At a certain factory, the number of first-shift workers is 2/3 the num

Question

At a certain factory, the number of first-shift workers is 2/3 the number of second-shift workers. Every day, each second-shift worker can make 4/3 as many light bulbs as each first-shift worker.

In the first column, identify a possible number of total light bulbs made on one day by the two shifts combined; in the second column, identify the corresponding number of total light bulbs that the first-shift workers made on the same day. Make only two selections, one in each column.

GMATratan · Accepted Answer

No of people is in ratio 2:1 (as it is 2/3 and 1/3)
Work done is in ratio 1:4 .
Combined work is 2:4 i.e 1:2 (2*1 and 1*4).
Skimming through all options, you can find 36 and 12 to fit this narrative.
Cheers

siddhantvarma · Answer

Let number of second shift workers be n
Then number of first shift workers = 2n/3

Let b the number of bulbs made by each worker in the first shift
Then number of bulbs made by each worker in the second shift is 4b/3

Total bulbs made by first shift workers: 2nb/3
Tota bulbs made by second shift workers: 4nb/3

Total bulbs by both: 6nb/3 => 2nb

Now try substituting value of 2nb (first column) to find nb and get 2nb/3 (second column)

If 2nb =3, nb. = 3/2 not possible => eliminate
If 2nb = 6, nb = 3 => 2/3 nb = 2 which is not present => eliminate
If 2nb = 12, nb = 6 => 2/3 nb = 4, again not present => eliminate
If 2nb = 24, nb = 12 => 2/3nb = 8, again not present => eliminate

Therefore only 36 should fit in. Let's check
2nb = 36 => nb = 18 => 2/3nb = 12

Hence Total Bulbs for Both Shifts (Column 1) = 36
Total First-Shift Bulbs (Column 2) = 12

poojaarora1818 · Answer

Solution:

Let the number of second shift workers = x
So, the number of first shift workers = \frac{ 2}{3x}

Production by each first shift worker = y
Production by each second shift worker=  \frac{4}{3y}

By bringing the above knowledge together, we can form an equation

Total = \frac{2}{3} xy + \frac{4}{3} xy

We can get 2xy +  \frac{4}{3} xy = 2xy

Now, we can look for the values for the total production by the first shift workers, which will be 12 among the options available. And when we put that into the equation, we get 12 +  \frac{4}{3} yx

12 +  \frac{2}{3}  xy2 = 36(total)

Hence, Total production by first shift workers = 12, and the Number of total light bulbs made by the two shifts = 36

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At a certain factory, the number of first-shift workers is 2/3 the num

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Total Bulbs for Both Shifts	Total First-Shift Bulbs	Value
		3
		6
		12
		24
		36

GMAT Two-part Analysis (TPA) Questions

At a certain factory, the number of first-shift workers is 2/3 the num

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