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555-605 (Medium)|   Math Related|         
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12 Days of Christmas GMAT Competition - Day 9: A plant must distribute 27 Dec 2024, 02:38
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Hello,
Line A: Maximum 42 hours
Line B: Maximum 20 hours
Line C: Maximum 12 hours

condition is that it should be more than half maximum
Line A: 0.5*42=21
Line B: 0.5*20=10
Line C: 0.5*12=6

we have to distribute 45 hours
currently as per condition we have total 37 (21+10+6) hours
we have currently need to adjust 8 hours
B can 16 or 17
if B is 16 then we can have 22 hours for A and 7 hours for C
if B is 17 then either we can have A as 22 or C as 7 both is not possible

Hence B 16 and C is 7 and A will be 22 all satisfy the condition

I hope it helps and if you like it please give kudos
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12 Days of Christmas GMAT Competition - Day 9: A plant must distribute 27 Dec 2024, 03:34
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Hi All,

Tyring to find value for C from the options,

C should be at minimun 7 as given that " Each line must receive more than half its maximum"

if C=7, then A+B= 38,

A should be minimum 22,therefore max value for B =38-22= 16

we do have an option for 16 hence our answer.


We can also try for when C=8, then A+B=37

A should be minimun 22, thereofre max value for B=37-22= 15

15 is not the option therefore rejected.


Therefore our answer B=16 and C=7
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12 Days of Christmas GMAT Competition - Day 9: A plant must distribute 27 Dec 2024, 03:46
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From the provided info:
21 < a <= 42
10 < b <= 20 . So b can only be 16 or 17 (1)
6 < c <= 12 . So c can only be 7 or 8 (2)

a + b + c = 45. Since min a = 22, max b + c = 45-22 = 23. From (1) & (2), we only have 1 option for this case: b = 16 and c = 7.
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12 Days of Christmas GMAT Competition - Day 9: A plant must distribute 27 Dec 2024, 04:02
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A plant must distribute 45 hours weekly among three production lines: A, B, and C.

  • Line A: Maximum 42 hours
  • Line B: Maximum 20 hours
  • Line C: Maximum 12 hours

Each line must receive more than half its maximum, all 45 hours must be used, and the number of hours allocated to each line must be an integer.

Select for Line B the hours that could have been allocated to Line B, and select for Line C the hours that could have been allocated to Line C that would be jointly consistent with the given information. Make only two selections, one in each column.

Each line must receive more than half its maximum and must be an integer.

So, A must receive, 42/2+1=22

Now, we are left with, 45-22=23 hours.
C must receive, 12/2+1=7, then B can receive 23-7=16.

Answer: B=16, C=7.
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12 Days of Christmas GMAT Competition - Day 9: A plant must distribute 27 Dec 2024, 04:41
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A plant must distribute 45 hours weekly among three production lines: A, B, and C.

Line A: Maximum 42 hours
Line B: Maximum 20 hours
Line C: Maximum 12 hours

Each line must receive more than half its maximum, all 45 hours must be used, and the number of hours allocated to each line must be an integer.

Select for Line B the hours that could have been allocated to Line B, and select for Line C the hours that could have been allocated to Line C that would be jointly consistent with the given information. Make only two selections, one in each column.
Line B Line C
6
7
8
16
17


Greater than 1/2 of 42 is >21
Greater than 1/2 of 20 is >10
Greater than 1/2 of 12 is >6

Thus total is 22+11+7=40 and we need 5 more hours so using the answer choices 22, 16, 7 is a possible combination

Ans 16,7
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12 Days of Christmas GMAT Competition - Day 9: A plant must distribute 27 Dec 2024, 04:42
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Line A must have at least 22 hours, Line B must have at least 11 hours and Line C must have at least 7 hours. Total: 40 hours.

As 45 hours must be used, we have 5 additional hours that must be distrubuted among the three lines.

With trial and error, the correct answer is Line B=16 and Line C=7.
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12 Days of Christmas GMAT Competition - Day 9: A plant must distribute 27 Dec 2024, 05:04
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The conditions means that Line must have at least 22, Line B at least 11 and Line C at least 7

Given the choices B can either be 16 or 17 while C can only be 7 or 8
Testing each case only 16+7 = 23 leaves a figure greater than 21 (45-23=22) Hence B is 16 and C is 7
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A plant must distribute 45 hours weekly among three production lines: A, B, and C.

  • Line A: Maximum 42 hours
  • Line B: Maximum 20 hours
  • Line C: Maximum 12 hours

Each line must receive more than half its maximum, all 45 hours must be used, and the number of hours allocated to each line must be an integer.

Select for Line B the hours that could have been allocated to Line B, and select for Line C the hours that could have been allocated to Line C that would be jointly consistent with the given information. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 9: A plant must distribute 27 Dec 2024, 05:48
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we need A+B+C=45,
such that A>21,B>10 and C> 6
let's use the options so put different values,

A B C = A+B+C
23 17 7 = 47
23 16 7 = 46
22 17 7 =46
22 16 7= 45

so B=16 and C= 7 should be the ans.
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A plant must distribute 45 hours weekly among three production lines: A, B, and C.

  • Line A: Maximum 42 hours
  • Line B: Maximum 20 hours
  • Line C: Maximum 12 hours

Each line must receive more than half its maximum, all 45 hours must be used, and the number of hours allocated to each line must be an integer.

Select for Line B the hours that could have been allocated to Line B, and select for Line C the hours that could have been allocated to Line C that would be jointly consistent with the given information. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 9: A plant must distribute 27 Dec 2024, 05:52
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A plant must distribute 45 hours weekly among three production lines: A, B, and C.

  • Line A: Maximum 42 hours
  • Line B: Maximum 20 hours
  • Line C: Maximum 12 hours

Each line must receive more than half its maximum, all 45 hours must be used, and the number of hours allocated to each line must be an integer.

Select for Line B the hours that could have been allocated to Line B, and select for Line C the hours that could have been allocated to Line C that would be jointly consistent with the given information. Make only two selections, one in each column.
Line BLine C
6
7
8
16
17


Given that, Each line must receive more than half its maximum, all 45 hours must be used, and the number of hours allocated to each line must be an integer.

So, for Line A = 21 < a <= 42................(1)
for Line B = 10 < a <= 20.................(2)
for Line C = 6 < a <= 12...................(3)

Putting Line C = 6 ( NOT possible...as per constraint (3) )
Putting Line C = 7, Line B = 16, Line A = 22 (all constraints satisfied)
Putting Line C = 7, Line B = 17, Line A = 21 ( NOT possible...as per constraint (1) )
Putting Line C = 8, Line B = 16, Line A = 21 ( NOT possible...as per constraint (1) )

thus, only Line B = 16; Line C = 7 satisfies all the constraints



Line B = 16
Line C = 7 is the CORRECT answer
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12 Days of Christmas GMAT Competition - Day 9: A plant must distribute 27 Dec 2024, 06:27
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Solution Explanation:
We need to allocate 45 hours among three production lines (A, B, and C) with the following constraints:
  1. Line A:
    • Minimum: More than half of 42 → >21 hours
    • Maximum: 42 hours
  2. Line B:
    • Minimum: More than half of 20 → >10 hours
    • Maximum: 20 hours
  3. Line C:
    • Minimum: More than half of 12 → >6 hours
    • Maximum: 12 hours
All allocations must be integers, and the total must add up to 45 hours.
Step-by-Step Allocation:
  1. Possible Hours for Each Line:
    • Line A: 22 to 42 hours
    • Line B: 11 to 20 hours
    • Line C: 7 to 12 hours
  2. Given Options:
    • Line B: 6, 7, 8, 16, 17
    • Line C: 6, 7, 8, 16, 17
  3. Determine Valid Selections:
    • For Line B:
      • Valid Options (must be >10): 16, 17
    • For Line C:
      • Valid Options (must be >6 and ≤12): 7, 8
  4. Check Combinations:
    • Option 1:
      • Line B = 16
      • Line C = 7
      • Line A = 45 - 16 - 7 = 22 (Valid, since >21)
    • Option 2:
      • Line B = 16
      • Line C = 8
      • Line A = 45 - 16 - 8 = 21 (Invalid, since ≤21)
    • Option 3:
      • Line B = 17
      • Line C = 7
      • Line A = 45 - 17 - 7 = 21 (Invalid, since ≤21)
    • Option 4:
      • Line B = 17
      • Line C = 8
      • Line A = 45 - 17 - 8 = 20 (Invalid, since <21)
  5. Valid Combination:
    • Line B = 16 hours
    • Line C = 7 hours
    • Line A = 22 hours
Final Answer:
Line BLine C
167
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12 Days of Christmas GMAT Competition - Day 9: A plant must distribute 27 Dec 2024, 06:58
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From the task, we get:
  • \(21<a<=42\)
  • \(10<b<=20\)
  • \(6<c<=12\)

Then, the minimal value for A is 22; for B it's 11 and for C it's 7.

From the suggested answers, B can be only 16 and 17.
  • Checking 16, we get \(a+c=45-16=29\), and with the minimal value for c=7 we also get a=22; this is consistent.
  • Checking 17, we get \(a+c= 45-17=28\), and with the minimal value for c=7 we also get a=21; this is inconsistent as A must be above 21.

The answer is b=16 and c=7.
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12 Days of Christmas GMAT Competition - Day 9: A plant must distribute 27 Dec 2024, 08:02
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Distribute 45 hrs among A, B, C

More than half max for each line

A > 21
B > 10
C > 6

Question : Possible B ? C?

In given options possible B = 16, 17

In given options possible C = 7, 8, 16, 17

Assume A has lowest possible = 22

Remaining = 23hrs

B has atleast 11 and C has atleast 7, remaining 5 hrs can be distributed between B and C

Maximum B can have = 11 + 5 = 16

(B, C) = (16, 7)



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A plant must distribute 45 hours weekly among three production lines: A, B, and C.

  • Line A: Maximum 42 hours
  • Line B: Maximum 20 hours
  • Line C: Maximum 12 hours

Each line must receive more than half its maximum, all 45 hours must be used, and the number of hours allocated to each line must be an integer.

Select for Line B the hours that could have been allocated to Line B, and select for Line C the hours that could have been allocated to Line C that would be jointly consistent with the given information. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 9: A plant must distribute 27 Dec 2024, 08:07
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A>21
B>10
C>6

Therefore keeping A min = 22 based on options keeping C min at 7 and checking if B works. B 17 works when C @ 7 imo this is the answer
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A plant must distribute 45 hours weekly among three production lines: A, B, and C.

  • Line A: Maximum 42 hours
  • Line B: Maximum 20 hours
  • Line C: Maximum 12 hours

Each line must receive more than half its maximum, all 45 hours must be used, and the number of hours allocated to each line must be an integer.

Select for Line B the hours that could have been allocated to Line B, and select for Line C the hours that could have been allocated to Line C that would be jointly consistent with the given information. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 9: A plant must distribute 27 Dec 2024, 08:16
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Total Hours A+B+C = 45
Max(A) = 42 Min(A) = 42/2 = 21
Max(B) = 20 Min(B) = 20/2 = 10
Max(C) = 12 Min(C) = 12/2 = 6

Now, we know that min should be more than half of maximum,
So,
22<= A <=42
11<= B <=20
7<= C <=12

These are the possible valid ranges
Now,
A = 45 - B - C and should satisfy above ranges
Lets substitute value 1 by 1
B = 16, C=7
A = 45 -16-7 = 22 (This is valid)

Since we see this to be valid, we can assume the rest as invalid
So,
B = 16
C = 7
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12 Days of Christmas GMAT Competition - Day 9: A plant must distribute 27 Dec 2024, 08:23
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line a - must be b/w 22 and 42
line b - must be b/w 11 and 20
line c - must be between 11 and 12

hours(a) + hours(b) + hours(c) = 45

testing possible values of a,b,and c
(I)
b=17,c=8
a = 20
Not valid

(II)
b=16, c=8
a = 21
valid

Answer -
line b = 16
line c = 8
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A plant must distribute 45 hours weekly among three production lines: A, B, and C.

  • Line A: Maximum 42 hours
  • Line B: Maximum 20 hours
  • Line C: Maximum 12 hours

Each line must receive more than half its maximum, all 45 hours must be used, and the number of hours allocated to each line must be an integer.

Select for Line B the hours that could have been allocated to Line B, and select for Line C the hours that could have been allocated to Line C that would be jointly consistent with the given information. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 9: A plant must distribute 27 Dec 2024, 08:23
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IMO

Line B: 16 hours
Line C: 7 hours


Lets analyze the
Constraints:
  • Line A: Maximum 42 hours, must receive more than half its maximum (more than 21 hours).
  • Line B: Maximum 20 hours, must receive more than half its maximum (more than 10 hours).
  • Line C: Maximum 12 hours, must receive more than half its maximum (more than 6 hours).
  • Total hours to be distributed: 45 hours.


Now for B the only possibility from the option is

either 16 or 17

if we take 16 then

B= 16
A>= 22( can't be 21)

then c is 7 which is the answer because of the constraint c can be less than 7
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12 Days of Christmas GMAT Competition - Day 9: A plant must distribute 27 Dec 2024, 08:40
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Line A: Maximum 42 hours, Minimum: 42 / 2 = 21 hours
line B: Maximum 20 hours, Minimum: 20 / 2 = 10 hours
line C: Maximum 12 hours, Minimum: 12 / 2 = 6 hours

Line B
Possible values: 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
Line C
Possible values: 7, 8, 9, 10, 11, 12

Trial and error with the possibilities
we get b = 16 and c = 8



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A plant must distribute 45 hours weekly among three production lines: A, B, and C.

  • Line A: Maximum 42 hours
  • Line B: Maximum 20 hours
  • Line C: Maximum 12 hours

Each line must receive more than half its maximum, all 45 hours must be used, and the number of hours allocated to each line must be an integer.

Select for Line B the hours that could have been allocated to Line B, and select for Line C the hours that could have been allocated to Line C that would be jointly consistent with the given information. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 9: A plant must distribute 27 Dec 2024, 08:56
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Eliminate answer "6" as:
LINE A > 21
LINE B > 10
LINE C > 6

A+B+C = 45
A<= 42; B<= 20; C<= 12

Trying values starting with the most limited option, C then prove with the rest of variables.

C = 7 then A+B = 38 and given A must be at least 22, 38-22= 16 which is an available option for B.

C=7
B=16
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12 Days of Christmas GMAT Competition - Day 9: A plant must distribute 27 Dec 2024, 09:01
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Given lower limits of half their maximum and their maximum values I'd try plugging in the answers given restrictions.

Do not try 6 as an option, since it does not comply with the restriction on C so

A+B+C = 45

C = 7 then A+B = 45 - 7= 38

A must be more than 21, let's try with 22 so B = 38-22= 16

B =16 and C = 7
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12 Days of Christmas GMAT Competition - Day 9: A plant must distribute 19 Mar 2026, 20:01
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Great question — let me walk through this step by step.

First, let's figure out the valid range for each line. Each line must receive MORE than half its maximum (and the hours must be integers):

- Line A: More than half of 42 = more than 21, so at least 22. Range: 22 to 42.
- Line B: More than half of 20 = more than 10, so at least 11. Range: 11 to 20.
- Line C: More than half of 12 = more than 6, so at least 7. Range: 7 to 12.

Also, A + B + C = 45.

Now let's check which answer choices even fall in the valid range for each line:

- Line B (11–20): Only 16 and 17 qualify from the choices.
- Line C (7–12): Only 7 and 8 qualify from the choices.

So we have four possible combinations. Let's test each by computing Line A = 45 - B - C, and checking if A falls in its range of 22 to 42:

1. B = 16, C = 7 → A = 45 - 16 - 7 = 22. Is 22 in [22, 42]? YES.
2. B = 16, C = 8 → A = 45 - 16 - 8 = 21. Is 21 in [22, 42]? NO — too low.
3. B = 17, C = 7 → A = 45 - 17 - 7 = 21. Is 21 in [22, 42]? NO — too low.
4. B = 17, C = 8 → A = 45 - 17 - 8 = 20. Is 20 in [22, 42]? NO — too low.

Only combination 1 works! Line B = 16 (Row 4) and Line C = 7 (Row 2).

Key Insight: The key trap here is that three of the four combinations fail because they push Line A below its minimum of 22. The word 'jointly' in the question stem is the hint — you must verify that both selections work together, not just individually.

Answer: 4A, 2B
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