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# A restaurant serves only tacos and enchiladas. If 60% of all who ate

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A restaurant serves only tacos and enchiladas. If 60% of all who ate  [#permalink]

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Updated on: 01 Oct 2016, 02:41
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85% (hard)

Question Stats:

48% (02:01) correct 52% (02:20) wrong based on 263 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.

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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Re: A restaurant serves only tacos and enchiladas. If 60% of all who ate  [#permalink]

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29 Sep 2016, 14:48
3
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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Re: A restaurant serves only tacos and enchiladas. If 60% of all who ate  [#permalink]

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30 Sep 2016, 21:28
1
joannaecohen wrote:
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

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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Re: A restaurant serves only tacos and enchiladas. If 60% of all who ate  [#permalink]

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09 Oct 2016, 02:32
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  [#permalink]

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09 Oct 2016, 02:35
1
yashrakhiani wrote:
is it allowed to assume that everybody ordered something? i think its not allowed on the gmat.

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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Re: A restaurant serves only tacos and enchiladas. If 60% of all who ate  [#permalink]

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18 Dec 2018, 13:23
keats wrote:
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.

$$? = x\,\,\,\,\left( {{\rm{see}}\,\,{\rm{figure}}} \right)$$

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

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

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

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

Regards,
Fabio.
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Re: A restaurant serves only tacos and enchiladas. If 60% of all who ate   [#permalink] 18 Dec 2018, 13:23
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