Machine X can produce 3 widgets every 2 minutes and Machine Y produces

Efficiency of Machine X = 3/2 widgets per minute
Efficiency of Machine Y = 5/3 widgets per minute

So, In 6 Minutes X Produces 3/2*6 = 9 widgets
And In 6 Minutes X Produces 5/3*6 = 10 widgets

Thus, in 6 minutes Machine X and Y produces 19 widgets and X's contribution is 9/19 widgets, Answer must be (E)

One approach: find (Part X : Part Y)
Then (Part X : Whole X+Y)

I. Change the time, find (part: part) ratio, then (part: whole)
Use ANY easier time period to find PART : PART ratio

Relative portions that X and Y finish will not change as long as time worked is the same
\(X\)'s part of total production is: \(\frac{X}{X+Y}\)

(1) Change the time period.
• X's output + Y's output = total output

• Total output for each is:

\(X\): \(r_{x}*T=W_{x}\)

\(Y\): \(r_{y}*T=W_{y}\)

Same time worked? Then number of widgets each makes depends ONLY on their rates.

(2): compare rates with a time that is easier than 25 minutes
• Use LCM of 6 minutes to get an identical time period worked, which will yield
relative portions of total work each produces

\(X\)'s rate in 6 minutes: \(\frac{3w}{2min}=\frac{9w}{6min}\)

\(Y\)'s rate in 6 minutes: \(\frac{5w}{3min}=\frac{10w}{6min}\)

• The part of production finished by X?

\(\frac{X}{(X+Y)}=\frac{9}{9+10}=\frac{9}{19}\)

Answer E

II. Harder: TOTAL output in 25 minutes
In 25 minutes, X finishes \(\frac{X_{w}}{Total_{w}}\)

• \(X\), total output:

\(W_{x}=r_{x}*25\)

\(W_{x}=(\frac{3w}{2min}*25min)=\frac{75}{2}w\)

• \(Y\), total output

\(W_{y}=r_{y}*25\)

\(W_{y}=(\frac{5w}{3min}*25min)=\frac{125}{3}w\)


• Overall total output (X + Y):

\((X+Y)=(\frac{75}{2}w+\frac{125}{3}w)=\)

\((\frac{225}{6w}+\frac{250w}{6}w)=\frac{475}{6}w\)

• X finishes what part of total production?

\(\frac{X}{Total}=\frac{(\frac{75}{2}w)}{(\frac{475}{6}w)}=\)

\((\frac{75}{2}w*\frac{6}{475}w)=\) \(\frac{225w}{475w}\)

Divide by 25:

X finishes \(\frac{9}{19}\) of production

Answer E

Machine X’s rate is 3/2, and Machine Y’s rate is 5/3. Their combined rate is (3/2 + 5/3). We can create the expression:

(3/2)/(3/2 + 5/3)

Multiplying the expression by 6/6 we have:

9/(9 + 10) = 9/19

No matter the amount of time they work together, Machine X will always produce 9/19 of the combined output.

Answer: E

For X, 3 widgets every 2 minutes = 9 widgets every 6 minutes.
For Y, 5 widgets every 3 minutes = 10 widgets every 6 minutes.
Thus, every 6 minutes:
Number of widgets produced by X = 9
Number of widgets produced by Y = 10
Total number of widgets produced by X and Y together = 9+10 = 19

Since X produces 9 of every 19 widgets that are produced, we get:
\(\frac{X}{total }= \frac{9}{19}\)

While I got the answer right, I think this question is actually wrong. You can't have 41.66 and 37.5 widgets, and if the two machines are working separately you can't add those up. The number of widgets should be an integer and therefore the answer should be 9/10.

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.