I28-23

Question

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.

Bunuel · Answer

Official Solution:

Since each line must receive more than half its maximum:
 
• A got at least 42/2 + 1 = 22 hours, leaving for B and C at most 45 - 22 = 23 hours.
 
• B must receive at least 20/2 + 1 = 11 hours.
 
• C must receive at least 12/2 + 1 = 7 hours.
 
Thus:
 
11 ≤ B ≤ 20
 
7 ≤ C ≤ 12
 
From the total allocation:
 
18 ≤ B + C ≤ 23
 
From the options, only B = 16 and C = 7 satisfy these conditions.

Correct answer:

Line B  "16"

Line C  "7"

Shivang29 · Answer

I like the solution - it’s helpful.

MegB07 · Answer

Hi, Here its given that

11 ≤ B ≤ 20 
 7 ≤ C ≤ 12

equal to = 18 ≤ B + C ≤ 23 - but 20 + 12 = 32. If are given limit is 23, then how and why are we adding the two.

Bunuel · Answer

Because A must get at least 22 hours, at most 45 - 22 = 23 hours remain for B and C together. So even though 20 + 12 = 32, total hours limit B + C to 23.
That’s why we use 18 ≤ B + C ≤ 23.

I28-23

Prep Toolkit

Top 5 GMAT Debrief Videos

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards