12 Days of Christmas GMAT Competition - Day 10: At a publishing

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.

x	y
		76
		124
		170
		342
		512

(A) For calculating x, i.e. the total number of pages reviewed by 1:30 p.m

A works for 9/2 hrs
B works for 7/2 hrs
A works for 5/2 hrs
A works for 3/2 hrs
A works for 0 hrs
So, Total pages reviewed = (12 * 9/2) + (16 * 7/2) + (18 * 5/2) + (10 * 3/2) = 170 pages


(A) For calculating y, i.e. the total number of pages reviewed by 6:00 p.m


In excess of 170 pages, all the machines A, B, C, D and E work for additional 9/2 hrs (i.e. 1: 30 pm to 6 :00 pm)

So, Total pages reviewed = 170 + (12 + 16 + 18 + 10 + 20) * 9/2
= 170 + 342 pages
So, Total pages reviewed = 512 pages



x= 170,
y = 512; is the CORRECT answer

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.

Solution:
Till 1:30.
1:30-9=4.5, 1:30-10=3.5, 1:30-11=2.5, 1:30-12=1.5, 1:30-1:30=0 (12*4.5+16*3.5+18*2.5+10*1.5+0=170 -> first column.
From 1:30 to 6:
6-1:30=4.5. 4.5*(12+16+18+10+20)=342. 342+170=512=> Second column

Editor A-
Rate of reviewing= 12 pages/ hr.
Time taken by him by 1:30 pm = 4.5 hr (since started at 9 am)

Total no. of pages reviewed by 1:30pm= 12x 4.5= 54 pages

Editor B-
Rate of reviewing= 16 pages/ hr.
Time taken by him by 1:30 pm = 3.5 hr (since started at 10am)

Total no. of pages reviewed by 1:30pm= 16x3.5=56

Editor C-
Rate of reviewing= 18 pages/ hr.
Time taken by him by 1:30 pm = 2.5 hr (since started at 11 am)

Total no. of pages reviewed by 1:30pm= 18x2.5= 45

Editor D-
Rate of reviewing= 10 pages/ hr.
Time taken by him by 1:30 pm = 1.5 hr (since started at 12 pm)

Total no. of pages reviewed by 1:30pm=
10x1.5= 15

Editor E-
Rate of reviewing= 20 pages/ hr.
Time taken by him by 1:30 pm = 0 hr (since started at 1:30 pm)

Total no. of pages reviewed by 1:30pm= 0x20= 0 pages

therefor, x= 54+56+45+15= 170.


Now, for 6:00pm

Editor A-
Rate of reviewing= 12 pages/ hr.
Time taken by him by 6 pm = 9 hr

Total no. of pages reviewed by 6pm= 12x 9= 108 pages

Editor B-
Rate of reviewing= 16 pages/ hr.
Time taken by him by 6 pm = 8 hr

Total no. of pages reviewed by 6pm= 16x8=128

Editor C-
Rate of reviewing= 18 pages/ hr.
Time taken by him by 6 pm = 7 hr

Total no. of pages reviewed by 6pm= 18x7= 126

Editor D-
Rate of reviewing= 10 pages/ hr.
Time taken by him by 6 pm = 6hr

Total no. of pages reviewed by 6pm=
10x6= 60

Editor E-
Rate of reviewing= 20 pages/ hr.
Time taken by him by 6 pm = 4.5hr

Total no. of pages reviewed by 6pm= 4.5x20= 90 pages

therefor, y= 108+128+126+60+90= 512 pages.

Ans- x=170, y=512

Total pages by 1:30pm

A worked from 9 am to 1:30pm which is 4h and 30min = 4*12 + 6= 54 pages
B worked 3 h and half = 48 + 8 = 56 pages
C worked 2h and half = 2*18 + 9 = 45 pages
D worked 1 hours and half = 10 + 5 = 15 pages
E did not work until 1:30 so = 0
Sum = 170 select for x

Y total pages by 6pm

A= 9*12 =108
B = 8*16=128
C = 7*18=126
D= 6*10=60
E = 4*20 + 10 = 90

Sum = 512 select for y

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 up to 1:30,

A: 4x12+6=54
B: 3x16+8=56
C: 2x18+9=45
D: 1x10+5= 15
In total= 170

Now, calculate up to 6,

A: 9x12=108
B: 8x16=128
C: 7x18=126
D: 6x10= 60
E: 4x20+10=90
In total= 512

Answer: x=170, y=512

Total hours for the first question 'x'

A = 4*12 + 6 = 48 + 6 = 54
B = 3*16 + 8 = 56
C = 2*18 + 9 = 45
D = 10 + 5 = 15
E = 0

Total hours = 15 + 45 + 56 + 54 = 170

Total hours for 'y'

A = 9*12 = 108
B = 8*16 = 128
C = 7*18 = 126
D= 6*10 = 60
E = 4*20 + 10 = 90

Total hours for 'y' = 90 + 60 + 126 + 128 + 108 = 512

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.

Solution:
Firstly, calculate y.

The number of pages read by each editors are,

Editor A: 9 hours review time - 12*9 = 108;
Editor B: 8 hours review time - 16*8 = 128;
Editor C: 7 hours review time - 18*7 = 126;
Editor D: 6 hours review time - 10*6 = 60;
Editor E: 4.5 hours review time - (20*4) + 10 = 90;

Total pages read by the 5 editors = 512; - Option E

To calculate x, 4 editors have reviewed pages less than 1:30 pm and every 30 mins count half of the pages reviewed.
Editor A: 12*4 + 6 = 54;
Editor B: 16*3 + 8 = 56;
Editor C: 18*2 + 9 = 45;
Editor D: 10 + 5 = 15;

Total pages read by the 4 editors till 1:30 pm = 170; - Option C

i) for the first column -
A - 4.5 * 12 = 54
B - 3.5 * 16 = 56
C - 2.5 * 18 = 45
D - 1.5 * 10 = 15

Total = 170

ii) For the second column,
A - 9 * 12 = 108
B - 8 * 16 = 128
C - 7 * 18 = 126
D - 6 * 10 = 60
E - 4.5 * 20 = 90

Total = 512

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

total pages by 1:30pm - x=54+56+45+15=170

For y pages
Editor A: 9 hours × 12 pages/hour = 108 pages
Editor B: 8 hours × 16 pages/hour = 128 pages
Editor C: 7 hours × 18 pages/hour = 126 pages
Editor D: 6 hours × 10 pages/hour = 60 pages
Editor E: 4.5 hours × 20 pages/hour = 90 pages

Total pages by 6:00 p.m. - y=108+128+126+60+90=512

Answer - x = 170
y = 512

Pages reviewed by 1:30 p.m. (x):

• Editor A: Worked for 4.5 hours (9:00 a.m. to 1:30 p.m.) at 12 pages/hour.
  4.5×12=54 pages.
• Editor B: Worked for 3.5 hours (10:00 a.m. to 1:30 p.m.) at 16 pages/hour.
  3.5×16=56pages.
• Editor C: Worked for 2.5 hours (11:00 a.m. to 1:30 p.m.) at 18 pages/hour.
  2.5×18=45 pages.
• Editor D: Worked for 1.5 hours (12:00 p.m. to 1:30 p.m.) at 10 pages/hour.
  1.5×10=15 pages.
• Editor E: Started at 1:30 p.m., so no pages reviewed by 1:30 p.m.
  0 pages.

Total pages by 1:30 p.m.:
x=54+56+45+15+0=170


Pages reviewed by 6:00 p.m. (y):

• Editor A: Worked for 9 hours (9:00 a.m. to 6:00 p.m.) at 12 pages/hour.
  9×12=108 pages.
• Editor B: Worked for 8 hours (10:00 a.m. to 6:00 p.m.) at 16 pages/hour.
  8×16=128pages.
• Editor C: Worked for 7 hours (11:00 a.m. to 6:00 p.m.) at 18 pages/hour.
  7×18=126pages.
• Editor D: Worked for 6 hours (12:00 p.m. to 6:00 p.m.) at 10 pages/hour.
  6×10=60 pages.
• Editor E: Worked for 4.5 hours (1:30 p.m. to 6:00 p.m.) at 20 pages/hour.
  4.5×20=90 pages.

Total pages by 6:00 p.m.:
y=108+128+126+60+90=512

I do not know the quick solution for this, just calculate by hand, and the final result is 170 and 542

et's calculate the total number of pages reviewed by 1:30 p.m. and by 6:00 p.m.

Total Pages Reviewed by 1:30 p.m.
Editor A:

Started at 9:00 a.m.

Worked for 4.5 hours (from 9:00 a.m. to 1:30 p.m.)

Pages reviewed:
12
×
4.5
=
54

Editor B:

Started at 10:00 a.m.

Worked for 3.5 hours (from 10:00 a.m. to 1:30 p.m.)

Pages reviewed:
16
×
3.5
=
56

Editor C:

Started at 11:00 a.m.

Worked for 2.5 hours (from 11:00 a.m. to 1:30 p.m.)

Pages reviewed:
18
×
2.5
=
45

Editor D:

Started at 12:00 p.m.

Worked for 1.5 hours (from 12:00 p.m. to 1:30 p.m.)

Pages reviewed:
10
×
1.5
=
15

Editor E:

Started at 1:30 p.m.

Worked for 0 hours (since 1:30 p.m. is the starting time)

Pages reviewed:
20
×
0
=
0

Total pages reviewed by 1:30 p.m.:

54
+
56
+
45
+
15
+
0
=
170
Total Pages Reviewed by 6:00 p.m.
Editor A:

Worked for 9 hours (from 9:00 a.m. to 6:00 p.m.)

Pages reviewed:
12
×
9
=
108

Editor B:

Worked for 8 hours (from 10:00 a.m. to 6:00 p.m.)

Pages reviewed:
16
×
8
=
128

Editor C:

Worked for 7 hours (from 11:00 a.m. to 6:00 p.m.)

Pages reviewed:
18
×
7
=
126

Editor D:

Worked for 6 hours (from 12:00 p.m. to 6:00 p.m.)

Pages reviewed:
10
×
6
=
60

Editor E:

Worked for 4.5 hours (from 1:30 p.m. to 6:00 p.m.)

Pages reviewed:
20
×
4.5
=
90

Total pages reviewed by 6:00 p.m.:

108
+
128
+
126
+
60
+
90
=
512
So, the correct selections are:

x: 170

y: 512

Up to 1:30 pm
Editor A: 12*4.5 = 54
Editor B: 16*3.5 = 56
Editor C: 18*2.5 = 45
Editor D: 10*1.5 = 15
Editor E: 0

Total = 54+56+45+15 = 170

Up to 6:00 pm - Additional
Editor A: 12*4.5 = 54
Editor B: 16*4.5 = 72
Editor C: 18*4.5 = 81
Editor D: 10*4.5 = 45
Editor E: 20*4.5 = 90

Total Additional = 54+72+81+45+90 = 342
Total = 170+342 = 512

Therefore number of page by 1:30 pm is 170 and that of page by 6:00 pm is 512