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Karina´s mother has already bought T attraction tickets to distribute

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GMATH Teacher
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Karina´s mother has already bought T attraction tickets to distribute  [#permalink]

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New post 05 Mar 2019, 09:33
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Difficulty:

  25% (medium)

Question Stats:

81% (01:52) correct 19% (01:36) wrong based on 26 sessions

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GMATH practice exercise (Quant Class 14)

Karina´s mother has already bought T attraction tickets to distribute to Karina´s friends for the party at the Alice-In-Wonderland amusement park. How many extra attraction tickets must Karina´s mother buy if Karina decides to give four tickets to each of her friends?

(1) If Karina decides to give two attraction tickets to each of her friends, 25 attraction tickets will remain not distributed.
(2) If Karina decides to give three attraction tickets to each of her friends, Karina´s mother must buy 15 extra attraction tickets.

_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
GMATH Teacher
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Re: Karina´s mother has already bought T attraction tickets to distribute  [#permalink]

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New post 05 Mar 2019, 15:00
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fskilnik wrote:
GMATH practice exercise (Quant Class 14)

Karina´s mother has already bought T attraction tickets to distribute to Karina´s friends for the party at the Alice-In-Wonderland amusement park. How many extra attraction tickets must Karina´s mother buy if Karina decides to give four tickets to each of her friends?

(1) If Karina decides to give two attraction tickets to each of her friends, 25 attraction tickets will remain not distributed.
(2) If Karina decides to give three attraction tickets to each of her friends, Karina´s mother must buy 15 extra attraction tickets.

\(N\,\, = \,\,\,\# \,\,{\rm{friends}}\)

\(? = 4N - T\)

\(\left( 1 \right)\,\,T = 2N + 25\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {N,T} \right) = \left( {20,65} \right)\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{?}}\,\,{\rm{ = }}\,\,15 \hfill \cr
\,{\rm{Take}}\,\,\left( {N,T} \right) = \left( {25,75} \right)\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{?}}\,\,{\rm{ = }}\,\,25\,\, \hfill \cr} \right.\)

\(\left( 2 \right)\,\,T + 15 = 3N\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {N,T} \right) = \left( {20,45} \right)\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{?}}\,\,{\rm{ = }}\,\,35 \hfill \cr
\,{\rm{Take}}\,\,\left( {N,T} \right) = \left( {25,60} \right)\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{?}}\,\,{\rm{ = }}\,\,40\,\, \hfill \cr} \right.\)

\(\left( {1 + 2} \right)\,\,\,\left\{ \matrix{
\,T + 15 = 3N \hfill \cr
\,T = 2N + 25\,\,\,\left( * \right) \hfill \cr} \right.\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( - \right)} \,\,\,\,\,15 = N - 25\,\,\,\,\, \Rightarrow \,\,\,\,\,N = 40\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,T = 105\,\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.\)


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)
Our high-level "quant" preparation starts here: https://gmath.net
GMAT Club Bot
Re: Karina´s mother has already bought T attraction tickets to distribute   [#permalink] 05 Mar 2019, 15:00
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Karina´s mother has already bought T attraction tickets to distribute

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