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Bunuel
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
are answer options given correct??

You've taken 82 as 81. That's why you're getting 32 as the answer :)
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swatato ;

thanks edited.. :)

swatato
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Bunuel
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
are answer options given correct??

You've taken 82 as 81. That's why you're getting 32 as the answer :)
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Bunuel
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.

A is the correct answer.
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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


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

213 = 82 + 113 - Both + 51

Both = 33

Answer C
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Bunuel
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

Answer: A
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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

It can be written: 82+113-both+51 = 213
So, both = 33
Answer: A
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