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Karina´s mother has already bought T attraction tickets to

by fskilnik@GMATH » Tue Mar 05, 2019 8:24 am

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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.

Answer: [spoiler]_____(C)__[/spoiler]
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Source: — Data Sufficiency |
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by fskilnik@GMATH » Tue Mar 05, 2019 1:49 pm

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fskilnik@GMATH 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)
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