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14 Apr 2026, 06:10
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
60% (03:34) correct
40%
(03:04)
wrong
based on 42
sessions
History
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Time
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Not Attempted Yet
An assembly plant operates a morning shift and an afternoon shift. On Monday, a total of \(T\) workers were late. On Tuesday, 36 workers were late: twice as many workers were late on the morning shift as on Monday morning, and \(\frac{1}{3}\) as many workers were late on the afternoon shift as on Monday afternoon. On Wednesday, 54 workers were late: three times as many workers late on the morning shift as on Monday morning, and 9 fewer workers late on the afternoon shift than on Monday afternoon. In terms of \(T\), how many workers were late on the morning shift on Monday?
(A) \(\frac{3}{11}T\)
(B) \(\frac{5}{11}T\)
(C) \(\frac{6}{11}T\)
(D) \(\frac{5}{6}T\)
(E) \(\frac{8}{11}T\)
(A) \(\frac{3}{11}T\)
(B) \(\frac{5}{11}T\)
(C) \(\frac{6}{11}T\)
(D) \(\frac{5}{6}T\)
(E) \(\frac{8}{11}T\)
14 Apr 2026, 06:22
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The key is to set up two variables and write two equations — this is a classic simultaneous equations Problem Solving question, and the trap is getting tangled in the words before you even set up anything.
Let m = workers late on morning shift Monday, a = workers late on afternoon shift Monday. So T = m + a.
1. Tuesday condition: twice as many on morning, 1/3 as many on afternoon, total = 36.
That gives us: 2m + a/3 = 36. Multiply everything by 3: 6m + a = 108.
2. Wednesday condition: three times as many on morning, 9 fewer on afternoon, total = 54.
That gives us: 3m + (a - 9) = 54, which simplifies to: 3m + a = 63.
Now subtract equation 2 from equation 1:
(6m + a) - (3m + a) = 108 - 63
3m = 45
m = 15
Plug back into 3m + a = 63: 45 + a = 63, so a = 18.
T = 15 + 18 = 33.
Morning workers on Monday as a fraction of T: 15/33 = 5/11. So m = 5T/11.
Answer: B.
The trap most people fall into is setting up the Wednesday equation wrong — the problem says "9 fewer workers late on the afternoon shift than on Monday afternoon," so it's (a - 9), not (a + 9). Flip that sign and you'll get a totally different answer that looks plausible. Worth double-checking that condition before moving on.
Let m = workers late on morning shift Monday, a = workers late on afternoon shift Monday. So T = m + a.
1. Tuesday condition: twice as many on morning, 1/3 as many on afternoon, total = 36.
That gives us: 2m + a/3 = 36. Multiply everything by 3: 6m + a = 108.
2. Wednesday condition: three times as many on morning, 9 fewer on afternoon, total = 54.
That gives us: 3m + (a - 9) = 54, which simplifies to: 3m + a = 63.
Now subtract equation 2 from equation 1:
(6m + a) - (3m + a) = 108 - 63
3m = 45
m = 15
Plug back into 3m + a = 63: 45 + a = 63, so a = 18.
T = 15 + 18 = 33.
Morning workers on Monday as a fraction of T: 15/33 = 5/11. So m = 5T/11.
Answer: B.
The trap most people fall into is setting up the Wednesday equation wrong — the problem says "9 fewer workers late on the afternoon shift than on Monday afternoon," so it's (a - 9), not (a + 9). Flip that sign and you'll get a totally different answer that looks plausible. Worth double-checking that condition before moving on.
14 Apr 2026, 06:28
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We get two equations for x and y where x=Mor shift of Monday and y= Afternoon shift of Monday.
We get x=15 and y=18
So T=33
Morning shift = 33*x
15 = 33*x => x = 15/33 or 5/11
So T*5/11
Answer: Option B
We get x=15 and y=18
So T=33
Morning shift = 33*x
15 = 33*x => x = 15/33 or 5/11
So T*5/11
Answer: Option B
kevincan
