Several recent studies suggest that a child born into a family whose

Pronoun error in centre.
Themselves is wrong for a child. A is out.
E is very bad construction.
family where...wrong. where is used for physical location. D out.
Themselves can refers to children or members. B out.
C is correct. All errors are addressed.

(A) a child born into a family whose members have allergies will probably themselves develop allergies
=> mismatch as "a child" is a singular noun while "themselves" is a plural reflexive pronoun

(B) children born into families whose members have allergies will probably themselves develop allergies
=> correct use of relative pronoun "whose" and reflexive pronoun "themselves" which refers to "children"

(C) a child born into a family the members of which have allergies will probably develop an allergy
=> the use of "of which" is not approriate => a "whose" between "family" and "members" is preferred

(D) in those families where members have allergies, children will probably develop allergies themselves
=> "those" is quite a redundant & the relative pronoun "where" is not approriate here as "where" refers to place

(E) children born into a family in which there are allergies will themselves probably develop an allergy
=> the use of "in which" is not correct as "in which" refers to place & "there are allergies" sounds awkward as if the allergies are not of family members.
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Several recent studies suggest that a child born into a family whose members have allergies will probably themselves develop allergies following the onset of a minor viral infection.

(A) a child born into a family whose members have allergies will probably themselves develop allergies ---- SV error in saying 'a child and themselves'

(B) children born into families whose members have allergies will probably themselves develop allergies -- fair enough and a good choice

(C) a child born into a family the members of which have allergies will probably develop an allergy. --- 'an allergy' is a wrong word implying that the child is vulnerable to a single allergy. The child is susceptible to a variety of allergies is the intent of the prompt.
(D) in those families where members have allergies, children will probably develop allergies themselves -- where cannot refer to families.

(E) children born into a family in which there are allergies will themselves probably develop an allergy. --- the members have allergies and not the families. In addition, the allusion to 'an allergy' is wrong

B is the best.
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A reflexive Pronoun means action done by subject on itself/oneself.

The use of 'themselves' in choice B illogically indicates that children are themselves performing the action of setting in allergies.

Hence, IMHO, Choice B is incorrect on the basis of illogical meaning.

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Several recent studies suggest that a child born into a family whose members have allergies will probably themselves develop allergies following the onset of a minor viral infection.

(A) a child born into a family whose members have allergies will probably themselves develop allergies- a child …. Themselves … wrong
(B) children born into families whose members have allergies will probably themselves develop allergies - subject and verb agree, correct use of whose
(C) a child born into a family the members of which have allergies will probably develop an allergy - allergies and allergy not parallel
(D) in those families where members have allergies, children will probably develop allergies themselves - modifier error
(E) children born into a family in which there are allergies will themselves probably develop an allergy - allergies and allergy not parallel

pretty easy with and i chose b as an option

GMATNinja Please help ..why is C a wrong option? Everything seems fine with C.