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by fskilnik@GMATH » Sun Feb 24, 2019 2:06 pm

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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

Answer: [spoiler]____(C)__[/spoiler]
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by fskilnik@GMATH » Mon Feb 25, 2019 11:44 am
fskilnik@GMATH 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
$$?\,\,\,:\,\,\,{\rm{possible}}\,\,{\rm{amounts}}\,\,\,\,\left( {{\rm{with}}\,\,6\,\,{\rm{coins}}} \right)$$
$${\rm{I}}.\,\,\,76 = 1 \cdot 1 + 3 \cdot 25 = 1 \cdot 1 + 2 \cdot 25 + 2 \cdot 10 + 1 \cdot 5\,\,\,\, \Rightarrow \,\,\,\,1\,{\rm{penny}}\,,\,\,1\,{\rm{nickel}}\,,\,\,2\,\,{\rm{dimes}}\,,\,\,2\,\,{\rm{quarters}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{possible!}}$$
$${\rm{II}}.\,\,81 = 76 + 5 = 1 \cdot 1 + 2 \cdot 25 + 3 \cdot 10\,\,\,\, \Rightarrow \,\,\,\,1\,{\rm{penny}}\,,\,\,3\,\,{\rm{dimes}}\,,\,\,2\,\,{\rm{quarters}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{possible!}}$$
$${\rm{III}}{\rm{.}}\,\,29\,\,\, \Rightarrow \,\,\,\,4\,{\rm{pennies}}\,\,{\rm{ ARE}}\,\,\,\,{\rm{needed}} \ldots \,\,{\rm{exactly}}\,\,{\rm{2}}\,\,{\rm{coins}}\,\,{\rm{for}}\,\,25{\rm{?}}\,\,\,{\rm{impossible}}!$$
$${\rm{IV}}{\rm{.}}\,\,{\rm{101}}\,\,\,\, \Rightarrow \,\,\,\,1\,{\rm{penny IS}}\,\,{\rm{needed}} \ldots \,\,{\rm{5}}\,\,{\rm{coins}}\,\,{\rm{for}}\,\,{\rm{100?}}\,\,\,\left\{ \matrix{
\,4 \cdot 25\,\,{\rm{impossible}}\,\,\left( {{\rm{only}}\,\,5\,\,{\rm{coins}}\,\,{\rm{in}}\,\,{\rm{total}}} \right) \hfill \cr
\,3 \cdot 25\,\,{\rm{impossible}}\,\,\left( {2\,\,{\rm{not - quarters}}\,\,{\rm{adding}}\,\,25?} \right) \hfill \cr
\,2 \cdot 25\,\,{\rm{impossible }}\left( {3\,\,{\rm{not - quarters}}\,\,{\rm{adding}}\,\,50?} \right) \hfill \cr
\,1 \cdot 25\,\,{\rm{impossible }}\left( {4\,\,{\rm{not - quarters}}\,\,{\rm{adding}}\,\,75?} \right)\, \hfill \cr} \right.$$

The correct answer is (C).


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

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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