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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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Math Expert V
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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: $$\frac{2}{3}y+2y=120$$ --> $$y=45$$)

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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)
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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

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

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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

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

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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.

Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

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
Page: 280
Difficulty: 600

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

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

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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?
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HCalum11 wrote:
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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Bunuel 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:

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.

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

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First theory (from MGMAT)

Concrete value
If a Data Sufficiency question asks for the concrete value of one element of a ratio, you will need
BOTH the concrete value of another element of the ratio AND the relative value of two elements
of the ratio.

Relative value
If a Data Sufficiency question asks for the relative value of two pieces of a ratio, ANY statement
that gives the relative value of ANY two pieces of the ratio will be sufficient.

We can solve this question using ratios
D= # of double-Scoop portions served
T= # Total portions served

(1) At the picnic, 60 percent of the guests were served a double scoop of ice cream.
This statement tells us that the ratio of D/T = 3/5 Not Sufficient (See explanation above - we are asked to find the concrete Value)

(2) A total of 120 scoops of ice cream were served to all the guests at the picnic.
Not sufficient because we need add. a ratio od D/T to answer this question

(1+2) D/S = 3/5 so we have 3x+5x = 120
X = 15 --> D=3*15 =45 (C) Correct, can be calculated, BUT if you know the theory you don't need to calculate by DS Questions, it's enoough to know whether it can be calculated or not.

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

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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: $$\frac{2}{3}y+2y=120$$ --> $$y=45$$)

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: $$\frac{2}{3}y+2y=120$$ --> $$y=45$$)

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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GMAT 1: 600 Q44 V27 Re: At a certain picnic, each of the guests was served either a  [#permalink]

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Why not do:

1)3/5(total)=double

2)total=120

1)+2) sufficient.

Am I oversimplifying this?
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Re: At a certain picnic, each of the guests was served either a  [#permalink]

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I have a question here:

Why cant we do this? x being a single sccop of ice cream: x+ 2x= 120 , hence x =40 , 2x =80 => no of people = 40

and B sufficient.

+Bunuel
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pkh99 wrote:
I have a question here:

Why cant we do this? x being a single sccop of ice cream: x+ 2x= 120 , hence x =40 , 2x =80 => no of people = 40

and B sufficient.

+Bunuel

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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