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Apr 2808:00 AM PDT
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27 Apr 2026, 17:19
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Difficulty:
55%
(hard)
Question Stats:
56% (02:51) correct
44%
(03:09)
wrong
based on 9
sessions
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All employees of Celtic Systems are either programmers or systems analysts. On Monday, one programmer was absent, and programmers made up \(\frac{1}{7}\) of the employees present. On Tuesday, two systems analysts were absent, and programmers made up \(\frac{1}{5}\) of the employees present. On Wednesday, two programmers and two systems analysts were absent.
What fraction of the employees present on Wednesday were programmers?
(A) \(\frac{2}{25}\)
(B) \(\frac{1}{10}\)
(C) \(\frac{2}{19}\)
(D) \(\frac{1}{9}\)
(E) \(\frac{1}{8}\)
What fraction of the employees present on Wednesday were programmers?
(A) \(\frac{2}{25}\)
(B) \(\frac{1}{10}\)
(C) \(\frac{2}{19}\)
(D) \(\frac{1}{9}\)
(E) \(\frac{1}{8}\)
kevincan
Let us take programmers to be p and system analysts to be s.
On Monday, one programmer was absent, and programmers made up \(\frac{1}{7}\) of the employees present.
So, the number of programmers present is p-1, while total becomes p+s-1.
It is given that p-1=\([fraction]1/7[/fraction\)] (p+s-1)
7p-7=p+s-1 or 6p-6=s
Next
On Tuesday, two systems analysts were absent, and programmers made up \(\frac{1}{5}\) of the employees present.
So, the number of programmers present remains p, while total becomes p+s-2.
It is given that p=1/5 (p+s-2)
5p=p+s-2 or 4p+2=s
From the above two equations
\(4p+2=6p-6\) or p=4
We can also find s as 4p+2 or 18.
On Wednesday, with two of each absent, the total becomes 4+18-2×2 = 18 while programmer are 4-2 or 2.
Thus as a fraction of total, programmer are 2/18 or 1/9
27 Apr 2026, 21:31
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N = total
P = programmer
Monday: N = 7(P-1) + 1 --> 1 programmer absent
Tuesday: N = 5P + 2 --> 2 analyst absent
P = 4 and N = 22
Wednesday: 2/18 == 1/9
Ans D.
Hope it helps.
P = programmer
Monday: N = 7(P-1) + 1 --> 1 programmer absent
Tuesday: N = 5P + 2 --> 2 analyst absent
P = 4 and N = 22
Wednesday: 2/18 == 1/9
Ans D.
Hope it helps.
