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Scoops of ice cream

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by tonebeeze » Tue Mar 29, 2011 7:00 pm
At a picnic, each of the guests was served either a single scoop or 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.


I got the answer correct, but can someone walk me through the algebra so that I work on my algebraic translations. Thanks.

OA = C
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Source: — Data Sufficiency |

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by Anurag@Gurome » Tue Mar 29, 2011 7:24 pm
tonebeeze wrote:At a picnic, each of the guests was served either a single scoop or 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.


I got the answer correct, but can someone walk me through the algebra so that I work on my algebraic translations. Thanks.

OA = C
Let no. of guests who are served single scoop = S
Let no. of guests who are served double scoop = D
So, total no. of guests = S + D

(1) D = 0.60(S + D), one equation, two variables. So, (1) is NOT SUFFICIENT.
(2) S + D = 120, one equation, two variables. So, (2) is NOT SUFFICIENT.

Combining (1) and (2), we get 0.4D = 0.6S and S + D = 120, we have 2 equation, 2 variables, which can be solved to find D. Hence, SUFFICIENT.
The correct answer is C.
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by GMATGuruNY » Wed Mar 30, 2011 12:40 am
tonebeeze wrote:At a picnic, each of the guests was served either a single scoop or 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.
.
Anurag's approach is great for anyone comfortable with the algebra. Please note, however, that the equation for statement 2 should be S + 2D = 120:
Total number of scoops = 120.
S = number of scoops served to the single-scoop guests.
2D = number of scoops served to the double-scoop guests.
Thus, S + 2D = 120.

Here's an approach that bypasses the algebra:

Statement 1: 60 percent of the guests were served a double scoop.
Plug in a number in order to determine what fraction of the scoops were served to the double-scoop guests.
Let guests = 10.
Then .6*10 = 6 guests were served a double scoop, 10-6 = 4 guests were served a single scoop.
The number of scoops served to the 6 double-scoop guests = 2*6 = 12, the number of scoops served to the 4 single-scoop guests = 1*4 = 4.
Total scoops = 12+4 = 16.
Thus, the double-scoop guests were served 12/16 = 3/4 of the scoops.
No way to determine the number of double-scoop guests.
Insufficient.

Statement 2: A total of 120 scoops were served.
No way to determine the number of double-scoop guests.
Insufficient.

Statements 1 and 2 combined:
The double-scoops guests were served 3/4 * 120 = 90 scoops.
Since each double-scoop guest was served 2 scoops, the number of double-scoop guests = 90/2 = 45.
Sufficient.

The correct answer is C.
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by Strongt » Wed May 04, 2011 2:06 am
Is it a rule of thumb that whenever we have an unknown varibable, we need two linear equations to solve for the unknown?
I get similar questions a lot on DS and I find it to be my weakness point.
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by djiddish98 » Thu May 05, 2011 12:34 pm
Strongt wrote:Is it a rule of thumb that whenever we have an unknown varibable, we need two linear equations to solve for the unknown?
I get similar questions a lot on DS and I find it to be my weakness point.
Look out for when the DS is setup like this...

What is 2x + 3y?

Statement 1 - 4x+6y = 8

There are two variables, but if you divide statement 1 by 2, you end up solving for 2x+3y.

For this question - I got a little thrown by the wording. When it asked for how many, I thought at first that 60% could be an answer. Perhaps something like "what is the total number of guests that received 2 scoops" would be better language.
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