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# In a survey of 140 people it was found that 115 people

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Senior Manager
Joined: 30 May 2005
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In a survey of 140 people it was found that 115 people [#permalink]

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02 Jul 2005, 07:01
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In a survey of 140 people it was found that 115 people regularly use a telephone; 39 people regularly write letters; 64 people regularly use e-mail; 28 people regularly use a telephone and write letters; 53 people regularly use a telephone and e-mail; 10 people regularly use e-mail and regularly write letters; and 3 people regularly write letters and use a telephone and e-mail.

How many people do not regularly use either telephone or letters or e-mail?

A. 14
B. 13
C. 12
D. 11
E. 10
Director
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02 Jul 2005, 07:19
I pick E

140 - (34 + 28 +1 + 1 +53 + 10 + 3)
140 - 130
= 10
Director
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02 Jul 2005, 07:47
AJB77 wrote:
Can you please post explanations?

ABJ,

I drew venn diagrams and that's why i summarized the venn diagrams above.

(115 - 81) = 34 = Telephone users alone.
Since 115 counts the number of T U L and T U E twice, we subract 28 and 53 (81) from 115 to get the number Telephone users.

39 - 38 = 1= Letters users alone (same rationale as above)

64 - 63 = 1 = E-mail users alone (same as above)

140 - (34 + 1 + 1 + 28 + 53 + 10 +3)
140 - 130
= 10

Another alternative way is to fill out the venn diagrams from inside out.

start from the middle and put 3
Intersection of T and L is 28 -3 = 25
Intersection of T and E is 53-3 = 50
Intersection of L and E is 10 -3 = 7

T alone 115 - (25 + 3+ 50) = 37
L alone 39 - (25 + 3 + 7) = 4
E alone 64 - (50 + 3 + 7) = 4.

140 - (3 + 25 + 50 + 7 + 37 + 4 + 4) should be the number of people using neither L, T or E.
140 -130
= 10
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02 Jul 2005, 17:42
One more for E

AUBUC = A + B + C - [AnB + BnC + AnC] + AnBnC
= 115 + 39 + 64 - [28 + 10 + 53] + 3
= 130
So number of people who do not use any one of these are: 140 - 130
02 Jul 2005, 17:42
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# In a survey of 140 people it was found that 115 people

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