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Joe’s pie shop serves only chocolate pies and coconut crea

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by vinni.k » Sat Mar 11, 2017 8:59 am
Joe's pie shop serves only chocolate pies and coconut cream pies. On a given day, Joe sold 200 pies, with each customer buying either one coconut cream pie, one chocolate pie, or one of each. If 80 customers bought both a coconut cream and a chocolate pie, how many chocolate pies did Joe sell?

1. 40 customers did not buy a chocolate pie.
2. 120 customers bought a coconut cream pie.

OA is D

Is the following table correct ?
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sat Mar 11, 2017 9:06 am
Be careful.

I also made the mistake of assuming that 200 represents the total number of customers, when it actually represents the number of PIES sold.

We know that each shopper bought EITHER 1 pie OR 2 pies.
We're told that 80 customers bought both a coconut cream and a chocolate pie. So, those 80 customers accounted for 160 pies sold.
The remaining 40 pies were sold 1 per customer. So, this accounts for another 40 customers.

So, the TOTAL number of customers = 80 + 40 = 120 (not 200)




Aside: for others wondering about the table, this approach is known as the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of students, and the two characteristics are:
- bought chocolate pie or did not buy chocolate pie
- bought coconut cream pie or did not buy coconut cream pie

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Sat Mar 11, 2017 3:36 pm, edited 1 time in total.
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by [email protected] » Sat Mar 11, 2017 10:56 am
Hi vinni.k,

There's a problem with your table. I'm going to give you a hint so that you can reattempt this question:

[spoiler]According to the prompt, 80 people bought BOTH a chocolate pie and a coconut cream pie - so that's a total of 160 pies sold. Your table should either focus on the number of pies sold OR the number of total customers - but the rows and columns can't do both[/spoiler]

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Contact Rich at [email protected]
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by vinni.k » Sun Mar 12, 2017 4:30 am
[email protected] wrote:Your table should either focus on the number of pies sold OR the number of total customers - but the rows and columns can't do both
Brent@GMATPrepNow wrote:assuming that 200 represents the total number of customers, when it actually represents the number of PIES sold
We know that each shopper bought EITHER 1 pie OR 2 pies.
We're told that 80 customers bought both a coconut cream and a chocolate pie. So, those 80 customers accounted for 160 pies sold.
The remaining 40 pies were sold 1 per customer. So, this accounts for another 40 customers.

So, the TOTAL number of customers = 80 + 40 = 120 (not 200)
So, lets take the TOTAL number of customers = 80 + 40 = 120
Statement 1 says - 40 customers did not buy a chocolate pie. (so this fills the remaining number of 40 customers out of 120)

Statement 2 says - 120 customers bought a coconut cream pie.
please check the table below for both the statements about focusing only on the customers & please also check the explanation from veritas book that considers 200 as total no. of customers(my next post)
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by vinni.k » Sun Mar 12, 2017 4:34 am
200 as total number of customers. According to this explanation i made first matrix table and got 160 for number of customers who bought chocolate pie.
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by Brent@GMATPrepNow » Sun Mar 12, 2017 7:26 am
vinni.k wrote: So, lets take the TOTAL number of customers = 80 + 40 = 120
Statement 1 says - 40 customers did not buy a chocolate pie. (so this fills the remaining number of 40 customers out of 120)

Statement 2 says - 120 customers bought a coconut cream pie.
please check the table below for both the statements about focusing only on the customers & please also check the explanation from veritas book that considers 200 as total no. of customers(my next post)
That new table looks good.
I think the Veritas people will agree that there are 160 customers (and 200 pies sold)

Cheers,
Brent
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by vinni.k » Sun Mar 12, 2017 10:24 am
Is the table for 200 pies with 160 customers correct ? if it is, then how can i justify statement 2 - 120 customers bought a coconut cream pie.
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by DavidG@VeritasPrep » Sun Mar 12, 2017 10:43 am
That new table looks good.
I think the Veritas people will agree that there are 160 customers (and 200 pies sold)

Cheers,
Brent
I'll double-check with the author for the intent, but yep, according to the prompt as written there had to have been 120 customers for those 200 pies sold. (If 80 people purchased both, that's 80 chocolate and 80 coconut pies purchased. If 40 people did not buy chocolate and everyone bought pies, those 40 had to have purchased coconut pies. So we've got 80 people who purchased both pies (160 pies total) and 40 who purchased only coconut pies, for a total of 120 customers.
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by DavidG@VeritasPrep » Sun Mar 12, 2017 10:46 am
vinni.k wrote:Is the table for 200 pies with 160 customers correct ? if it is, then how can i justify statement 2 - 120 customers bought a coconut cream pie.
Careful: we can make a table for customers - someone can purchase both a coconut and a chocolate pie, so that "both" category is perfectly logical. But we can't do it for pies, as a pie cannot be both chocolate and coconut cream. (At least in the context of this question. Chocolate coconut cream pies do exist, and no decent human should be forced to live in a world in which they didn't.)
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by Brent@GMATPrepNow » Sun Mar 12, 2017 10:51 am
DavidG@VeritasPrep wrote:Chocolate coconut cream pies do exist, and no decent human should be forced to live in a world in which they didn't.
Truer words were never been spoken!
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by vinni.k » Mon Mar 13, 2017 8:45 am
Thank you for clarifying the doubt :D
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