GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 17 Oct 2019, 03:31

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Schezwan restaurant offers 5 chicken, prawn, beef, vegetable & tofu

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
B
Joined: 08 Aug 2018
Posts: 40
Location: India
GMAT 1: 720 Q49 V40
GPA: 4
WE: Engineering (Energy and Utilities)
Schezwan restaurant offers 5 chicken, prawn, beef, vegetable & tofu  [#permalink]

Show Tags

New post 23 Sep 2018, 01:40
6
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

34% (01:32) correct 66% (01:42) wrong based on 67 sessions

HideShow timer Statistics

Schezwan restaurant offers 5 chicken, prawn, beef, vegetable & tofu entrees served with either garlic or chili sauce. In how many ways can 3 entrees be served if no entry is served more than once?

A. 10
B. 60
C. 80
D. 100
E. 120
Most Helpful Expert Reply
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4006
Location: Canada
Re: Schezwan restaurant offers 5 chicken, prawn, beef, vegetable & tofu  [#permalink]

Show Tags

New post 23 Sep 2018, 09:17
4
Top Contributor
1
PLUTO wrote:
Schezwan restaurant offers 5 chicken, prawn, beef, vegetable & tofu entrees served with either garlic or chili sauce. In how many ways can 3 entrees be served if no entry is served more than once?
Answer Options: -

A. 10
B. 60
C. 80
D. 100
E. 120


Take the task of creating a meal and break it into stages.

Stage 1: Select 3 entrees
Since the order in which we select the entrees does not matter, we can use combinations.
We can select 3 entrees from 5 entrees in 5C3 ways (10 ways)
So, we can complete stage 1 in 10 ways

If anyone is interested, we have a video (below) on calculating combinations (like 5C3) in your head

ASIDE: We now have our 3 entrees, but we don't have a sauce for each entree.

Stage 2: Choose a sauce for one of of the entrees
We have 2 choices (garlic or chili sauce), so we can complete stage 2 in 2 ways

Stage 3: Choose a sauce for another entree
We have 2 choices (garlic or chili sauce), so we can complete stage 3 in 2 ways

Stage 4: Choose a sauce for the last remaining entree
We have 2 choices (garlic or chili sauce), so we can complete stage 4 in 2 ways

By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus create a meal) in (10)(2)(2)(2) ways (= 80 ways)

Answer: C

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

RELATED VIDEOS



_________________
Test confidently with gmatprepnow.com
Image
General Discussion
Intern
Intern
avatar
B
Joined: 19 Sep 2018
Posts: 16
Re: Schezwan restaurant offers 5 chicken, prawn, beef, vegetable & tofu  [#permalink]

Show Tags

New post 23 Sep 2018, 02:06
2
I would say it is a tricky question since it is ambiguous.
There are 2 sources of confusion:
1) Do we count chicken, prawn, beef, and chicken, beef, prawn as same or as a different way of serving? I guess we can conclude that in one way, so we will need divide by 3!
2) Do we serve a sauce on the entree? Can we order a garlic chicken and chili beef? So we need to multiply by 8? can we order chicken without sauce? We will need to multiply by 27. Do we get a sauce in Panda Express way, we will need to multiply by 2, 3 or 4 depends on whether we can reject both or take both.

Anyway, with all this in mind, we can calculate that we have 5*4*3=60/3! = 10 * 8 = 80
Since answer C
But if you will calculate an ordered permutation 60 and multiply by 2 Panda Express style, you will get incorrect 120
Manager
Manager
User avatar
S
Joined: 17 Mar 2018
Posts: 70
Reviews Badge
Re: Schezwan restaurant offers 5 chicken, prawn, beef, vegetable & tofu  [#permalink]

Show Tags

New post 23 Sep 2018, 06:32
Can someone help solve this question with a clear method?
Intern
Intern
avatar
B
Joined: 08 Aug 2018
Posts: 40
Location: India
GMAT 1: 720 Q49 V40
GPA: 4
WE: Engineering (Energy and Utilities)
Re: Schezwan restaurant offers 5 chicken, prawn, beef, vegetable & tofu  [#permalink]

Show Tags

New post 23 Sep 2018, 06:37
Hi,

I am really confused.

1> I first tried to answer assuming ordered permutation way and got 120.
2> If it is not ordered but rather a combination of 3 items (out of chicken/beef/prawn/veg/tofu) in one entry, then their should be 5C3 ways of combining them - 10 ways which then should be multiplied by 2 ways of adding sauce. So the answer was 20.

Can someone please clearly lay down the strategy if there are subtle nuances in the question?
Manager
Manager
avatar
B
Joined: 12 Mar 2018
Posts: 110
Re: Schezwan restaurant offers 5 chicken, prawn, beef, vegetable & tofu  [#permalink]

Show Tags

New post 23 Sep 2018, 08:58
could anyone explain the solution please? I cannot reach 80 anyhow.
Manager
Manager
avatar
B
Joined: 12 Mar 2018
Posts: 110
Re: Permutation & Combination question  [#permalink]

Show Tags

New post 23 Sep 2018, 09:34
thank you GMATPrepNow
this is hard to conceive, probably i've never faced this type of question
Intern
Intern
avatar
B
Joined: 12 Jan 2017
Posts: 34
Location: United States (NY)
Schools: Booth '21 (D)
GMAT 1: 710 Q47 V41
GPA: 3.48
Re: Schezwan restaurant offers 5 chicken, prawn, beef, vegetable & tofu  [#permalink]

Show Tags

New post 23 Sep 2018, 11:52
GMATPrepNow wrote:
PLUTO wrote:
Schezwan restaurant offers 5 chicken, prawn, beef, vegetable & tofu entrees served with either garlic or chili sauce. In how many ways can 3 entrees be served if no entry is served more than once?
Answer Options: -

A. 10
B. 60
C. 80
D. 100
E. 120


Take the task of creating a meal and break it into stages.

Stage 1: Select 3 entrees
Since the order in which we select the entrees does not matter, we can use combinations.
We can select 3 entrees from 5 entrees in 5C3 ways (10 ways)
So, we can complete stage 1 in 10 ways

If anyone is interested, we have a video (below) on calculating combinations (like 5C3) in your head

ASIDE: We now have our 3 entrees, but we don't have a sauce for each entree.

Stage 2: Choose a sauce for one of of the entrees
We have 2 choices (garlic or chili sauce), so we can complete stage 2 in 2 ways

Stage 3: Choose a sauce for another entree
We have 2 choices (garlic or chili sauce), so we can complete stage 3 in 2 ways

Stage 4: Choose a sauce for the last remaining entree
We have 2 choices (garlic or chili sauce), so we can complete stage 4 in 2 ways

By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus create a meal) in (10)(2)(2)(2) ways (= 80 ways)

Answer: C

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

RELATED VIDEOS




Why do you have so many stages? Why wouldn't it be just two stages? I thought of just 2, the entrees and the sauces. So it would be 20 in total, or 5C3 * 2.
Another way I thought of was if you cannot repeat an entree, there are 24 options (5*2 + 4*2 + 3*2).

Can you explain why both of these solutions are wrong?
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4006
Location: Canada
Re: Schezwan restaurant offers 5 chicken, prawn, beef, vegetable & tofu  [#permalink]

Show Tags

New post 23 Sep 2018, 13:43
Top Contributor
RefError wrote:
Why do you have so many stages?


It helps to avoid errors :)

RefError wrote:
I thought of just 2, the entrees and the sauces. So it would be 20 in total, or 5C3 * 2.
Another way I thought of was if you cannot repeat an entree, there are 24 options (5*2 + 4*2 + 3*2).
Can you explain why both of these solutions are wrong?


What do your values stand for?

While my solution might LOOK longer than it needs to be, I don't write out every stage on my notepad. HOWEVER, I make it very clear to myself what each is occurring at each stage.
So, for example, in your 2-stage solution, 5C3 * 2, what does 5C3 represent and what does 2 represent?

Likewise, in your other solution, 5*2 + 4*2 + 3*2, what does each part represent?

Once you start articulating what each stage represents, your solutions will improve.

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4006
Location: Canada
Re: Schezwan restaurant offers 5 chicken, prawn, beef, vegetable & tofu  [#permalink]

Show Tags

New post 23 Sep 2018, 13:44
Top Contributor
faltan wrote:
thank you GMATPrepNow
this is hard to conceive, probably i've never faced this type of question


It's a tricky question.
It's also poorly-worded.

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
Intern
Intern
avatar
B
Joined: 12 Jan 2017
Posts: 34
Location: United States (NY)
Schools: Booth '21 (D)
GMAT 1: 710 Q47 V41
GPA: 3.48
Re: Schezwan restaurant offers 5 chicken, prawn, beef, vegetable & tofu  [#permalink]

Show Tags

New post 24 Sep 2018, 07:23
GMATPrepNow wrote:
RefError wrote:
Why do you have so many stages?


It helps to avoid errors :)

RefError wrote:
I thought of just 2, the entrees and the sauces. So it would be 20 in total, or 5C3 * 2.
Another way I thought of was if you cannot repeat an entree, there are 24 options (5*2 + 4*2 + 3*2).
Can you explain why both of these solutions are wrong?


What do your values stand for?

While my solution might LOOK longer than it needs to be, I don't write out every stage on my notepad. HOWEVER, I make it very clear to myself what each is occurring at each stage.
So, for example, in your 2-stage solution, 5C3 * 2, what does 5C3 represent and what does 2 represent?

Likewise, in your other solution, 5*2 + 4*2 + 3*2, what does each part represent?

Once you start articulating what each stage represents, your solutions will improve.

Cheers,
Brent


Okay, here you go...
1. Why do you have 4 stages rather than two? You have 4 stages for entree * sauce * sauce * sauce. Why? Why not two stages for Entrees and Sauces. With two stages you would do the exact same thing you did, but without the additional two stage. 5C3 (choose 3 entrees from five entrees) * 2 (sauces).
2. Why is it also not appropriate to calculate as Option 1 + Option 2 + Option 3? Option 1 = 5 entrees * 2 sauces. Option 2 = 4 entrees * 2 sauces. Option 3 = 3 entrees * 2 sauces.
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4006
Location: Canada
Re: Schezwan restaurant offers 5 chicken, prawn, beef, vegetable & tofu  [#permalink]

Show Tags

New post 24 Sep 2018, 07:49
Top Contributor
RefError wrote:
1. Why do you have 4 stages rather than two? You have 4 stages for entree * sauce * sauce * sauce. Why? Why not two stages for Entrees and Sauces. With two stages you would do the exact same thing you did, but without the additional two stage. 5C3 (choose 3 entrees from five entrees) * 2 (sauces).

It would help if you actually defined each stage.
For example:
STAGE 1: Choose 3 entrees
This stage can be completed in 5C3 (aka 10) ways

STAGE 2: What is happening here?
Is it "Choose a sauce"?
If so, which entree are you choosing a sauce for? Each entree must have its own accompanying sauce.
So, for example, ONE outcome (aka meal) might be: chicken with chili sauce, beef with garlic sauce, and vegetable with chili sauce

RefError wrote:
Okay, here you go...
2. Why is it also not appropriate to calculate as Option 1 + Option 2 + Option 3? Option 1 = 5 entrees * 2 sauces. Option 2 = 4 entrees * 2 sauces. Option 3 = 3 entrees * 2 sauces.


This looks like you are repeating many possible meals. So, your answer will be far too big.
_________________
Test confidently with gmatprepnow.com
Image
Intern
Intern
avatar
B
Joined: 29 Nov 2015
Posts: 5
Re: Schezwan restaurant offers 5 chicken, prawn, beef, vegetable & tofu  [#permalink]

Show Tags

New post 23 Apr 2019, 11:50
GMATPrepNow wrote:
PLUTO wrote:
Schezwan restaurant offers 5 chicken, prawn, beef, vegetable & tofu entrees served with either garlic or chili sauce. In how many ways can 3 entrees be served if no entry is served more than once?
Answer Options: -

A. 10
B. 60
C. 80
D. 100
E. 120


Take the task of creating a meal and break it into stages.

Stage 1: Select 3 entrees
Since the order in which we select the entrees does not matter, we can use combinations.
We can select 3 entrees from 5 entrees in 5C3 ways (10 ways)
So, we can complete stage 1 in 10 ways

If anyone is interested, we have a video (below) on calculating combinations (like 5C3) in your head

ASIDE: We now have our 3 entrees, but we don't have a sauce for each entree.

Stage 2: Choose a sauce for one of of the entrees
We have 2 choices (garlic or chili sauce), so we can complete stage 2 in 2 ways

Stage 3: Choose a sauce for another entree
We have 2 choices (garlic or chili sauce), so we can complete stage 3 in 2 ways

Stage 4: Choose a sauce for the last remaining entree
We have 2 choices (garlic or chili sauce), so we can complete stage 4 in 2 ways

By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus create a meal) in (10)(2)(2)(2) ways (= 80 ways)

Answer: C


I appreciate your solution and it is well explained. Can you please help me understand what I am doing wrong in the following approach,

Stage 1: No of ways to make 1st entree (select 1 base from 5 and select 1 sauce from 2) = 5C1 x 2C1 = 10
Stage 2: No of ways to make 2nd entree (select 1 base from 4 remaining and select 1 sauce from 2) = 4C1 x 2C1 = 8
Stage 3: No of ways to make 3rd entree (select 1 base from 3 remaining and select 1 sauce from 2) = 3C1 x 2C1 = 6

Total number of ways = 10 x 8 x 6 = 480
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4006
Location: Canada
Re: Schezwan restaurant offers 5 chicken, prawn, beef, vegetable & tofu  [#permalink]

Show Tags

New post 24 Apr 2019, 10:15
Top Contributor
priarav wrote:
PLUTO wrote:
Schezwan restaurant offers 5 chicken, prawn, beef, vegetable & tofu entrees served with either garlic or chili sauce. In how many ways can 3 entrees be served if no entry is served more than once?
Answer Options: -

A. 10
B. 60
C. 80
D. 100
E. 120



I appreciate your solution and it is well explained. Can you please help me understand what I am doing wrong in the following approach,

Stage 1: No of ways to make 1st entree (select 1 base from 5 and select 1 sauce from 2) = 5C1 x 2C1 = 10
Stage 2: No of ways to make 2nd entree (select 1 base from 4 remaining and select 1 sauce from 2) = 4C1 x 2C1 = 8
Stage 3: No of ways to make 3rd entree (select 1 base from 3 remaining and select 1 sauce from 2) = 3C1 x 2C1 = 6

Total number of ways = 10 x 8 x 6 = 480


The problem with your solution is that you have counted each unique meal 6 times.

In your solution, we COULD choose:
- chicken with garlic sauce in stage 1, prawn with chili sauce in stage 2, and beef with garlic sauce in stage 3
or
- chicken with garlic sauce in stage 1, beef with garlic sauce in stage 2, and prawn with chili sauce in stage 3
or
- prawn with chili sauce in stage 1, chicken with garlic sauce in stage 2, and beef with garlic sauce in stage 3
or
- prawn with chili sauce in stage 1, beef with garlic sauce in stage 2, and chicken with garlic sauce in stage 3
or
- beef with garlic sauce in stage 1, prawn with chili sauce in stage 2, and chicken with garlic sauce in stage 3
or
- beef with garlic sauce in stage 1, chicken with garlic sauce in stage 2, and prawn with chili sauce in stage 3

Notice that all 6 meals are the SAME.
Since you have counted each unique meal 6 times, we must divide your answer by 6 to get 460/6 = 80

Does that help?

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
Intern
Intern
avatar
B
Joined: 29 Nov 2015
Posts: 5
Re: Schezwan restaurant offers 5 chicken, prawn, beef, vegetable & tofu  [#permalink]

Show Tags

New post 24 Apr 2019, 11:25
GMATPrepNow wrote:
The problem with your solution is that you have counted each unique meal 6 times.

In your solution, we COULD choose:
- chicken with garlic sauce in stage 1, prawn with chili sauce in stage 2, and beef with garlic sauce in stage 3
or
- chicken with garlic sauce in stage 1, beef with garlic sauce in stage 2, and prawn with chili sauce in stage 3
or
- prawn with chili sauce in stage 1, chicken with garlic sauce in stage 2, and beef with garlic sauce in stage 3
or
- prawn with chili sauce in stage 1, beef with garlic sauce in stage 2, and chicken with garlic sauce in stage 3
or
- beef with garlic sauce in stage 1, prawn with chili sauce in stage 2, and chicken with garlic sauce in stage 3
or
- beef with garlic sauce in stage 1, chicken with garlic sauce in stage 2, and prawn with chili sauce in stage 3

Notice that all 6 meals are the SAME.
Since you have counted each unique meal 6 times, we must divide your answer by 6 to get 460/6 = 80

Does that help?

Cheers,
Brent


Hi Brent,
This does help. Thank you for clearing this up. I really appreciate it.
Best Regards,
GMAT Club Bot
Re: Schezwan restaurant offers 5 chicken, prawn, beef, vegetable & tofu   [#permalink] 24 Apr 2019, 11:25
Display posts from previous: Sort by

Schezwan restaurant offers 5 chicken, prawn, beef, vegetable & tofu

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne