Four cards are chosen from a standard deck: two aces (one of Spades, a

since its P or OR so we need to add cases:
case 1: negative : (-1*1),(-2*1),(-1*2),(-2*2) ; 4 cases
case 2 : odd : ( -1*1),(-2*-1)*(-2*1)*(2*-1)*(2*1) : 5 cases
and odd & -ve : ( -1*1),(-2*1) , ( 2*-1) ; 3 cases

total ; 4+5+3 = 12 cases
and we have total multiple cases of ( -1,1) and ( 2,-2 ) ; which can make total of 8 pairs
so P would be 8/12 ; 67%
IMO D

\(\left\{ { - 2, - 1,1,2} \right\}\,\, \to \,\,{\rm{two}}\,{\rm{different}}\,\,{\rm{chosen}}\)

\(? = P\left( {{\rm{odd}}\,\,{\rm{or}}\,\,{\rm{negative}}\,\,{\rm{product}}} \right)\)

\({\rm{6}}\,\,{\rm{equiprobable}}\,\,{\rm{outcomes}}\,\,:\,\,\,\left\{ \matrix{\\
\,\left\{ { - 2, - 1} \right\},\left\{ {1,2} \right\}\,\,\,\,\left( {{\rm{product}}\,\,2} \right) \hfill \cr \\
\,\left\{ { - 2,1} \right\},\left\{ { - 1,2} \right\}\,\,\,\,\left( {{\rm{product}}\,\, - 2} \right)\,\,\,::\,\,\,2\,\,{\rm{favorable}}\,\,{\rm{outcomes}} \hfill \cr \\
\,\left\{ { - 2,2} \right\}\,\,\,\,\left( {{\rm{product}}\,\, - 4} \right)\,\,\,::\,\,\,1\,\,{\rm{favorable}}\,\,{\rm{outcome}} \hfill \cr \\
\,\left\{ { - 1,1} \right\}\,\,\,\,\left( {{\rm{product}}\,\, - 1} \right)\,\,\,::\,\,\,1\,\,{\rm{favorable}}\,\,{\rm{outcome}} \hfill \cr} \right.\)

\(?\,\, = \,\,{{2 + 1 + 1} \over 6}\,\, = \,\,{2 \over 3}\,\, \cong \,\,67\%\)


The correct answer is (D).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.