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nislam
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A certain company with 118 employees offered three different training c 04 Oct 2021, 09:20
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65% (hard)

Question Stats:

61% (02:43) correct 39% (02:52) wrong based on 129 sessions

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A certain company with 118 employees offered three different training courses, one in CPR, one in spreadsheet skills, and one in touch-typing. Each employee was required to take at least two of these courses, and some employees took all three of the courses. If 71 employees took the CPR course, 102 employees took the spreadsheet skills course, and 89 employees took the touch-typing course, how many employees took all three courses?

A) 12

B) 26

C) 48

D) 71

E) 86
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B
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A certain company with 118 employees offered three different training c 04 Oct 2021, 09:35
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If all 118 employees took just 2 courses, the total number of courses taken would be 118*2=236. But some employees (X) took 3 courses (meaning, one additional course each).
so the final formula would be
118*2 + x = 262 total number of courses (71+102+89)
x=262-236=26
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A certain company with 118 employees offered three different training c Updated on: 02 Oct 2024, 23:33
Originally posted by imslogic on 02 Oct 2024, 20:37.
Last edited by imslogic on 02 Oct 2024, 23:33, edited 1 time in total.
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Bunuel

Using the equation Total=G1+G2+G3-Both-2(All)+Neither, I get 13.

118=71+102+89-118-2(All)+0
2(All)=262-236
2(All)=26
All=13

Am I using the formula incorrectly or is the answer incorrect? Please advise. Thank you!

Posted from my mobile device
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A certain company with 118 employees offered three different training c 02 Oct 2024, 23:05
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nislam

A certain company with 118 employees offered three different training courses, one in CPR, one in spreadsheet skills, and one in touch-typing. Each employee was required to take at least two of these courses, and some employees took all three of the courses.

If 71 employees took the CPR course, 102 employees took the spreadsheet skills course, and 89 employees took the touch-typing course, how many employees took all three courses?

Attachment:
Screenshot 2024-10-03 at 11.35.10 AM.png
Screenshot 2024-10-03 at 11.35.10 AM.png [ 45.83 KiB | Viewed 1252 times ]

A + B + C + x = 118 (1)
A + B + x = 71 (2)
A + C + x = 102 (3)
B + C + x = 89 (4)

(2) + (3) + (4)
2(A+B+C+x) + x = 71 + 102 + 89 = 262
2*118 + x = 236 + x = 262
x = 262 - 236 = 26

26 employees took all three courses.

IMO B
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A certain company with 118 employees offered three different training c 02 Oct 2024, 23:39
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Hi Kinshook,

When you add (2),(3), and (4), shouldn't there be a total of 3x as each equation has one x variable?

Also, can you look at my post and advice the reason that the formula, which is correct, is not working?

Thanks!
Kinshook
nislam

A certain company with 118 employees offered three different training courses, one in CPR, one in spreadsheet skills, and one in touch-typing. Each employee was required to take at least two of these courses, and some employees took all three of the courses.

If 71 employees took the CPR course, 102 employees took the spreadsheet skills course, and 89 employees took the touch-typing course, how many employees took all three courses?

Attachment:
Screenshot 2024-10-03 at 11.35.10 AM.png

A + B + C + x = 118 (1)
A + B + x = 71 (2)
A + C + x = 102 (3)
B + C + x = 89 (4)

(2) + (3) + (4)
2(A+B+C+x) + x = 71 + 102 + 89 = 262
2*118 + x = 236 + x = 262
x = 262 - 236 = 26

26 employees took all three courses.

IMO B
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A certain company with 118 employees offered three different training c 03 Oct 2024, 00:48
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imslogic


A certain company with 118 employees offered three different training courses, one in CPR, one in spreadsheet skills, and one in touch-typing. Each employee was required to take at least two of these courses, and some employees took all three of the courses. If 71 employees took the CPR course, 102 employees took the spreadsheet skills course, and 89 employees took the touch-typing course, how many employees took all three courses?

A) 12

B) 26

C) 48

D) 71

E) 86

Bunuel

Using the equation Total=G1+G2+G3-Both-2(All)+Neither, I get 13.

118=71+102+89-118-2(All)+0
2(All)=262-236
2(All)=26
All=13

Am I using the formula incorrectly or is the answer incorrect? Please advise. Thank you!

Posted from my mobile device

Show more

118 there is not correct because the number of people who took exactly two of the classes is not 118, it's 118 minus those who took all three classes. So, the equation should be:

118 = 71 + 102 + 89 - (118 - x) - 2x + 0
x = 26

imslogic
Hi Kinshook,

When you add (2),(3), and (4), shouldn't there be a total of 3x as each equation has one x variable?

Also, can you look at my post and advice the reason that the formula, which is correct, is not working?

Thanks!
Kinshook
nislam

A certain company with 118 employees offered three different training courses, one in CPR, one in spreadsheet skills, and one in touch-typing. Each employee was required to take at least two of these courses, and some employees took all three of the courses.

If 71 employees took the CPR course, 102 employees took the spreadsheet skills course, and 89 employees took the touch-typing course, how many employees took all three courses?

Attachment:
Screenshot 2024-10-03 at 11.35.10 AM.png

A + B + C + x = 118 (1)
A + B + x = 71 (2)
A + C + x = 102 (3)
B + C + x = 89 (4)

(2) + (3) + (4)
2(A+B+C+x) + x = 71 + 102 + 89 = 262
2*118 + x = 236 + x = 262
x = 262 - 236 = 26

26 employees took all three courses.

IMO B

Posted from my mobile device
Show more

When you add (2), (3), and (4) you get 2A + 2B + 2C + 3x, which equals to 2(A + B + C + x) + x
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A certain company with 118 employees offered three different training c 03 Oct 2024, 00:58
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Thank you Bunuel.

Bunuel
imslogic


A certain company with 118 employees offered three different training courses, one in CPR, one in spreadsheet skills, and one in touch-typing. Each employee was required to take at least two of these courses, and some employees took all three of the courses. If 71 employees took the CPR course, 102 employees took the spreadsheet skills course, and 89 employees took the touch-typing course, how many employees took all three courses?

A) 12

B) 26

C) 48

D) 71

E) 86

Bunuel

Using the equation Total=G1+G2+G3-Both-2(All)+Neither, I get 13.

118=71+102+89-118-2(All)+0
2(All)=262-236
2(All)=26
All=13

Am I using the formula incorrectly or is the answer incorrect? Please advise. Thank you!

Posted from my mobile device


118 there is not correct because the number of people who took exactly two of the classes is not 118, it's 118 minus those who took all three classes. So, the equation should be:

118 = 71 + 102 + 89 - (118 - x) - 2x + 0
x = 26

imslogic
Hi Kinshook,

When you add (2),(3), and (4), shouldn't there be a total of 3x as each equation has one x variable?

Also, can you look at my post and advice the reason that the formula, which is correct, is not working?

Thanks!
Kinshook
nislam

A certain company with 118 employees offered three different training courses, one in CPR, one in spreadsheet skills, and one in touch-typing. Each employee was required to take at least two of these courses, and some employees took all three of the courses.

If 71 employees took the CPR course, 102 employees took the spreadsheet skills course, and 89 employees took the touch-typing course, how many employees took all three courses?

Attachment:
Screenshot 2024-10-03 at 11.35.10 AM.png

A + B + C + x = 118 (1)
A + B + x = 71 (2)
A + C + x = 102 (3)
B + C + x = 89 (4)

(2) + (3) + (4)
2(A+B+C+x) + x = 71 + 102 + 89 = 262
2*118 + x = 236 + x = 262
x = 262 - 236 = 26

26 employees took all three courses.

IMO B

Posted from my mobile device

When you add (2), (3), and (4) you get 2A + 2B + 2C + 3x, which equals to 2(A + B + C + x) + x
Show more

Posted from my mobile device
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