. This statement is also sufficient.

Both statements alone are sufficient to answer this question.

I have solved this way:

E
S
E+S 1.000 18

(1)

E 1.000 M
S 3.000 M
E+S 1.000 18
3.000 / M + 1.000 / M = 1.000 / 18 >>> M = 72 SOLVE

(2)

1.000 / 72 + 1.000 / x = 1.000 / 18 >>>>> x = 24 SOLVE

Answer: D

It is clear for me statement 2, but I didn't understand how can I solve the question using statement 1.

Can someone can help me?

Thaaaanks

Let E and S be the number of envelopes/hour produced by Eric and Scott resp.

Per statement 1, You are given that 3E=S ---> in M minutes, Eric can produce 3 times as many envelopes as produced by Scott. IN 1 hour, they will produce each

--->Eric = EM/60 Scott = 3EM/60 . In 18 hours, they produce,

3EM*18/60+EM*18/60 = X ---> X= 72EM/60

Thus, from above, number of envelopes produced by Eric in 1 hour = EM/60 ---> time for him to produce X (=72EM/60) envelopes =X/(EM/60) = (72EM/60)/(EM/60) = 72 hours.

Hence statement 1 is sufficient.

Hope this helps.

My bad. Thanks for pointing it out. I have corrected the typos in my solution above although nothing would change as this is a DS question and any unique value will make statement 1 sufficient.

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.