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Bunuel
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A company has 50 employees, of which 22 studied accounting, 15 studied 19 Jan 2022, 07:45
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C
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45% (medium)

Question Stats:

66% (01:49) correct 34% (01:59) wrong based on 349 sessions

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A company has 50 employees, of which 22 studied accounting, 15 studied finance and 14 studied marketing. Nine employees have done just two courses and only one made ​​the three courses. How many employees have no training?

(A) 0
(B) 9
(C) 10
(D) 11
(E) 26
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C
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natheodore
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A company has 50 employees, of which 22 studied accounting, 15 studied 19 Jan 2022, 08:23
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Using the 3 venn diagram chart -
1 subj = a , b, c
2 subj = d, e, f
3 subj = g
No subj =i

a+b+c+d+e+f+g+i = 50
Taking the values of the 1 subj studied,

a+b+c+ 2(d+e+f) + 3(g) = 51
Take out d+e+f+2g=11
a+…+g = 40
50-40 =10

Ans is C

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LucienH
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A company has 50 employees, of which 22 studied accounting, 15 studied 20 Oct 2023, 09:49
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Total Number of Observations = Sum of the groups - # present in two groups - 2*(# present in the three groups) - # in None of the groups

50 = 22 + 15 + 14 - 9 -2*(1) - None
None = 50 - 40 = 10
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A company has 50 employees, of which 22 studied accounting, 15 studied 30 Oct 2024, 12:42
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Hi Bunuel,

Can you help with the solution please.

Bunuel
A company has 50 employees, of which 22 studied accounting, 15 studied finance and 14 studied marketing. Nine employees have done just two courses and only one made the three courses. How many employees have no training?

(A) 0
(B) 9
(C) 10
(D) 11
(E) 26
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A company has 50 employees, of which 22 studied accounting, 15 studied 30 Oct 2024, 18:23
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Hello

Total: 51 trainings and 50 employees, but:
1 person has 3 trainings so we can deduce 2 of the 51 = 49
9 people have 2 trainings so we can deduce 9 to the 49 = 40 people have trainings and there are 50 employees, so 10 on them have no trainings.

Hope that helps
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Bunuel
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A company has 50 employees, of which 22 studied accounting, 15 studied 31 Oct 2024, 03:37
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7Amulya
Hi Bunuel,

Can you help with the solution please.

Bunuel
A company has 50 employees, of which 22 studied accounting, 15 studied finance and 14 studied marketing. Nine employees have done just two courses and only one made the three courses. How many employees have no training?

(A) 0
(B) 9
(C) 10
(D) 11
(E) 26
Show more

This should help to solve: ADVANCED OVERLAPPING SETS PROBLEMS

Total = Accounting + Finance + Marketing - (Those who studied exactly 2 courses) - 2*(Those who studied exactly 3 courses) + (Those who studied neither of the courses).

50 = 22 + 15 + 14 - 9 - 2*1 + (Those who studied neither of the courses).

So, (Those who studied neither of the courses) = 10.

Answer: C.
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A company has 50 employees, of which 22 studied accounting, 15 studied 31 Oct 2024, 10:14
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Thank You so much Bunuel!!
Bunuel
7Amulya
Hi Bunuel,

Can you help with the solution please.

Bunuel
A company has 50 employees, of which 22 studied accounting, 15 studied finance and 14 studied marketing. Nine employees have done just two courses and only one made the three courses. How many employees have no training?

(A) 0
(B) 9
(C) 10
(D) 11
(E) 26

This should help to solve: ADVANCED OVERLAPPING SETS PROBLEMS

Total = Accounting + Finance + Marketing - (Those who studied exactly 2 courses) - 2*(Those who studied exactly 3 courses) + (Those who studied neither of the courses).

50 = 22 + 15 + 14 - 9 - 2*1 + (Those who studied neither of the courses).

So, (Those who studied neither of the courses) = 10.

Answer: C.
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HarshavardhanR
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A company has 50 employees, of which 22 studied accounting, 15 studied 31 Oct 2024, 23:02
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I = exactly 1
II = exactly 2
III = exactly 3
N = none

(1) I + II + III + N = 50
(2) I + 2(II) + 3(III) = 51

(2) - (1)

II + 2(III) - N = 1

=> N = II + 2(III) - 1 = 9 + 2(1) - 1 = 11 - 1 = 10. Choice C.

Harsha
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A company has 50 employees, of which 22 studied accounting, 15 studied 07 Nov 2024, 06:23
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Hey, I didn't understand this part- "- 2*(Those who studied exactly 3 courses)". Why did you multiply it with 2?
Bunuel
7Amulya
Hi Bunuel,

Can you help with the solution please.

Bunuel
A company has 50 employees, of which 22 studied accounting, 15 studied finance and 14 studied marketing. Nine employees have done just two courses and only one made the three courses. How many employees have no training?

(A) 0
(B) 9
(C) 10
(D) 11
(E) 26

This should help to solve: ADVANCED OVERLAPPING SETS PROBLEMS

Total = Accounting + Finance + Marketing - (Those who studied exactly 2 courses) - 2*(Those who studied exactly 3 courses) + (Those who studied neither of the courses).

50 = 22 + 15 + 14 - 9 - 2*1 + (Those who studied neither of the courses).

So, (Those who studied neither of the courses) = 10.

Answer: C.
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Bunuel
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A company has 50 employees, of which 22 studied accounting, 15 studied 07 Nov 2024, 07:05
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Nandita__
Hey, I didn't understand this part- "- 2*(Those who studied exactly 3 courses)". Why did you multiply it with 2?
Show more

That is explained in the link provided at the beginning of the solution. That’s why it’s included there.
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A company has 50 employees, of which 22 studied accounting, 15 studied 07 Nov 2024, 10:25
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A company has 50 employees, of which 22 studied accounting, 15 studied finance and 14 studied marketing. Nine employees have done just two courses and only one made the three courses. How many employees have no training?

(A) 0
(B) 9
(C) 10
(D) 11
(E) 26

Thinking critically, we know that since sum of all who studied is more(22+15+14 - 50 = 1) than total employees, atleast one employee studied atleast two courses or may be three(in which case some employees did not train in any course).
Case A: Two courses
Out of 22 accounting ones 1 studied finance
Out of 15 finance ones 1 studied accounting
14 studied only marketing

Total = (21 + 14 + 14)(1 course) + 1(2 courses) = 50
Hence all employee got trained

Case B: Three courses
Out of 22 accounting ones 1 studied finance and marketing also
Out of 15 finance ones 1 studied accounting and marketing also
Out of 14 marketing ones 1 studied finance and accounting also

Total = (21 + 14 + 13)(1 course) + 1(3 courses) + 1(no training) = 50
Hence all employee got trained

Here have Case B works for us which needs tweaking as per given data.

Out of 22 accounting ones 9 studied finance also and 1 all three courses
Out of 15 finance ones 9 studied accounting also and 1 all three courses
Out of 14 marketing ones 1 studied all three courses

Total = (12 + 5 + 13)(1 course) + 9(2 courses) + 1(3 courses) + 10(no training) = 50
Hence 10 employees got no training


Answer C.
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