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

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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.

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


Guys, I am finding the explanation of the solution of this problem given in OG-12 insufficient .

can anyone please elaborate why the answer is C , IMO it should be E.
[Reveal] Spoiler: OA

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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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New post 14 Apr 2012, 13:13
Bunuel wrote:
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 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.

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Lstadt wrote:
Bunuel wrote:
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 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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New post 04 May 2014, 08:39
Bunuel wrote:
Lstadt wrote:

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).


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?

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russ9 wrote:
Bunuel wrote:
Lstadt wrote:

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).


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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New post 07 May 2014, 04:07
G = total guests
G.4= Get a single scoop
G.6= Get 2 scoops
G.4 + 2(G.6) = 120 scoops
G1.6=120
G= 5/8 *120 = 75
G*.6 = 45

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Lstadt wrote:
Bunuel wrote:
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 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.



I too faced the same issue and later realized the reason for confusion. The short answer, I believe, is ambiguity: the question leaves some room for interpretation of the wordings.

Let's look at the specific part of the question:
....A total of 120 scoops of ice cream were served....

This can be interpreted in two ways:
1. scoops as 'servings'
This would mean a total of 120 servings of ice cream were given out.
Clearly then, the answer cannot be derived since we cannot compute what proportion of those 120 servings were 1 scoop variants versus the proportion of servings that were 2 scoop varients.

2. Scoops as, well, individual scoops of ice cream
Here, the interpretation is that '120 scoops' refers to total count (or sum) of scoops that had been served (i.e. the sum of single + double scoops. If I served 1 single scoop and 1 double scoop, then the total number of scoops served would be 1+2=3)

Then the problem is definitely solvable.
How?
The problem provides the information that they were in the ratio 2:1 (The ratio of 1-scoop servings to 2-scoop servings)

Thus, I could set up the equation x + 2x =120
where x= number of single scoops given out and
2x= number of double scoops given out.

I just hope such ambiguous questions will not pop up during the official exam attempt.

Eh, on second thought, it wouldn't matter: The pace and environment in the test center will make everything such a blur that one wouldn't even be in a position to detect ambiguity in hind sight :lol:

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New post 13 Jan 2016, 21:40
Bunuel wrote:
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.


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

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sarathvr wrote:
Bunuel wrote:
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.


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

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New post 15 Dec 2017, 07:35
amod243 wrote:
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.

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


Guys, I am finding the explanation of the solution of this problem given in OG-12 insufficient .

can anyone please elaborate why the answer is C , IMO it should be E.



Let the guests who took Double Scoop : D
Let the guests who took Single Scoop : S

Total Guests comprise of all people who took Single scoop & Double scoops = D + S . There fore G = D + S - Equation 1

Statement 1: .6(D+S)=D ( As it is stated that 60 % of guests had double scoops) ( Alone insufficient)
Statement 2: D + S = 120 ( Alone insufficient)

Therefore together we have 2 variables & 2 equations. Hence C

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Re: At a certain picnic, each of the guests was served either a   [#permalink] 15 Dec 2017, 07:35
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