Is it the wording?

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jzw: Senior | Next Rank: 100 Posts; Posts: 79; Joined: Mon Feb 13, 2012 3:02 pmFollowed by: 3 members; Thanked: 2 times

by jzw » Mon Mar 05, 2012 9:20 am

#61 in the official guide - data sufficiency

"At a certain picnic, each of the guests were 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) A 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.

Stem: guests (x) either got ss (y) or ds (z).
Target: how many guests (x) got ds (z)?

AD BCE

(1) tells me that 60% of guests got ds while the remaining 40% got ss.
- no reference point with totals or partials in numbers so no way to know how much of something is what %.
- insufficient

BCE

(2) tells me the total number of scoops served.
- no reference point as to how many are double or single.
- insufficient

CE

the answer is C, I chose E. how are both sufficient? what am I not seeing with the wording? had they used the term "single scoops" or "double scoops" instead of the term "scoops" in statement (2) I'd see how to figure out the answer. but how does known the total number of scoops help? how do we know how many we're single or double? can someone pls show in idiot proof fashion. Thanks!

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Source: Beat The GMAT — Problem Solving | Mon Mar 05, 2012 9:20 am

Neo Anderson: Senior | Next Rank: 100 Posts; Posts: 92; Joined: Thu Oct 06, 2011 8:06 am; Thanked: 18 times

by Neo Anderson » Mon Mar 05, 2012 9:48 am

Stem: guests (x) either got ss (y) or ds (z).
Target: how many guests (x) got ds (z)?

AD BCE

(1) tells me that 60% of guests got ds while the remaining 40% got ss.
- no reference point with totals or partials in numbers so no way to know how much of something is what %.
- insufficient

BCE

(2) tells me the total number of scoops served.
- no reference point as to how many are double or single.
- insufficient

CE

you are absolutely right till this point, however, considering 1 and 2 together

from 1 and 2. => total guests 4N + 6N = 120

=> N=12

=> thus no of guests who were served with DS is 6N = 6 X 12 = 72
thus sufficient
and hence the answer C

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krusta80: Master | Next Rank: 500 Posts; Posts: 143; Joined: Mon Mar 14, 2011 3:13 amFollowed by: 5 members; Thanked: 34 times

by krusta80 » Mon Mar 05, 2012 1:55 pm

jzw wrote:#61 in the official guide - data sufficiency

"At a certain picnic, each of the guests were 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) At total of 120 scoops of ice cream were served to all the guests at the picnic.

Stem: guests (x) either got ss (y) or ds (z).
Target: how many guests (x) got ds (z)?

AD BCE

(1) tells me that 60% of guests got ds while the remaining 40% got ss.
- no reference point with totals or partials in numbers so no way to know how much of something is what %.
- insufficient

BCE

(2) tells me the total number of scoops served.
- no reference point as to how many are double or single.
- insufficient

CE

the answer is C, I chose E. how are both sufficient? what am I not seeing with the wording? had they used the term "single scoops" or "double scoops" instead of the term "scoops" in statement (2) I'd see how to figure out the answer. but how does known the total number of scoops help? how do we know how many we're single or double? can someone pls show in idiot proof fashion. Thanks!

Alrighty, let's see what we can do with this...

Let s denote the number of single scoops served
Let d denote the number of double scoops served

From part A, we are given:
d = .6 * (d+s), since d+s represents the total number of guests served
.4*d = .6*s
d = 3s/2

From part B, we are given:
s+2*d = 120 --> in other words, to get the total scoops, we count the single scoops once and the double scoops twice

Now we have two equations for two unknowns: s and d

Let's plug in 3s/2 for d in the second equation...

s+3s = 120
4s = 120
s = 30 single scoops served
d = 45 double scoops served

Answer is C

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jzw: Senior | Next Rank: 100 Posts; Posts: 79; Joined: Mon Feb 13, 2012 3:02 pmFollowed by: 3 members; Thanked: 2 times

by jzw » Mon Mar 05, 2012 3:37 pm

noticing that neo and krusta got the same end result (C) but used slightly different formulas in order to work them. only reason i'm asking is because the numbers end up different; is there a right or wrong way to get this? meaning, did one of these way accidentally lead to the correct answer whereas had said method been used in a different question it may have led us down to a different result? just want to make sure i understand the mechanics of how this works so i can replicate it on future problems. thanks for the assistance!

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krusta80: Master | Next Rank: 500 Posts; Posts: 143; Joined: Mon Mar 14, 2011 3:13 amFollowed by: 5 members; Thanked: 34 times

by krusta80 » Mon Mar 05, 2012 6:35 pm

jzw wrote:noticing that neo and krusta got the same end result (C) but used slightly different formulas in order to work them. only reason i'm asking is because the numbers end up different; is there a right or wrong way to get this? meaning, did one of these way accidentally lead to the correct answer whereas had said method been used in a different question it may have led us down to a different result? just want to make sure i understand the mechanics of how this works so i can replicate it on future problems. thanks for the assistance!

The reason Neo and I have different answers is because we are from different versions of the Matrix....

I kid.

The reason for our different numbers is that I interpreted the question quite literally by counting each double-scoop served as two scoops rather than one. Neo assumed that the number of scoops equalled the number of desserts served (aka a double-scoop is a type of scoop and a single scoop is a type of scoop).

I'm actually loving that we came up with different answers; it shows how data sufficiency can be solved without number crunching (sometimes).

At the heart of this problem is recognizing the key to solving for unknown variables: you need at least as many formulas as variables to do so. Each of us came up with two linear equations to solve for the number of single scoops and the number of double scoops, and we could have safely stopped there.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Mar 05, 2012 7:30 pm

Let the no. of people who were served single scoop of ice cream = S
and the no. of people who were served double scoop of ice cream = D

(1) At the picnic, 60 percent of the guests were served a double scoop of ice-cream.
Then S : D = 40 : 60 = 2 : 3, but using this we cannot find the value of D; NOT sufficient.

(2) A total of 120 scoops of ice-cream were served to all the guests at the picnic.
S + 2D = 120, which is again NOT sufficient to find D.

Combining (1) and (2), we have 2 equation: S = 2D/3 and S + 2D = 120
Solving we get, 2D/3 + 2D = 120; which can be solved for D; SUFFICIENT.

The correct answer is C.

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