Data Sufficiency

BTGmoderatorDC wrote:If Pei ordered a total of 63 bottles of Cola, Root Beer and Ginger Ale for a part. How many Cola bottles did she order?

(1) The no of bottles of root beer Pei order was 80% of bottles of ginger ale that she ordered
(2) The no of bottles of cola Pei order was 75% of total no. of bottles of ginger ale and root beer that she ordered
Source: GMAT Prep

$$\left( * \right)\,\,\,C + R + G = 63\,\,\,\,\,\,\left( {C,R,G\,\, \ge 1\,\,\,{\rm{ints}}} \right)$$
$$? = C$$

$$\left( 1 \right)\,\,R = {4 \over 5}G\,\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {C,R,G} \right)\,\,\mathop = \limits^{\left( * \right)} \,\,\left( {63 - 9,4,5} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 63 - 9 \hfill \cr
\,{\rm{Take}}\,\,\left( {C,R,G} \right)\,\,\mathop = \limits^{\left( * \right)} \,\,\left( {63 - 18,8,10} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 63 - 18 \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{INSUFF}}.$$

$$\left( 2 \right)\,\,C = {3 \over 4}\left( {R + G} \right)\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,C + {4 \over 3}C = 63\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,C\,\,{\rm{unique}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}{\rm{.}}$$


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

Regards,
Fabio.