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

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.
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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)

Let the total number of guests be 100x
1) 60x , where x can be anything --->Insufficient
2) Clearly insufficient
1+2) No of guests who are served single scoop = 40x
No of guests who are served double scoop = 60x
Total no of scoops served - 40x (1) + 60x(2) = 160x
Total no of scoops served is 120
Thus 120 = 160x
We can get Unique value of 60x which will 60x (120/160) = 45 --->Sufficient

Answer C

1) Only a percentage is given. Nothing can be said from that. 60% of 10 is 6. 60% of 100 is 60 and so on.
2)Only total number of scoops served is given. It can be 50 ppl double scoop, 20 ppl single scoop or 40 ppl double scoop, 40 ppl single scoop and so on.

1 & 2 together

2*.6*x + 1*.4*x = 120

One equation, one unknown. Easily solvable. Hence answer is C

1.6*x = 120

x = 75

So. no. of ppl to whom double scoop was served = .6*75 = 45

without any calculation we can solve DS (in this precise scenario)

To have a solution we need total of the guests AND a % or a ratio or something to make the information manageable. otherwise we can't solve

1) we have a % but nothing else. insuff

2) we have the total but nothing else. insuff

Together we have what we are looking for C \(must\) be the answer

We could save precious seconds for other questions, tougher.
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statement one we know the following
double scoop = 0.60 X
single scoop = 0.40 X
no other information insufficient

statement 2
we are given the total and no other info again insufficient

combining 1 and 2

2*0.60X +0.40X = 120
1.20X +0.40X = 120
1.60X = 120
x=120/1.6 = 75

sufficient we didn't need to do the above steps we know there was 1 unknown and 1 equation

Answer is C

Statement 1:
Double scoop , D = 60% of Total, T
=> Single scoop, S= 40% of T
=> D/S=3/2

and D+S =T
Not suff to find T.

Statement 2:
2D +S =120
Not suff to find T.

However combining two statements we have 2 equations to find S and D. And hence we can find T.
Ans C.

Hello Bunuel,

Why can't we just assume that Y (double scope) = 2 X ?

So we will have X + 2 x = 120 hence B is enough.

Because we don't know whether the # of guests who were served a single scoop of ice-cream (x) equals to the # of guests who were served a double scoop ice-cream (y).
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What if there was 100 people at the party, then 60 people get a double scoop (so 120 scoops are given out), and 0 people get single scoops? Based on this my answer was E since the problem states that people are served EITHER a single scoop OR double scoop. How can you answer this question without knowing how many people are at the party?

This case is not possible because it violates info given in the stem: each of the guests was served either a single scoop or a double scoop ice-cream.

As for the # of the guests, we can get it when we combine the statements:
30 of the guests were served a single scoop of ice-cream;
45 of the guests were served a double scoop of ice-cream.

Total = 30 + 45 = 75 guests.

For more check here: at-a-certain-picnic-each-of-the-guests-was-served-either-a-140734.html#p1131491

Hope it helps.
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Hi Bunuel,

I seemed to make the same mistake and still can't figure out why it's wrong.

If we make equation B: S + 2S = 120, we get S = 40 and since 2S = D, the number of double scoops served to people were 80 scoops, therefore 40 double scoops therefore 40 people?

This equation doesn't take into account the number of people at the picnic, so how are you assuming that the number of guests who indulged in the single scoop to be the same as the double scoop?

OK, maybe examples will help...

(2) A total of 120 scoops of ice-cream were served to all the guests at the picnic.

We can have the following cases:

0 single scoop ice-cream and 60 double scoop ice-cream were served. Number of people = 0 + 60 = 60.
2 single scoop ice-cream and 59 double scoop ice-cream were served. Number of people = 2 + 59 = 61.
4 single scoop ice-cream and 58 double scoop ice-cream were served. Number of people = 4 + 58 = 62.
6 single scoop ice-cream and 57 double scoop ice-cream were served. Number of people = 6 + 57 = 63.
...
118 single scoop ice-cream and 1 double scoop ice-cream were served. Number of people = 118 + 1 = 119.
120 single scoop ice-cream and 0 double scoop ice-cream were served. Number of people = 120 + 0 = 120.

Please re-read carefully solution here: at-a-certain-picnic-each-of-the-guests-was-served-either-a-90254.html#p1041259
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Hi Bunuel, probably a silly question but can you please tell me how you got the second equation?

x is number of people served single scoop
y is number of people served double scoop.

So how can you assume that double the people had a double scoop??? x+2y=120

If x the # of people served single scoop, then how many scoops of ice-cream those x people consume? 1*x.
If y the # of people served double scoop, then how many scoops of ice-cream those y people consume? 2*y.

So, if x+y people consumed 120 scoops, then 1*x + 2*y = 120.
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\(5\,G\,\,{\rm{guests}}\,\,\,\left\{ \matrix{\\
\,x\,\,{\rm{guests}}\,\,\,::\,\,{\rm{one}}\,\,{\rm{2 - balls}}\,\,{\rm{ice - cream}}\,\,{\rm{each}} \hfill \cr \\
\,\left( {5G - x} \right)\,\,{\rm{guests}}\,\,\,::\,\,{\rm{one}}\,\,1{\rm{ - ball}}\,\,{\rm{ice - cream}}\,\,{\rm{each}} \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\,;\,\,\,\,\,\,\,\,\,\,\,? = x\,\,\)

\(\left( 1 \right)\,\,\,\,\,{x \over {5G}} = \,{3 \over 5}\,\,\,\,\, \Rightarrow \,\,\,\,x = 3G\,\,\,\left\{ \matrix{\\
\,{\rm{Take}}\,\,\left( {x,G} \right) = \left( {3,1} \right)\,\,\,\,\,\left[ {5G = 5} \right]\,\,\,\,\,\, \Rightarrow \,\,\,\,? = 3\,\,\, \hfill \cr \\
\,{\rm{Take}}\,\,\left( {x,G} \right) = \left( {6,2} \right)\,\,\,\,\,\left[ {5G = 10} \right]\,\,\,\,\,\, \Rightarrow \,\,\,\,? = 6\,\, \hfill \cr} \right.\)


\(\left( 2 \right)\,\,x \cdot 2 + \left( {5G - x} \right) \cdot 1 = 120\,\,\,\,\left[ {{\rm{balls}}\,\,{\rm{of}}\,\,{\rm{ice - cream}}} \right]\)

\(\left\{ \matrix{\\
\,{\rm{Take}}\,\,\left( {x,G} \right) = \left( {10,22} \right)\,\,\,\, \Rightarrow \,\,\,\,? = 10\,\,\, \hfill \cr \\
\,{\rm{Take}}\,\,\left( {x,G} \right) = \left( {20,20} \right)\,\,\,\, \Rightarrow \,\,\,\,? = 20\,\, \hfill \cr} \right.\)


\(\left( {1 + 2} \right)\,\,\,\left\{ \matrix{\\
\,x = 3G \hfill \cr \\
\,x \cdot 2 + \left( {5G - x} \right) \cdot 1 = 120 \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,G\,\,\,{\rm{unique}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,x\,\,\,{\rm{unique}}\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}{\rm{.}}\)


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

Regards,
Fabio.
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Given: At a certain picnic, each of the guests was served either a single scoop or a double scoop of ice cream.

Target question: How many of the guests were served a double scoop of ice cream?

Statement 1: At the picnic, 60 percent of the guests were served a double scoop of ice cream.
Since we have no information about the total number of people at the picnic, we can't answer the target question with certainty.
Statement 1 is NOT SUFFICIENT

Statement 2: A total of 120 scoops of ice cream were served to all the guests at the picnic.
There are several scenarios that satisfy statement 2. Here are two:
Case a: 118 people received 1 scoop, and 1 person received 2 scoops (for a total of 120 scoops). In this case, the answer to the target question is 1 person received two scoops
Case b: 116 people received 1 scoop, and 2 people received 2 scoops (for a total of 120 scoops). In this case, the answer to the target question is 2 people received two scoops
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Let S = the number of people who received a single scoop
Let D = the number of people who received a double scoop
This means S + D = the TOTAL number of people at the picnic.

Statement 1 tells us that the number of people who received a double scoop = 60% of the total number of people at the picnic
Substitute values to get: D = 0.6(S+ D)
Expand: D = 0.6S + 0.6D
Subtract D from both sides to get: 0 = 0.6S - 0.4D

Statement 2 tells us that A total of 120 scoops of ice cream were served to all the guests at the picnic.
S = the total number of scoops given to people who received 1 scoop, and 2D = the total number of scoops given to people who received 2 scoops.
So, we can write: S + 2D = 120

So, we now have the following system:
0 = 0.6S - 0.4D
0 = 0.6S - 0.4D

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 S and D, 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.

Answer: C

Cheers,
Brent

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