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Little Julia created a 5-digit integer choosing 5 distinct chips, one

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Little Julia created a 5-digit integer choosing 5 distinct chips, one  [#permalink]

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New post 07 Mar 2019, 08:09
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A
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D
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Difficulty:

  55% (hard)

Question Stats:

63% (02:22) correct 38% (02:59) wrong based on 32 sessions

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GMATH practice exercise (Quant Class 18)

Image

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

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Re: Little Julia created a 5-digit integer choosing 5 distinct chips, one  [#permalink]

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New post 07 Mar 2019, 11:44
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fskilnik wrote:
GMATH practice exercise (Quant Class 18)

Image

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


Lets see the number of 5-digit integers that can be formed such that "three central digits add up to 9".

From the given digits only 5+3+1 = 9, hence the middle three digits are 5,3,1 and the for the remaining two digits we 4 options - 2, 7, 8, 9.

Hence for:

1st digit = 4 ways
5th digit = 3 ways
middle 3 digits can be formed in 3! ways as we have three digits
So total ways = 4*3*3*2*1 = 72 ways

Now if Julia selected a 6 digits number, Max can select the same number with a probability of 1/72 as only way will match out of 72.

Hence D is the correct answer.
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Little Julia created a 5-digit integer choosing 5 distinct chips, one  [#permalink]

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New post 07 Mar 2019, 12:45
fskilnik wrote:
GMATH practice exercise (Quant Class 18)

Image

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.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
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Little Julia created a 5-digit integer choosing 5 distinct chips, one  [#permalink]

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New post 07 Mar 2019, 13:28
eabhgoy wrote:
Thank you sir
Hi eabhgoy!

Thank YOU for your contribution!

See you in other posts and success in your studies/activities!

Regards,
Fabio.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
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Little Julia created a 5-digit integer choosing 5 distinct chips, one   [#permalink] 07 Mar 2019, 13:28
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