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keats
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A restaurant serves only tacos and enchiladas. If 60% of all who ate Updated on: 01 Oct 2016, 02:41
Originally posted by keats on 29 Sep 2016, 14:19.
Last edited by Bunuel on 01 Oct 2016, 02:41, edited 1 time in total.
RENAMED THE TOPIC.
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Difficulty:

85% (hard)

Question Stats:

49% (02:04) correct 51% (02:16) wrong based on 480 sessions

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A restaurant serves only tacos and enchiladas. If 60% of all who ate at the restaurant on a certain day ordered tacos, what percentage of those who ate at the restaurant ordered enchiladas that day?

(1) Half of those who ordered tacos also ordered enchiladas.
(2) 3/4 as many people ordered both enchiladas and tacos as ordered only enchiladas.
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D
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A restaurant serves only tacos and enchiladas. If 60% of all who ate 29 Sep 2016, 14:48
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I think this problem is missing stating that everyone ordered food at the restaurant that day. Can anyone Bunuel clarify this?

If this is assumed you can get to D, if not it would be E.

Lets assume the number of people is 100 (works well w/ %)
If 60% ordered tacos then 60 people ordered tacos and 40 ordered enchiladas.


(1) Half of those who ordered tacos also ordered enchiladas.

If 60 ppl ordered tacos, then 30 of those ordered enchiladas. If we assume everyone ordered something then we know 30 ordered ONLY tacos, meaning 70 ordered Enchiladas (70%)
suff

(2) 3/4 as many people ordered both enchiladas and tacos as ordered only enchiladas.

If we know 60 people ordered tacos set the number of people who ordered only enchiladas to x. Then the people who ordered both tacos and enchiladas is .75x. Because everyone ordered some food we know that the number of people who didn't order tacos is 40 (if 60 ordered tacos then 40 didn't). .75 of that number is 30 30+40=70 or 70%

suff
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A restaurant serves only tacos and enchiladas. If 60% of all who ate 30 Sep 2016, 21:28
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joannaecohen
I think this problem is missing stating that everyone ordered food at the restaurant that day. Can anyone Bunuel clarify this?

If this is assumed you can get to D, if not it would be E.

Lets assume the number of people is 100 (works well w/ %)
If 60% ordered tacos then 60 people ordered tacos and 40 ordered enchiladas.


(1) Half of those who ordered tacos also ordered enchiladas.

If 60 ppl ordered tacos, then 30 of those ordered enchiladas. If we assume everyone ordered something then we know 30 ordered ONLY tacos, meaning 70 ordered Enchiladas (70%)
suff

(2) 3/4 as many people ordered both enchiladas and tacos as ordered only enchiladas.

If we know 60 people ordered tacos set the number of people who ordered only enchiladas to x. Then the people who ordered both tacos and enchiladas is .75x. Because everyone ordered some food we know that the number of people who didn't order tacos is 40 (if 60 ordered tacos then 40 didn't). .75 of that number is 30 30+40=70 or 70%

suff
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Well said, i was making that dangerous assumption too...and I hate doing that because I have been burned before assuming in sets problems that "everyone ordered something" or similar. I set it up as a simple A/Not A table and since percentages were used I just made the total out of 100.

Well explained joannaecohen
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A restaurant serves only tacos and enchiladas. If 60% of all who ate 09 Oct 2016, 02:32
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is it allowed to assume that everybody ordered something? i think its not allowed on the gmat.
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A restaurant serves only tacos and enchiladas. If 60% of all who ate 09 Oct 2016, 02:35
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yashrakhiani
is it allowed to assume that everybody ordered something? i think its not allowed on the gmat.
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Yes, you are right. Assuming these things is NOT allowed on GMAT.

But for this question, we are clearly mentioned that "60% of all who ate at the restaurant ". I hope its clear now.
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A restaurant serves only tacos and enchiladas. If 60% of all who ate 18 Dec 2018, 13:23
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keats
A restaurant serves only tacos and enchiladas. If 60% of all who ate at the restaurant on a certain day ordered tacos, what percentage of those who ate at the restaurant ordered enchiladas that day?

(1) Half of those who ordered tacos also ordered enchiladas.
(2) 3/4 as many people ordered both enchiladas and tacos as ordered only enchiladas.
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\(? = x\,\,\,\,\left( {{\rm{see}}\,\,{\rm{figure}}} \right)\)




\(\left( 1 \right)\,\,\,\left[ {{\rm{Blue}}} \right]\,\,\,100 = 60 + x - 30\,\,\,\left( {{\rm{simplifier}}} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,x\,\,{\rm{unique}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.\)


\(\left( 2 \right)\,\,\,\left[ {{\rm{Red}}} \right]\,\,\,\,\left\{ \matrix{\\
{3 \over 4}\left( {x - {\rm{both}}} \right) = {\rm{both}}\,\,\,\,\,\left( {\rm{I}} \right) \hfill \cr \\
100 = 60 + \left( {x - {\rm{both}}} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,40 = x - {\rm{both}}\,\,\,\,\,\left( {{\rm{II}}} \right)\,\,\, \hfill \cr} \right.\)

\(\left( {\rm{I}} \right)\,\,{\rm{in}}\,\,\left( {{\rm{II}}} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,40 = {4 \over 3}\left( {{\rm{both}}} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{both}} = 30\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {{\rm{II}}} \right)} \,\,\,\,\,\,x\,\,{\rm{unique}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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A restaurant serves only tacos and enchiladas. If 60% of all who ate 03 Dec 2020, 09:23
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can someone explain this using 2*2 matrix ? I got C using that.
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A restaurant serves only tacos and enchiladas. If 60% of all who ate 03 Dec 2020, 12:21
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keats
A restaurant serves only tacos and enchiladas. If 60% of all who ate at the restaurant on a certain day ordered tacos, what percentage of those who ate at the restaurant ordered enchiladas that day?

(1) Half of those who ordered tacos also ordered enchiladas.
(2) 3/4 as many people ordered both enchiladas and tacos as ordered only enchiladas.
Show more

To organize the data, use the following matrix:

The center box -- which represents neither tacos nor enchiladas -- has a value of 0 because everyone who eats at the restaurant must order tacos and/or enchiladas, the only two foods available.

Prompt: 60% of all who ate at the restaurant on a certain day ordered tacos.
The following matrix is yielded:

Note:
In the resulting matrix, only enchiladas = 40.

Statement 1: Half of those who ordered tacos also ordered enchiladas
Since half of the 60 taco-eaters also ordered enchiladas, both tacos and enchiladas = 30.
The following matrix is yielded:

Thus, total enchiladas = 70.
SUFFICIENT.

Statement 2: 3/4 as many people ordered both enchiladas and tacos as ordered only enchiladas
Since only enchiladas = 40, both enchiladas and tacos \(= \frac{3}{4}*40 = 30\).
The following matrix is yielded:

Thus, total enchiladas = 70.
SUFFICIENT.

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D

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A restaurant serves only tacos and enchiladas. If 60% of all who ate 23 Apr 2023, 17:00
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Quote:
is it allowed to assume that everybody ordered something? i think its not allowed on the gmat.
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For those who need clarity on this, it's in the Stem:
Quote:
A restaurant serves only tacos and enchiladas...
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Since the question is only concerned with those who ate, and since the restaurant only serves tacos and enchiladas, you can safely make a Venn Diagram assuming only tacos and enchiladas
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A restaurant serves only tacos and enchiladas. If 60% of all who ate 06 Jan 2025, 10:49
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notice how it says the restaurant only serves tacos & enchiladas. so answer should be D
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