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

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Re: At a certain picnic, each of the guests was served either a  [#permalink]

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New post 15 Jun 2018, 08:43
Bunuel wrote:
SOLUTION

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 of ice-cream?

(1) At the picnic, 60 percent of the guests were served a double scoop of ice-cream --> \(\frac{x}{y}=\frac{4}{6}=\frac{2}{3}\), where \(x\) is the # of people served single scoop and \(y\) the # of people served double scoop. Clearly insufficient to calculate single numerical value of \(y\).

(2) A total of 120 scoops of ice-cream were served to all the guests at the picnic --> \(1*x+2*y=120\). Again not sufficient.

(1)+(2) \(x=\frac{2}{3}y\) and \(x+2y=120\): we have 2 distinct linear equations with 2 unknowns, hence we can solve for \(x\) and \(y\). Sufficient. (Just to illustrate: \(\frac{2}{3}y+2y=120\) --> \(y=45\))

Answer: C.

Hello, please how come its not alright to use a smart number for statement 1?
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Re: At a certain picnic, each of the guests was served either a  [#permalink]

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New post 21 Oct 2018, 13:58
Bunuel wrote:
At a certain picnic, each of the guests was served either a single scoop or a double scoop of ice cream. How many of the guests were served a double scoop of ice cream?

(1) At the picnic, 60 percent of the guests were served a double scoop of 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.
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Re: At a certain picnic, each of the guests was served either a  [#permalink]

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New post 15 May 2019, 11:53
nigina93 wrote:
St 1 gives us just percentage but no real number. it can be either 6, 60, 180, anything. So not suff.
St 2 gives us the total number of guests but gives no information about the ratio of people served single scoop ice cream to the ratio of people served double scoop ice cream . Not suff
Both statements combined together give us the exact number of people served double scoop ice cream since we have percentage and total number of guests. (C)


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Re: At a certain picnic, each of the guests was served either a  [#permalink]

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New post 18 May 2019, 00:57
Bunuel wrote:
At a certain picnic, each of the guests was served either a single scoop or a double scoop of ice cream. How many of the guests were served a double scoop of ice cream?

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

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Question: 61
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Seems to be pretty easy.
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Re: At a certain picnic, each of the guests was served either a  [#permalink]

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New post 07 Jun 2019, 00:42
At a certain picnic, each of the guests was served either a single scoop or a double scoop of ice cream. How many of the guests were served a double scoop of ice cream?

(1) At the picnic, 60 percent of the guests were served a double scoop of ice cream.
(2) A total of 120 scoops of ice cream were served to all the guests at the picnic.
--------
Let x: the number of guests served a double scoop of ice-cream
y: the number of guests served a single scoop of ice-cream
The target question: x =????--> So we need to find out an actual number with no previously mentioned info either % or actual numbers.

St1: We know only % of the guests were served a double scoop of ice cream.--->Not enough info-->NS
St2: x + y = 120. No specific info for each type of ice-cream served-->NS
St1 + St2: We have % for a double scoop of ice cream, and the total number of scoop of ice-cream served.--->Sufficient-->The answer is C
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Re: At a certain picnic, each of the guests was served either a   [#permalink] 07 Jun 2019, 00:42

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