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

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15 Oct 2012, 04:41

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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.

Practice Questions Question: 61 Page: 280 Difficulty: 600

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

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15 Oct 2012, 04:41

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

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

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15 Oct 2012, 05:12

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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

Answer C _________________

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

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15 Oct 2012, 08:57

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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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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.

Practice Questions Question: 61 Page: 280 Difficulty: 600

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

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19 Oct 2012, 05:07

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

Answer: C.

Kudos points given to everyone with correct solution. Let me know if I missed someone. _________________

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

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23 Oct 2013, 05:25

What is the problem with my equation? What did I miss? A) Is clearly insufficient But for B) I tried this: 120 = 2*(0,6*x)+1*(0,4*x) With x being the # of people who had ice cream.

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

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23 Oct 2013, 06:49

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Marcoson wrote:

What is the problem with my equation? What did I miss? A) Is clearly insufficient But for B) I tried this: 120 = 2*(0,6*x)+1*(0,4*x) With x being the # of people who had ice cream.

You used info given in the first statement for the second statement. _________________

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

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04 Feb 2014, 18:20

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?

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

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05 Feb 2014, 01:43

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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.

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

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08 Feb 2015, 18:21

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

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24 May 2015, 04:06

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.

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