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IMO

x=170

y=512



To determine the total number of pages reviewed by 1:30 p.m. (x) and by 6:00 p.m. (y), we need to calculate the number of pages each editor reviewed during those times.

Calculation of Pages Reviewed by 1:30 p.m. (x):


  1. Editor A:

    • Started at 9:00 a.m.
    • Reviewing speed: 12 pages per hour
    • Time from 9:00 a.m. to 1:30 p.m.: 4.5 hours
      Pages reviewed by A=12×4.5=54 pages
  2. Editor B:

    • Started at 10:00 a.m.
    • Reviewing speed: 16 pages per hour
    • Time from 10:00 a.m. to 1:30 p.m.: 3.5 hours
      Pages reviewed by B=16×3.5=56 pages
  3. Editor C:

    • Started at 11:00 a.m.
    • Reviewing speed: 18 pages per hour
    • Time from 11:00 a.m. to 1:30 p.m.: 2.5 hours
      Pages reviewed by C=18×2.5=45 pages
  4. Editor D:

    • Started at 12:00 p.m.
    • Reviewing speed: 10 pages per hour
    • Time from 12:00 p.m. to 1:30 p.m.: 1.5 hours
      Pages reviewed by D=10×1.5=15 pages
  5. Editor E:

    • Started at 1:30 p.m.
    • Reviewing speed: 20 pages per hour
    • Time from 1:30 p.m. to 1:30 p.m.: 0 hours (has not started yet)
      Pages reviewed by E=0 pages
Summing up the pages reviewed by 1:30 p.m.:
x=54+56+45+15+0=170 pages

Calculation of Pages Reviewed by 6:00 p.m. (y):
  1. Editor A:

    • Time from 9:00 a.m. to 6:00 p.m.: 9 hours
      Pages reviewed by A=12×9=108 pages
  2. Editor B:

    • Time from 10:00 a.m. to 6:00 p.m.: 8 hours
      Pages reviewed by B=16×8=128 pages
  3. Editor C:

    • Time from 11:00 a.m. to 6:00 p.m.: 7 hours
      Pages reviewed by C=18×7=126 pages
  4. Editor D:

    • Time from 12:00 p.m. to 6:00 p.m.: 6 hours
      Pages reviewed by D=10×6=60 pages
  5. Editor E:

    • Time from 1:30 p.m. to 6:00 p.m.: 4.5 hours
      Pages reviewed by E=20×4.5=90 pages
Summing up the pages reviewed by 6:00 p.m.:
y=108+128+126+60+90=512 pages
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x=170 and y=512
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At a publishing company, five editors—A through E—review manuscripts at different but constant speeds, starting at different times and continuing until 6:00 p.m. on the same day:

  • Editor A: Started at 9:00 a.m., reviewing 12 pages per hour.
  • Editor B: Started at 10:00 a.m., reviewing 16 pages per hour.
  • Editor C: Started at 11:00 a.m., reviewing 18 pages per hour.
  • Editor D: Started at 12:00 p.m., reviewing 10 pages per hour.
  • Editor E: Started at 1:30 p.m., reviewing 20 pages per hour.

Select for x the total number of pages reviewed by 1:30 p.m., and for y the total number of pages reviewed by 6:00 p.m. Make only two selections, one in each column.
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Computing the total made by 1.30pm we get 170 (from multiplying the time by the rate per review).
For the total you just pick two extreme options for editor E and A whose review past 1:30 combined is 198. Adding that to the initial 170 we are already past 342 meaning the other choice can only be 512
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At a publishing company, five editors—A through E—review manuscripts at different but constant speeds, starting at different times and continuing until 6:00 p.m. on the same day:

  • Editor A: Started at 9:00 a.m., reviewing 12 pages per hour.
  • Editor B: Started at 10:00 a.m., reviewing 16 pages per hour.
  • Editor C: Started at 11:00 a.m., reviewing 18 pages per hour.
  • Editor D: Started at 12:00 p.m., reviewing 10 pages per hour.
  • Editor E: Started at 1:30 p.m., reviewing 20 pages per hour.

Select for x the total number of pages reviewed by 1:30 p.m., and for y the total number of pages reviewed by 6:00 p.m. Make only two selections, one in each column.
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UPTO 1:30
A=54
B=5
C=45
D=15
E=0
Total=170

1:30 TO 6
A=54
B=72
C=81
D=45
E=90
Total=342

Total upto 6=170+342=512

Answer 170 & 512
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Bunuel
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At a publishing company, five editors—A through E—review manuscripts at different but constant speeds, starting at different times and continuing until 6:00 p.m. on the same day:

  • Editor A: Started at 9:00 a.m., reviewing 12 pages per hour.
  • Editor B: Started at 10:00 a.m., reviewing 16 pages per hour.
  • Editor C: Started at 11:00 a.m., reviewing 18 pages per hour.
  • Editor D: Started at 12:00 p.m., reviewing 10 pages per hour.
  • Editor E: Started at 1:30 p.m., reviewing 20 pages per hour.

Select for x the total number of pages reviewed by 1:30 p.m., and for y the total number of pages reviewed by 6:00 p.m. Make only two selections, one in each column.

Number of pages typed between 9:00 and 1:00 pm

[*]Editor A: 48
[*]Editor B: 48
[*]Editor C: 36
[*]Editor D: 15
[*]Editor E: 0

Number of pages typed between 1:00 pm and 1:30 pm

[*]Editor A: 6
[*]Editor B: 8
[*]Editor C: 9
[*]Editor D: 5
[*]Editor E: 0
Total : 170

Number of pages typed between 1:30 pm and 2:00 pm

[*]Editor A: 6
[*]Editor B: 8
[*]Editor C: 9
[*]Editor D: 5
[*]Editor E: 10

Number of pages typed between 2:00 pm and 6:00 pm

[*]Editor A: 48
[*]Editor B: 64
Editor C: 72
[*]Editor D: 40
[*]Editor E: 80
Total: 512


x = 170
y = 512
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For x (total pages reviewed by 1:30 p.m.):

Editor A: 12 pages/hour for 4.5 hours = 54 pages
Editor B: 16 pages/hour for 3.5 hours = 56 pages
Editor C: 18 pages/hour for 2.5 hours = 45 pages
Editor D: 10 pages/hour for 1.5 hours = 15 pages
Editor E: 0 pages (started at 1:30 p.m.)

Total = 54 + 56 + 45 + 15 = 170 pages. So, x = 170.

For y (total pages reviewed by 6:00 p.m.):

In the first half of the day, 170 pages were reviewed by 4 out of 5 editors. The second half of the day, with all editors working, will result in significantly more than 170 pages.
So, the total work for the day (first half + second half) will consequently be much higher than 340, with the only fitting option being y = 512.

Final answer: x = 170, y = 512.
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To calculate the number of pages x reviewed by 1:30 pm we can calculate it as:

9/2*12+7/2*16+5/2*18+3/2*10=170

To calculate the number of pages x reviewed by 6:00 pm we can calculate it as:
9*12+8*16+7*18+6*10+9/2*20=512

Hence the values are
X:170
Y:512
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h is hours and p is pages
Reviewed by 1:30pm,
A: 4.5h*12p = 54p
B: 3.4h*16p = 56p
C: 2.5h*18p = 45p
D: 1.5h*10p = 15p
E: 0p
Total (x) = 170p

Reviewed by 6pm,
A: 9h*12p = 108p
B: 8h*16p = 128p
C: 7h*18p = 126p
D: 6h*10p = 60p
E: 4.5h*20p = 90p
Total (y) = 512p
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Bunuel
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for the 12 Days of Christmas Competition

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At a publishing company, five editors—A through E—review manuscripts at different but constant speeds, starting at different times and continuing until 6:00 p.m. on the same day:

  • Editor A: Started at 9:00 a.m., reviewing 12 pages per hour.
  • Editor B: Started at 10:00 a.m., reviewing 16 pages per hour.
  • Editor C: Started at 11:00 a.m., reviewing 18 pages per hour.
  • Editor D: Started at 12:00 p.m., reviewing 10 pages per hour.
  • Editor E: Started at 1:30 p.m., reviewing 20 pages per hour.

Select for x the total number of pages reviewed by 1:30 p.m., and for y the total number of pages reviewed by 6:00 p.m. Make only two selections, one in each column.
Calculate Total Pages Reviewed by 1:30 p.m.:
Editor A:
  • 9:00 a.m. to 1:30 p.m.=4.5 hours
  • Pages reviewed: 12×4.5=54
Editor B:
  • 10:00 a.m. to 1:30 p.m.=3.5 hours
  • Pages reviewed: 16×3.5=56
Editor C:
  • 11:00 a.m. to 1:30 p.m.=2.5 hours
  • Pages reviewed: 18×2.5=45
Editor D:
  • 12:00 p.m. to 1:30 p.m.=1.5 hours
  • Pages reviewed: 10×1.5=15
Editor E:
  • Starts at 1:30 p.m., so contributes 0 pages before 1:30 p.m.
Total by (1:30 p.m.):
54+56+45+15=170

Calculate Total Pages Reviewed by 6:00 p.m.:
Editor A:
  • 9:00 a.m. to 6:00 p.m.= 9 hours
  • Pages reviewed: 12×9=108
Editor B:
  • 10:00 a.m. to 6:00 p.m.=8 hours
  • Pages reviewed: 16×8=128
Editor C:
  • 11:00 a.m. to 6:00 p.m.=7 hours
  • Pages reviewed: 18×7=126
Editor D:
  • 12:00 p.m. to 6:00 p.m.=6 hours
  • Pages reviewed: 10×6=60
Editor E:
  • 1:30 p.m. to 6:00 p.m.=4.5 hours
  • Pages reviewed: 20×4.5=90
Total by (6:00 p.m.):
108+128+126+60+90=512
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Please find the solution attached
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x = 170 and y = 512

x = 12*4.5 + 16*3.5 + 18*2.5 + 10*1.5 = 170
y = 12*9 + 16*8 + 18*7 + 10*6 + 20*4.5 = 512
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Bunuel
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At a publishing company, five editors—A through E—review manuscripts at different but constant speeds, starting at different times and continuing until 6:00 p.m. on the same day:

  • Editor A: Started at 9:00 a.m., reviewing 12 pages per hour.
  • Editor B: Started at 10:00 a.m., reviewing 16 pages per hour.
  • Editor C: Started at 11:00 a.m., reviewing 18 pages per hour.
  • Editor D: Started at 12:00 p.m., reviewing 10 pages per hour.
  • Editor E: Started at 1:30 p.m., reviewing 20 pages per hour.

Select for x the total number of pages reviewed by 1:30 p.m., and for y the total number of pages reviewed by 6:00 p.m. Make only two selections, one in each column.
Let's calculate the total number of pages reviewed by each editor by 1:30 p.m. and 6:00 p.m. and find the correct values for x (pages reviewed by 1:30 p.m.) and y (pages reviewed by 6:00 p.m.).
Total Pages Reviewed by 1:30 p.m. (x):
At 1:30 p.m., the editors who have been working are:
  • Editor A: Started at 9:00 a.m., so they have worked for 4.5 hours (from 9:00 a.m. to 1:30 p.m.).
    Pages reviewed = 4.5 hours * 12 pages/hour = 54 pages.
  • Editor B: Started at 10:00 a.m., so they have worked for 3.5 hours (from 10:00 a.m. to 1:30 p.m.).
    Pages reviewed = 3.5 hours * 16 pages/hour = 56 pages.
  • Editor C: Started at 11:00 a.m., so they have worked for 2.5 hours (from 11:00 a.m. to 1:30 p.m.).
    Pages reviewed = 2.5 hours * 18 pages/hour = 45 pages.
  • Editor D: Started at 12:00 p.m., so they have worked for 1.5 hours (from 12:00 p.m. to 1:30 p.m.).
    Pages reviewed = 1.5 hours * 10 pages/hour = 15 pages.
  • Editor E: Started at 1:30 p.m., so they have not reviewed any pages by 1:30 p.m.
Total pages reviewed by 1:30 p.m. (x) = 54 + 56 + 45 + 15 = 170 pages.
Total Pages Reviewed by 6:00 p.m. (y):
At 6:00 p.m., the editors who have been working are:
  • Editor A: Started at 9:00 a.m., so they have worked for 9 hours (from 9:00 a.m. to 6:00 p.m.).
    Pages reviewed = 9 hours * 12 pages/hour = 108 pages.
  • Editor B: Started at 10:00 a.m., so they have worked for 8 hours (from 10:00 a.m. to 6:00 p.m.).
    Pages reviewed = 8 hours * 16 pages/hour = 128 pages.
  • Editor C: Started at 11:00 a.m., so they have worked for 7 hours (from 11:00 a.m. to 6:00 p.m.).
    Pages reviewed = 7 hours * 18 pages/hour = 126 pages.
  • Editor D: Started at 12:00 p.m., so they have worked for 6 hours (from 12:00 p.m. to 6:00 p.m.).
    Pages reviewed = 6 hours * 10 pages/hour = 60 pages.
  • Editor E: Started at 1:30 p.m., so they have worked for 4.5 hours (from 1:30 p.m. to 6:00 p.m.).
    Pages reviewed = 4.5 hours * 20 pages/hour = 90 pages.
Total pages reviewed by 6:00 p.m. (y) = 108 + 128 + 126 + 60 + 90 = 512 pages.
Conclusion:
  • x = 170 (total pages reviewed by 1:30 p.m.)
  • y = 512 (total pages reviewed by 6:00 p.m.)
So, the correct answer is:
  • x = 170
  • y = 512
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Rate of A=12/hour
Rate of B=16/h
Rate of C=18/h
Rate of D=10/h
Rate of E=20/h
from 9 AM to 1:30 PM total time {4.5 hours} work done by A
from 10 AM to 1:30 PM total time {3.5 hours} work done by B
from 11 AM to 1:30 PM total time {2.5 hours} work done by C
from 12 AM to 1:30 PM total time {1.5 hours} work done by D

so work done till 1:30 PM:
12*4.5+16*3.5+18*2.5+10*1.5={170} {yes present in the option}

now in order to calculate the work done by all till 6 PM,
we can calculate the overall rate of ABCDE from 1:30 PM which is {12+16+18+10+20=76}
so 76*4.5=342
and previous work is 170
so 170+342=512 {present in the option}
Bunuel
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This question was provided by GMAT Club
for the 12 Days of Christmas Competition

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At a publishing company, five editors—A through E—review manuscripts at different but constant speeds, starting at different times and continuing until 6:00 p.m. on the same day:

  • Editor A: Started at 9:00 a.m., reviewing 12 pages per hour.
  • Editor B: Started at 10:00 a.m., reviewing 16 pages per hour.
  • Editor C: Started at 11:00 a.m., reviewing 18 pages per hour.
  • Editor D: Started at 12:00 p.m., reviewing 10 pages per hour.
  • Editor E: Started at 1:30 p.m., reviewing 20 pages per hour.

Select for x the total number of pages reviewed by 1:30 p.m., and for y the total number of pages reviewed by 6:00 p.m. Make only two selections, one in each column.
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Explanation

  1. By 1:30 p.m.:
    • A works from 9:00 to 1:30 → 4.5 hours at 12 pph → 4.5 × 12 = 54 pages
    • B works from 10:00 to 1:30 → 3.5 hours at 16 pph → 3.5 × 16 = 56 pages
    • C works from 11:00 to 1:30 → 2.5 hours at 18 pph → 2.5 × 18 = 45 pages
    • D works from 12:00 to 1:30 → 1.5 hours at 10 pph → 1.5 × 10 = 15 pages
    • E starts at 1:30 → 0 pages by 1:30
    • Total by 1:30 p.m. = 54 + 56 + 45 + 15 + 0 = 170.
  2. By 6:00 p.m.:
    • A works 9:00 to 6:00 → 9 hours at 12 pph → 9 × 12 = 108 pages
    • B works 10:00 to 6:00 → 8 hours at 16 pph → 8 × 16 = 128 pages
    • C works 11:00 to 6:00 → 7 hours at 18 pph → 7 × 18 = 126 pages
    • D works 12:00 to 6:00 → 6 hours at 10 pph → 6 × 10 = 60 pages
    • E works 1:30 to 6:00 → 4.5 hours at 20 pph → 4.5 × 20 = 90 pages
    • Total by 6:00 p.m. = 108 + 128 + 126 + 60 + 90 = 512.

Answer is
X = 170
Y = 512
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The info gave us the following table


pages per hourstart time# hours to 1:30 pm# pages reviewed at 1:30 pm# pages reviewed at 6 pm
A129:00 AM4.554108
B1610:00 AM3.556128
C1811:00 AM2.545126
D1012:00 PM1.51560
E201:30 PM0090
Total 170512

So x = 170, y = 512
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Until 1:30 A completed 4 1/2 hrs ,B -3 1/2 hrs C- 2 1/2 hrs , D completes 1 1/2 hrs . mutiplying their efficiencies with rates we get 54,56,45,15 pages respectively. So together 170

Until 6:00 pm we get 9/2(12+16+18+20+10) = 342
Therefore total is 342+170 =512

x=170
y=512
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Hi everyone :)
Last day!


We are dealing here with a calculation and logic question.
Straight forward, we will build a table of the data:

StartingRate1:30pm6:00pm
A9:00125454
B10:00165672
C11:00184581
D12:00101545
E13:3020-90
Total170512

Our Answers are x=170 and y=512
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