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

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GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Karina´s mother has already bought T attraction tickets to distribute  [#permalink]

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05 Mar 2019, 09:33
00:00

Difficulty:

25% (medium)

Question Stats:

80% (01:57) correct 20% (01:40) wrong based on 40 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
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: Karina´s mother has already bought T attraction tickets to distribute  [#permalink]

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05 Mar 2019, 15:00
1
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
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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