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24 Feb 2019, 15:17
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
44% (02:43) correct
56%
(02:28)
wrong
based on 109
sessions
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Not Attempted Yet
You have access to an unlimited number of each of the following coins: pennies, nickels, dimes and quarters. Which of the following amounts CAN be made using exactly 6 of these coins? A penny is worth 1 cent. (A nickel is worth 5 cents. A dime is worth 10 cents. A quarter is worth 25 cents.)
I. 76 cents
II. 81 cents
III. 29 cents
IV. 101 cents
(A) None of them
(B) Exactly one of them
(C) Exactly two of them
(D) Exactly three of them
(E) All of them
I. 76 cents
II. 81 cents
III. 29 cents
IV. 101 cents
(A) None of them
(B) Exactly one of them
(C) Exactly two of them
(D) Exactly three of them
(E) All of them
Archit3110
25 Feb 2019, 08:15
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fskilnik
Quarter= 25 cents
Dime= 10 cents
Nickel= 5 cents
Penny= 1 cent
option
I. 76 cents ; 25*2 + 10*2 +5*1+1*1
II. 81 cents ; 25*2 + 3*10+ 1*1
are only possible
IMO C only two possible
25 Feb 2019, 12:55
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fskilnik
\(?\,\,\,:\,\,\,{\rm{possible}}\,\,{\rm{amounts}}\,\,\,\,\left( {{\rm{with}}\,\,6\,\,{\rm{coins}}} \right)\)
\({\rm{I}}.\,\,\,76 = 1 \cdot 1 + 3 \cdot 25 = 1 \cdot 1 + 2 \cdot 25 + 2 \cdot 10 + 1 \cdot 5\,\,\,\, \Rightarrow \,\,\,\,1\,{\rm{penny}}\,,\,\,1\,{\rm{nickel}}\,,\,\,2\,\,{\rm{dimes}}\,,\,\,2\,\,{\rm{quarters}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{possible!}}\)
\({\rm{II}}.\,\,81 = 76 + 5 = 1 \cdot 1 + 2 \cdot 25 + 3 \cdot 10\,\,\,\, \Rightarrow \,\,\,\,1\,{\rm{penny}}\,,\,\,3\,\,{\rm{dimes}}\,,\,\,2\,\,{\rm{quarters}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{possible!}}\)
\({\rm{III}}{\rm{.}}\,\,29\,\,\, \Rightarrow \,\,\,\,4\,{\rm{pennies\,\, ARE\,}}\,\,{\rm{needed}} \ldots \,\,{\rm{exactly}}\,\,{\rm{2}}\,\,{\rm{coins}}\,\,{\rm{for}}\,\,25{\rm{?}}\,\,\,{\rm{impossible}}!\)
\({\rm{IV}}{\rm{.}}\,\,{\rm{101}}\,\,\,\, \Rightarrow \,\,\,\,1\,{\rm{penny\,\, IS}}\,\,{\rm{needed}} \ldots \,\,{\rm{5}}\,\,{\rm{coins}}\,\,{\rm{for}}\,\,{\rm{100?}}\,\,\,\left\{ \matrix{\\
\,4 \cdot 25\,\,{\rm{impossible}}\,\,\left( {{\rm{only}}\,\,5\,\,{\rm{coins}}\,\,{\rm{in}}\,\,{\rm{total}}} \right) \hfill \cr \\
\,3 \cdot 25\,\,{\rm{impossible}}\,\,\left( {2\,\,{\rm{not - quarters}}\,\,{\rm{adding}}\,\,25?} \right) \hfill \cr \\
\,2 \cdot 25\,\,{\rm{impossible }}\left( {3\,\,{\rm{not - quarters}}\,\,{\rm{adding}}\,\,50?} \right) \hfill \cr \\
\,1 \cdot 25\,\,{\rm{impossible }}\left( {4\,\,{\rm{not - quarters}}\,\,{\rm{adding}}\,\,75?} \right)\, \hfill \cr} \right.\)
The correct answer is (C).
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
