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

Question

In a factory, the number of identical machines working on a task doubles daily. If the task was completed in 11 days, by the end of which day was 1/8 of the task completed?

A. Day 6
B. Day 7
C. Day 8
D. Day 9
E. Day 10

MartyMurray · Answer

We can brute force this one pretty quickly in the following way.

Let the number of machines on the first day be 1.

If the number of machines doubles daily, on each day, the number of machines was the following:

Day/Number of Machines on That Day

1/1
2/2
3/4
4/8
5/16
6/32
7/64
8/128
9/256
10/512
11/1024

So, the total number of machine days it took to complete the job is the sum of the machines working on all the days = 2047

2047/8 = 255 7/8

255 machine/days were completed on day 8.

255 7/8 machine days were completed early on day 9.

The correct answer is (D).

gmatophobia · Answer

1/8th of 100 = 12.5%

If 100% of the task was completed on Day 11 ➔ 50% of the task was completed on Day 10 ➔ 25% of the task was completed on Day 9 ➔ and 12.5% of the task was completed on Day 8.

Hence,  \frac{1}{8} th of the task was completed on Day 8.

Option C

mysterymanrog · Answer

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.

Adarsh_24 · Answer

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.

sujoykrdatta · Answer

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

sujoykrdatta · Answer

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

sujoykrdatta · Answer

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

sujoykrdatta · Answer

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

MartyMurray · Answer

It's not true.

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

Bunuel · Answer

Fixed the OA. Thank you!

Sandeepgurwa · Answer

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.

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

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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