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New post 24 Feb 2019, 15:17
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GMATH practice exercise (Quant Class 3)

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?

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

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Our high-level "quant" preparation starts here: https://gmath.net
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Re: You have access to an unlimited number of each of the following coins:  [#permalink]

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New post 25 Feb 2019, 08:15
fskilnik wrote:
GMATH practice exercise (Quant Class 3)

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?

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


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
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Re: You have access to an unlimited number of each of the following coins:  [#permalink]

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New post 25 Feb 2019, 12:55
fskilnik wrote:
GMATH practice exercise (Quant Class 3)

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?

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

\(?\,\,\,:\,\,\,{\rm{possible}}\,\,{\rm{amounts}}\,\,\,\,\left( {{\rm{with}}\,\,6\,\,{\rm{coins}}} \right)\)


\({\rm{I}}.\,\,\,76 = 1 \cdot 1 + 3 \cdot 25 = 1 \cdot 1 + 2 \cdot 25 + 2 \cdot 10 + 1 \cdot 5\,\,\,\, \Rightarrow \,\,\,\,1\,{\rm{penny}}\,,\,\,1\,{\rm{nickel}}\,,\,\,2\,\,{\rm{dimes}}\,,\,\,2\,\,{\rm{quarters}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{possible!}}\)

\({\rm{II}}.\,\,81 = 76 + 5 = 1 \cdot 1 + 2 \cdot 25 + 3 \cdot 10\,\,\,\, \Rightarrow \,\,\,\,1\,{\rm{penny}}\,,\,\,3\,\,{\rm{dimes}}\,,\,\,2\,\,{\rm{quarters}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{possible!}}\)

\({\rm{III}}{\rm{.}}\,\,29\,\,\, \Rightarrow \,\,\,\,4\,{\rm{pennies\,\, ARE\,}}\,\,{\rm{needed}} \ldots \,\,{\rm{exactly}}\,\,{\rm{2}}\,\,{\rm{coins}}\,\,{\rm{for}}\,\,25{\rm{?}}\,\,\,{\rm{impossible}}!\)

\({\rm{IV}}{\rm{.}}\,\,{\rm{101}}\,\,\,\, \Rightarrow \,\,\,\,1\,{\rm{penny\,\, IS}}\,\,{\rm{needed}} \ldots \,\,{\rm{5}}\,\,{\rm{coins}}\,\,{\rm{for}}\,\,{\rm{100?}}\,\,\,\left\{ \matrix{
\,4 \cdot 25\,\,{\rm{impossible}}\,\,\left( {{\rm{only}}\,\,5\,\,{\rm{coins}}\,\,{\rm{in}}\,\,{\rm{total}}} \right) \hfill \cr
\,3 \cdot 25\,\,{\rm{impossible}}\,\,\left( {2\,\,{\rm{not - quarters}}\,\,{\rm{adding}}\,\,25?} \right) \hfill \cr
\,2 \cdot 25\,\,{\rm{impossible }}\left( {3\,\,{\rm{not - quarters}}\,\,{\rm{adding}}\,\,50?} \right) \hfill \cr
\,1 \cdot 25\,\,{\rm{impossible }}\left( {4\,\,{\rm{not - quarters}}\,\,{\rm{adding}}\,\,75?} \right)\, \hfill \cr} \right.\)


The correct answer is (C).


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

Regards,
Fabio.
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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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Re: You have access to an unlimited number of each of the following coins:   [#permalink] 25 Feb 2019, 12:55
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