OG 61 - scoops

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OG 61 - scoops

by szDave » Thu Apr 11, 2013 1:28 am
61. 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.

How do you solve this question?

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by Anju@Gurome » Thu Apr 11, 2013 1:35 am
szDave wrote:61. 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 us assume the number of guests who are served single scoop is S and the number of guests who are served double scoop is D
So, total number of guests = S + D

We need to determine D.

Statement 1: D = 0.60(S + D)
As we don't know S, we cannot solve D.

Not sufficient

Statement 2: S + 2D = 120
As we don't know S, we cannot solve D.

Not sufficient

1 & 2 Together: We have 2 independent equation in 2 variables, which can be solved to find D.

Sufficient

The correct answer is C.
Last edited by Anju@Gurome on Thu Apr 11, 2013 3:57 am, edited 1 time in total.
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by GMATGuruNY » Thu Apr 11, 2013 3:39 am
szDave wrote:61. 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.

How do you solve this question?
Statement 2: Total scoops = 120
No way to determine the number of double-scoop guests.
INSUFFICIENT.

Statement 1: At the picnic, 60 percent of the guests were served a double scoop of ice cream
Thus, of every 100 guests:
60 guests received 2 scoops each, for a total of 120 scoops.
40 guests received 1 scoop each, for a total of 40 scoops.
Thus, of every 160 scoops, the fraction received by the double-scoop guests = 120/160 = 3/4.
No way to determine the number of double-scoop guests.
INSUFFICIENT.

Statement combined:
The double-scoop guests received 3/4 of the total number of scoops:
(3/4)120 = 90.
Since each of these guests received 2 scoops, the number of double-scoop guests = 90/2 = 45.
SUFFICIENT.

The correct answer is C.
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by GMATGuruNY » Thu Apr 11, 2013 3:52 am
Anju's approach above is great. Just one clarification:

Statement 2: Total scoops = 120
If S = the number of single-scoop guests and D = the number of double-scoop guests, then the equation here should read as follows:
S + 2D = 120.
The reason is that each double-scoop guest received 2 scoops.
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by Anju@Gurome » Thu Apr 11, 2013 4:01 am
GMATGuruNY wrote:Anju's approach above is great. Just one clarification:
Thanks for pointing it out, Mitch.
I've edited my reply.
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by Scott@TargetTestPrep » Tue Oct 30, 2018 10:24 am
szDave wrote:61. 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.
We are given that at a certain picnic, each of the guests was served either a single scoop or a double scoop of ice cream. Let's define two variables describing the number of scoops of ice cream for the picnic guests.

s = number of guests who received a single scoop of ice cream

d = number of guests who received a double scoop of ice cream

We need to determine how many of the guests were served a double scoop; that is, we need to determine the value of variable d.

Statement One Alone:

At the picnic, 60% of the guests were served a double scoop of ice cream.

Since we only know the percentage of the guests who were served a double scoop of ice cream and we do not know the total number of guests, we cannot determine the number of guests who were served a double scoop of ice cream, and thus we cannot determine a value for d. Statement one alone is not sufficient to answer the question.
Statement Two Alone:

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

Since we know that 120 scoops of ice cream were served to all the guests at the picnic, and each single scoop has 1 scoop and each double scoop has 2 scoops, we can create the following equation:

s + 2d = 120

We cannot determine a value for d. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Let t = total number of guests. From statement one, d = 0.6t. Furthermore, s = 0.4t. From statement two, we know s + 2d = 120. Rewriting the equation in terms of t, we have:

0.4t + 2(0.6t) = 120

0.4t + 1.2t = 120

1.6t = 120

t = 75

Since t = 75, d = 0.6 x 75 = 45. Thus, there were 75 guests, and 45 of them were served a double scoop of ice cream.

Answer: C

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