In a factory, the number of identical machines working on a task

We can reason our way out of this one:

If the machine doubles each day, then so does the quantity of work done. This implies that, if the work was all done on day 11, then day 10 must be half of the work.

If day 10 is half of the work, then day 9 must have had 1/4 of the work done (1/4 times 2 is 1/2)
If day 9 had 1/4 of the work, then day 8 must have had 1/8 of the work done.

Day 8 is the correct choice, answer choice C.

Is the high-lighted part really true?

If the first day had "x" amount of work, it will be x,2x,4x,8x,...,512x,1024x
Total work would be 2047x , while on 10th day the work completed is 512x.

All machines have the same efficiency. Assuming the efficiency as 1 unit per day, the number of units of work done on successive days are: 1 (day 1), 2 (day 2) , 4 (day 3) , 8 (day 4) , 16 (day 5) and so on
Total units of work in 11 days = 1 + 2 + 4 + ... 10^10 = 10^11 - 1 = 2047
One-eighth of the total = 1/8 * 2047 = 255 + 7/8
Cumulative units of work done in successive days:
Day 1 = 1
Day 2 = 1+2 = 3
Day 3 = 1+2+4 = 3+4 = 7
Day 4 = 7+8 = 15
Day 5 = 15+16 = 31
Day 6 = 31+32 = 63
Day 7 = 63+64 = 127
Day 8 = 127+128 = 255 - this is still short
Thus, the required answer is Day 9

Ans D

Hi
The reasoning doesn't work here
Each day, the work done is doubled. However, the work done on any day is not equal to the cumulative work on all provious days combined

The work done series is: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 (work on 11th day)
Cumulative work: 1, 3, 7, 15, 31, 63, 127, 255, 511, 1023 (total work in 10 days), 2047 (total work in 11 days) - Observe that work on the 11th day is not equal to the work done in 10 days; hence 1023 is not half the total work

Note: The logic could have worked if the work done series was 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 (work on 11th day)
Cumulative work: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 (total work in 10 days), 1024 (total work in 11 days) - Observe that work on the 11th day is now equal to the work done in 10 days


The answer should be Day 9

Hi
The reasoning doesn't work here
Each day, the work done is doubled. However, the work done on any day is not equal to the cumulative work on all provious days combined

The work done series is: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 (work on 11th day)
Cumulative work: 1, 3, 7, 15, 31, 63, 127, 255, 511, 1023 (total work in 10 days), 2047 (total work in 11 days) - Observe that work on the 11th day is not equal to the work done in 10 days; hence 1023 is not half the total work

Note: The logic could have worked if the work done series was 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 (work on 11th day)
Cumulative work: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 (total work in 10 days), 1024 (total work in 11 days) - Observe that work on the 11th day is now equal to the work done in 10 days


The answer should be Day 9

Bunuel
Please check the answer - it should be Day 9 (Option D)

It's not true.

The correct answer is (D), not (C).

Fixed the OA. Thank you!

The work done series is: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 (work on 11th day)
Cumulative work: 1, 3, 7, 15, 31, 63, 127, 255, 511, 1023 (total work in 10 days), 2047 (total work in 11 days) - Observe that work on the 11th day is not equal to the work done in 10 days; hence 1023 is not half the total work.
Therfore, total work is 2047 in total.
To know percentage completion eaxh day:
Day 1. 1/2047 = 0.0488%
Day 2. 3/2047 = 0.146%
Day 3. 7/2047 = 0.342%
Day 4. 15/2047 = 0.732%
Day 5. 31/2047 = 1.51%
Day 6. 63/2047 = 3.07%
Day 7. 127/2047 = 6.2%
Day 8. 255/2047 = 12.457%
Day 9. 511/2047 = 24.96%
Day 10. 1023/2047 = 49.97%
Day 11. 2047/2047 = 100%

On the compeletion of Day 8 Total work done is slightly less than 1/8th of the total work. Therefore, we are choosing day 9 as a answer.