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# You have access to an unlimited number of each of the following coins:

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GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 937

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24 Feb 2019, 14:17
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Difficulty:

95% (hard)

Question Stats:

35% (02:20) correct 65% (02:17) wrong based on 54 sessions

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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

_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 6320
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

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25 Feb 2019, 07:15
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
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 937

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25 Feb 2019, 11:55
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

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

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

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

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

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

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

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Re: You have access to an unlimited number of each of the following coins:   [#permalink] 25 Feb 2019, 11:55