Mr. Jones spends $25 on movie tickets for a party of adults

[AAPL]

Princeton Review

Mr. Jones spends $25 on movie tickets for a party of adults and children. How many children's tickets did he buy?

1) Adult movie tickets cost $3 each and children's tickets cost $2 each.
2) Mr. Jones buys a total of 11 tickets.

OA C

[fskilnik@GMATH]

Princeton Review

Mr. Jones spends $25 on movie tickets for a party of adults and children. How many children's tickets did he buy?

1) Adult movie tickets cost $3 each and children's tickets cost $2 each.
2) Mr. Jones buys a total of 11 tickets.
OA C

$$\left\{ \matrix{
\,A\,\,{\rm{adults}}\,\,{\rm{,}}\,\,\,{{\rm{p}}_{\rm{A}}} = {\rm{cost}}\,\,\left( {\rm{\$ }} \right)\,\,{\rm{per}}\,\,{\rm{ticket}} \hfill \cr
\,C\,\,{\rm{children}}\,\,{\rm{,}}\,\,\,{{\rm{p}}_{\rm{C}}} = {\rm{cost}}\,\,\left( {\rm{\$ }} \right)\,\,{\rm{per}}\,\,{\rm{ticket}} \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,\,A \cdot {p_A} + C \cdot {p_C} = 25\,\,\,\,\left( * \right)$$
$$? = C$$

$$\left( 1 \right)\,\,\left( {{p_A},{p_C}} \right) = \left( {3,2} \right)\,\,\,\,:\,\,\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {A,C} \right) = \left( {7,2} \right)\,\,\,\, \Rightarrow \,\,\,? = 2\,\,\,\,\,\,\,\left[ {\left( * \right)\,\,7 \cdot 3 + 2 \cdot 2 = 25} \right] \hfill \cr
\,{\rm{Take}}\,\,\left( {A,C} \right) = \left( {5,5} \right)\,\,\,\, \Rightarrow \,\,\,? = 5\,\,\,\,\,\,\,\left[ {\left( * \right)\,\,5 \cdot 3 + 5 \cdot 2 = 25} \right] \hfill \cr} \right.$$

$$\left( 2 \right)\,\,A + C = 11\,\,\,\,:\,\,\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {A,C} \right) = \left( {1,10} \right)\,\,{\rm{and}}\,\,\left( {{p_A},{p_C}} \right) = \left( {5,2} \right)\,\,\,\, \Rightarrow \,\,\,? = 10\,\,\,\,\,\,\,\,\left[ {\left( * \right)\,\,1 \cdot 5 + 10 \cdot 2 = 25} \right] \hfill \cr
\,{\rm{Take}}\,\,\left( {A,C} \right) = \left( {2,9} \right)\,\,{\rm{and}}\,\,\left( {{p_A},{p_C}} \right) = \left( {8,1} \right)\,\,\,\, \Rightarrow \,\,\,? = 9\,\,\,\,\,\,\,\,\left[ {\left( * \right)\,\,2 \cdot 8 + 9 \cdot 1 = 25} \right] \hfill \cr} \right.$$

$$\left( {1 + 2} \right)\,\,\left\{ \matrix{
\,3A + 2C = 25\,\,\,\,\left( * \right) \hfill \cr
\,A + C = 11 \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,3\left( {11 - C} \right) + 2C = 25\,\,\,\,\,\, \Rightarrow \,\,\,\,\,C\,\,{\rm{unique}}$$


The correct answer is therefore (C).


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

Regards,
Fabio.

[Brent@GMATPrepNow]

Princeton Review

Mr. Jones spends $25 on movie tickets for a party of adults and children. How many children's tickets did he buy?

1) Adult movie tickets cost $3 each and children's tickets cost $2 each.
2) Mr. Jones buys a total of 11 tickets.
OA C

Given: Mr. Jones spends $25 on movie tickets for a party of adults and children.

Target question: How many children's tickets did he buy?

Statement 1: Adult movie tickets cost $3 each and children's tickets cost $2 each.
There are several scenarios that satisfy statement 1. Here are two:
Case a: Mr. Jones bought 5 adult tickets and 5 children's tickets (for a total of $25). In this case, the answer to the target question is Mr. Jones bought 5 children's tickets
Case b: Mr. Jones bought 7 adult tickets and 2 children's tickets (for a total of $25). In this case, the answer to the target question is Mr. Jones bought 2 children's tickets
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Mr. Jones buys a total of 11 tickets.
There are several scenarios that satisfy statement 2. Here are two:
Case a: Mr. Jones bought 6 adult tickets (at $3 apiece) and 5 children's tickets (at $1.40 apiece). In this case, the answer to the target question is Mr. Jones bought 5 children's tickets
Case b: Mr. Jones bought 9 adult tickets (at $2 apiece) and 2 children's tickets (at $3.50 apiece). In this case, the answer to the target question is Mr. Jones bought 2 children's tickets
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Let A = number of adult tickets bought
Let C = number of children's tickets bought
Statement 1 (and the given information) tells us that 3A + 2C = 25
Statement 2 tells us that A + C = 11
At this point, we should recognize that we have a system of 2 linear equations with 2 variables. As such, we COULD solve this system for A and C, which means we COULD answer the target question.
ASIDE: Although we COULD solve the system of equations, we would never waste valuable time on test day doing so. We need only determine that we COULD answer the target question.
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent