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# Of the 213 people who responded to a genealogical poll, 82 said they

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Math Expert
Joined: 02 Sep 2009
Posts: 58422
Of the 213 people who responded to a genealogical poll, 82 said they  [#permalink]

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27 Feb 2019, 04:44
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Difficulty:

5% (low)

Question Stats:

95% (01:26) correct 5% (00:55) wrong based on 55 sessions

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Of the 213 people who responded to a genealogical poll, 82 said they have French ancestors and 113 said they have Italian ancestors. If 51 of the respondents said they have neither French nor Italian heritage, how many have both?

A. 33
B. 52
C. 69
D. 101
E. 124

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Of the 213 people who responded to a genealogical poll, 82 said they  [#permalink]

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Updated on: 27 Feb 2019, 10:05
Bunuel wrote:
Of the 213 people who responded to a genealogical poll, 82 said they have French ancestors and 113 said they have Italian ancestors. If 51 of the respondents said they have neither French nor Italian heritage, how many have both?

A. 33
B. 52
C. 69
D. 101
E. 124

-----------French---not french----total
italian------33------80----------113
not italian--49------51-----------100
total-------82-----131-----------213
IMO 33;A

Originally posted by Archit3110 on 27 Feb 2019, 05:54.
Last edited by Archit3110 on 27 Feb 2019, 10:05, edited 2 times in total.
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Re: Of the 213 people who responded to a genealogical poll, 82 said they  [#permalink]

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27 Feb 2019, 06:27
Neither= 51
Either French or Italian or both= 213-51=162
French= 82
Italian= 113
French + Italian + 2*french&Italian= 195
Therefore both French and Italian = 195-162= 33

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Re: Of the 213 people who responded to a genealogical poll, 82 said they  [#permalink]

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27 Feb 2019, 10:01
Archit3110 wrote:
Bunuel wrote:
Of the 213 people who responded to a genealogical poll, 82 said they have French ancestors and 113 said they have Italian ancestors. If 51 of the respondents said they have neither French nor Italian heritage, how many have both?

A. 33
B. 52
C. 69
D. 101
E. 124

-----------French---not french----total
italian------32------81----------113
not italian--49------51-----------100
total-------81-----132-----------213
IMO 32
Bunuel

You've taken 82 as 81. That's why you're getting 32 as the answer
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Re: Of the 213 people who responded to a genealogical poll, 82 said they  [#permalink]

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27 Feb 2019, 10:05
swatato ;

thanks edited..

swatato wrote:
Archit3110 wrote:
Bunuel wrote:
Of the 213 people who responded to a genealogical poll, 82 said they have French ancestors and 113 said they have Italian ancestors. If 51 of the respondents said they have neither French nor Italian heritage, how many have both?

A. 33
B. 52
C. 69
D. 101
E. 124

-----------French---not french----total
italian------32------81----------113
not italian--49------51-----------100
total-------81-----132-----------213
IMO 32
Bunuel

You've taken 82 as 81. That's why you're getting 32 as the answer
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Joined: 31 Oct 2013
Posts: 1465
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GPA: 3.68
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Re: Of the 213 people who responded to a genealogical poll, 82 said they  [#permalink]

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28 Feb 2019, 12:52
Bunuel wrote:
Of the 213 people who responded to a genealogical poll, 82 said they have French ancestors and 113 said they have Italian ancestors. If 51 of the respondents said they have neither French nor Italian heritage, how many have both?

A. 33
B. 52
C. 69
D. 101
E. 124

First point that we must take into account is 51 people don't like either one.

It means (213 - 51) = 162. people like France or Iltalian or both.

France = 82

Italian = 113

Total = 82 + 113 = 195.

both = 195 - 162 = 33.

Shortcut Formula:

Total = A + B - Both + Neither

213 = 82 + 113 - Both + 51

Both = 33.

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Joined: 28 Jul 2018
Posts: 11
Re: Of the 213 people who responded to a genealogical poll, 82 said they  [#permalink]

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28 Feb 2019, 13:22
Of the 213 people who responded to a genealogical poll, 82 said they have French ancestors and 113 said they have Italian ancestors. If 51 of the respondents said they have neither French nor Italian heritage, how many have both?

A. 33
B. 52
C. 69
D. 101
E. 124

Total = (French) + (Italian) - (Both) + Neither

213 = 82 + 113 - Both + 51

Both = 33

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Re: Of the 213 people who responded to a genealogical poll, 82 said they  [#permalink]

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03 Mar 2019, 20:04
Bunuel wrote:
Of the 213 people who responded to a genealogical poll, 82 said they have French ancestors and 113 said they have Italian ancestors. If 51 of the respondents said they have neither French nor Italian heritage, how many have both?

A. 33
B. 52
C. 69
D. 101
E. 124

We can create the equation:

Total = French + Italian - both + neither

213 = 82 + 113 - both + 51

213 = -both + 246

both = 33

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Re: Of the 213 people who responded to a genealogical poll, 82 said they   [#permalink] 03 Mar 2019, 20:04
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