At a certain picnic, each of the guests was served either a

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Source: Official Guide

At a certain picnic, each of the guests was served either a single scoop or a double scoop ice-cream. How many of the guests were served a double scoop ice-cream?

1. At the picnic, 60 percent of the guests were served a double scoop ice-cream.
2. A total of 120 scoops of ice-cream were served to all the guests at the picnic.

The OA is C.

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by deloitte247 » Sun Oct 21, 2018 11:03 am

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Question = How many of the guests were served a double scoop of ice-cream ?

Statement 1 =60% of guest were served a double scoop of ice-cream
$$Let\ no\ of\ guests\ served\ \sin gle\ scoop\ =x$$
$$Let\ no\ of\ guests\ served\ double\ scoop\ be\ =y$$
y=60%
x=100-60=40
$$\frac{x}{y}=\frac{40}{60}=\frac{2}{3},\ hence\ \frac{2y}{3}\ of\ the\ guest\ \ were\ served\ double\ scoop\ $$
Hence, statement 1 is INSUFFICIENT.

Statement 2= A total of 120 scoops of ice-cream were served to all guest at the picnic.
$$x+2y=120$$
we have no information regarding those who were served double scoop hence, Statement 2 is INSUFFICIENT.

Combining statement 1 and 2 together.
$$x=\frac{2y}{3}$$
$$x+2y=120$$
$$\frac{2y}{3}+2y=120$$
$$\frac{\frac{8y}{3}}{\frac{8}{3}}=\frac{120}{\frac{8}{3}}$$
$$y=120\cdot\frac{3}{8}=45$$
both statements together are SUFFICIENT
$$Option\ C$$

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by fskilnik@GMATH » Sun Oct 21, 2018 12:50 pm

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BTGmoderatorLU wrote:Source: Official Guide

At a certain picnic, each of the guests was served either a single scoop or a double scoop ice-cream. How many of the guests were served a double scoop ice-cream?

1. At the picnic, 60 percent of the guests were served a double scoop ice-cream.
2. A total of 120 scoops of ice-cream were served to all the guests at the picnic.
$$5\,G\,\,{\rm{guests}}\,\,\,\left\{ \matrix{
\,x\,\,{\rm{guests}}\,\,\,::\,\,{\rm{one}}\,\,{\rm{2 - balls}}\,\,{\rm{ice - cream}}\,\,{\rm{each}} \hfill \cr
\,\left( {5G - x} \right)\,\,{\rm{guests}}\,\,\,::\,\,{\rm{one}}\,\,1{\rm{ - ball}}\,\,{\rm{ice - cream}}\,\,{\rm{each}} \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\,;\,\,\,\,\,\,\,\,\,\,\,? = x\,\,$$
$$\left( 1 \right)\,\,\,\,\,{x \over {5G}} = \,{3 \over 5}\,\,\,\,\, \Rightarrow \,\,\,\,x = 3G\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {x,G} \right) = \left( {3,1} \right)\,\,\,\,\,\left[ {5G = 5} \right]\,\,\,\,\,\, \Rightarrow \,\,\,\,? = 3\,\,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {x,G} \right) = \left( {6,2} \right)\,\,\,\,\,\left[ {5G = 10} \right]\,\,\,\,\,\, \Rightarrow \,\,\,\,? = 6\,\, \hfill \cr} \right.$$
$$\left( 2 \right)\,\,x \cdot 2 + \left( {5G - x} \right) \cdot 1 = 120\,\,\,\,\left[ {{\rm{balls}}\,\,{\rm{of}}\,\,{\rm{ice - cream}}} \right]$$
$$\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {x,G} \right) = \left( {10,22} \right)\,\,\,\, \Rightarrow \,\,\,\,? = 10\,\,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {x,G} \right) = \left( {20,20} \right)\,\,\,\, \Rightarrow \,\,\,\,? = 20\,\, \hfill \cr} \right.$$
$$\left( {1 + 2} \right)\,\,\,\left\{ \matrix{
\,x = 3G \hfill \cr
\,x \cdot 2 + \left( {5G - x} \right) \cdot 1 = 120 \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,G\,\,\,{\rm{unique}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,x\,\,\,{\rm{unique}}\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}{\rm{.}}$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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