fskilnik wrote:
GMATH practice exercise (Quant Class 18)
Little Julia created a 5-digit integer choosing 5 distinct chips, one by one, among the 7 given ones shown above. "Can you do it in such a way that the three central digits add up to 9?", asked her teacher. And Julia did! If little Max was asked to do the same by his teacher, and Max chooses a correct possibility randomly, what is the probability that both children have chosen exactly the same 5-digit integer?
(A) 1/12
(B) 1/36
(C) 1/54
(D) 1/72
(E) 1/96
Very nice,
eabhgoy! (Kudos!)
(Just a small correction: "Now if Julia selected a
5 digits number, Max can...")
Here is our official solution:
\(?\,\, = \,\,{1 \over {\# \,\,{\rm{favorable}}\,\,{\rm{sequences}}}}\)
\({?_{temp}}\,\,\, = \,\,\,\# \,\,{\rm{favorable}}\,\,{\rm{sequences}}\)
\(\left\{ \matrix{
\,{\rm{3}}\,{\rm{central}}\,{\rm{digits}}\,{\rm{are}}\,\,{\rm{1,3,5}}\,\,\,\, \Rightarrow \,\,\,{{\rm{P}}_{\rm{3}}} = 3!\,\,\,{\rm{possibilities}} \hfill \cr
\,{\rm{first}}\,{\rm{and}}\,\,{\rm{last}}\,\,{\rm{digits}}\,\,\,{\rm{:}}\,\,\,{\rm{4}} \cdot {\rm{3}}\,\,{\rm{possibilities}} \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,{?_{temp}}\,\,\, = \,\,\,3!\, \cdot 4 \cdot 3\,\, = \,\,\,72\)
The correct answer is (D).
We follow the notations and rationale taught in the
GMATH method.
Regards,
Fabio.
_________________
Fabio Skilnik ::
GMATH method creator (Math for the GMAT)
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