|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
08 Dec 2020, 06:30
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
34% (02:21) correct
66%
(02:43)
wrong
based on 80
sessions
History
Date
Time
Result
Not Attempted Yet
A shop sells two kinds of rolls - egg roll and mutton roll. Onion, tomato, carrot, chili sauce and tomato sauce are the additional ingredients. You can have any combination of additional ingredients, or have standard rolls without any additional ingredients subject to the following constraints:
(a) You can have tomato sauce if you have an egg roll, but not if you have a mutton roll.
(b) You can have chili sauce ONLY if have onion or tomato or both.
How many different rolls can be ordered according to these rules?
A. 21
B. 33
C. 40
D. 42
E. 44
(a) You can have tomato sauce if you have an egg roll, but not if you have a mutton roll.
(b) You can have chili sauce ONLY if have onion or tomato or both.
How many different rolls can be ordered according to these rules?
A. 21
B. 33
C. 40
D. 42
E. 44
08 Dec 2020, 12:09
Kudos
Bookmarks
I'm not sure exactly what the question means by "standard rolls" (that wording suggests to me there's a third type of roll we need to consider). Assuming there are 2 types of roll, and five toppings, then with no restrictions, we'd have 2 choices of roll type, and for each topping we'd have 2 choices: use it or not. So there would be, with no restrictions, (2)(2^5) = 64 options.
But we have two restrictions. First, on the mutton roll, we don't have 2 choices for the tomato sauce topping, because we can't use it. So there are only 2^4 = 16 options for mutton rolls, and still 32 options for egg rolls, for 16+32 = 48 options in total.
Then from restriction b), we cannot specifically choose "yes, no, no" respectively for "chili, onion, tomato", on either type of roll. So for mutton rolls, since we have only one other topping we can use, there are 2 options we must exclude, and for egg rolls, with two other toppings, there are 2^2 = 4 options we must exclude. So the answer is 48 - 2 - 4 = 42.
But we have two restrictions. First, on the mutton roll, we don't have 2 choices for the tomato sauce topping, because we can't use it. So there are only 2^4 = 16 options for mutton rolls, and still 32 options for egg rolls, for 16+32 = 48 options in total.
Then from restriction b), we cannot specifically choose "yes, no, no" respectively for "chili, onion, tomato", on either type of roll. So for mutton rolls, since we have only one other topping we can use, there are 2 options we must exclude, and for egg rolls, with two other toppings, there are 2^2 = 4 options we must exclude. So the answer is 48 - 2 - 4 = 42.
18 Jun 2024, 00:15
Kudos
Bookmarks
2 standard rolls (meaning no additional toppings or sauces) = 2 rolls
To count the number of rolls with toppings, let's keep chilli sauce out of the discussion for a while since it has some restrictions.
There are 4 other toppings in total.
Egg roll with toppings (other than chilli sauce) = 4c1 + 4c2 + 4c3 + 4c4 = 15 rolls
Mutton roll with toppings (other than chilli and tomato sauce) = 3c1 + 3c2 + 3c3 = 7 rolls
Now let's consider the situations where we can add chilli sauce to the rolls.
There should either be onion or tomato topping, or both, in the rolls to add chilli sauce.
Egg rolls
No. of egg rolls not having eligible toppings = 2 + 1= 3
No. of egg rolls that can have chilli sauce = 15 - 3 = 12 rolls
Mutton rolls
No. of mutton rolls not having eligible toppings = 1
No. of mutton rolls that can have chilli sauce = 7 - 1 = 6 rolls
Therefore in total, there are 2 + 15 + 7 +12 + 6 = 42 combinations possible.
To count the number of rolls with toppings, let's keep chilli sauce out of the discussion for a while since it has some restrictions.
There are 4 other toppings in total.
Egg roll with toppings (other than chilli sauce) = 4c1 + 4c2 + 4c3 + 4c4 = 15 rolls
Mutton roll with toppings (other than chilli and tomato sauce) = 3c1 + 3c2 + 3c3 = 7 rolls
Now let's consider the situations where we can add chilli sauce to the rolls.
There should either be onion or tomato topping, or both, in the rolls to add chilli sauce.
Egg rolls
No. of egg rolls not having eligible toppings = 2 + 1= 3
No. of egg rolls that can have chilli sauce = 15 - 3 = 12 rolls
Mutton rolls
No. of mutton rolls not having eligible toppings = 1
No. of mutton rolls that can have chilli sauce = 7 - 1 = 6 rolls
Therefore in total, there are 2 + 15 + 7 +12 + 6 = 42 combinations possible.
