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27 Jun 2024, 01:30
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In a certain Italian recipe book, every recipe that includes oregano also includes basil, thyme, or both. The number of recipes that include basil but do not include either thyme or oregano is how much greater than the number of recipes that include thyme but do not include either oregano or basil?
(1) In the book, the total number of recipes which include basil is equal to the total number of recipes which include thyme.
(2) In the book, the total number of recipes which include both thyme and oregano is 12 greater than the total number of recipes which include both basil and oregano.
(1) In the book, the total number of recipes which include basil is equal to the total number of recipes which include thyme.
(2) In the book, the total number of recipes which include both thyme and oregano is 12 greater than the total number of recipes which include both basil and oregano.
27 Jun 2024, 05:41
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every recipe that includes oregano also includes basil, thyme, or both. That means there is no recipe with only Oregano - O
recipes that include basil but do not include either thyme or oregano - Recipes with Basil alone - B
recipes that include thyme but do not include either oregano or basil - Recipes with Thyme alone - T
Need to find \(B=T+x\)
Lets assign terms to recipes with only two ingredients - OB, OT, BT
recipes with three ingredients - OBT
Statement 1: Recipes include Basil = Recipes include Thyme
\(B+OB+BT+OBT = T+OT+BT+OBT\)
\(B+OB=T+OT\) .... eq 1.
Not Sufficient
Statement 2: recipes include both thyme and oregano = 12 + recipes include both basil and oregano
\(OT+OBT=12+OB+OBT\)
\(OT=12+OB\) .... eq 2.
Not Sufficient
Statements Combined:
Plugging eq 2. in eq 1. we get
\(B+OB=T+12+OB\)
\(B=T+12\)
Sufficient. Hence Answer is C
recipes that include basil but do not include either thyme or oregano - Recipes with Basil alone - B
recipes that include thyme but do not include either oregano or basil - Recipes with Thyme alone - T
Need to find \(B=T+x\)
Lets assign terms to recipes with only two ingredients - OB, OT, BT
recipes with three ingredients - OBT
Statement 1: Recipes include Basil = Recipes include Thyme
\(B+OB+BT+OBT = T+OT+BT+OBT\)
\(B+OB=T+OT\) .... eq 1.
Not Sufficient
Statement 2: recipes include both thyme and oregano = 12 + recipes include both basil and oregano
\(OT+OBT=12+OB+OBT\)
\(OT=12+OB\) .... eq 2.
Not Sufficient
Statements Combined:
Plugging eq 2. in eq 1. we get
\(B+OB=T+12+OB\)
\(B=T+12\)
Sufficient. Hence Answer is C
General Discussion
27 Jun 2024, 05:13
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Given - In a certain Italian recipe book, every recipe that includes oregano also includes basil, thyme, or both.
means all recipe that contains oregano will always have either basil or thyme or both.
Assuming O for oregano, B for Basil and T for thyme.
To find - The number of recipes that include basil but do not include either thyme or oregano is how much greater than the number of recipes that include thyme but do not include either oregano or basil?
means we need to check n(B U T' U O') - n(T U O' U B') = ? Lets check given statements.
1st - In the book, the total number of recipes which include basil is equal to the total number of recipes which include thyme.
n(B) = n(T),
But what possible combinations of n(B) and n(T) are possible individually so lets check that first
n(B) = Basil without oregano or thyme + Basil with oregano + Basil with Thyme - Basil with either organo or thyme.
n(B) = n(B U T' U O') + n(B U O) + n(B U T) - n(B U T U O)
Similarly,
n(T) = Thyme without oregano or Basil + Thyme with oregano + Thyme with Basil - Thyme with either oregano or basil.
n(T) = n(T U O' U B') + n(T U O) + n(B U T) - n(B U T U O)
After equating both and cancelling out common terms
n(B U T' U O') + n(B U O) = n(T U O) + n(T U O' U B') ---- (Eq 1)
But we dont have any information about n(B U O) & n(T U O) in this statement Hence Not sufficient.
2nd - In the book, the total number of recipes which include both thyme and oregano is 12 greater than the total number of recipes which include both basil and oregano.
n(T U O) = 12 + n(B U O)
n(T U O) - n(B U O) = 12
This we needed in statement 1 Hence now if put this in eq 1
We will get n(B U T' U O') - n(T U O' U B') = 12
Answer C.
means all recipe that contains oregano will always have either basil or thyme or both.
Assuming O for oregano, B for Basil and T for thyme.
To find - The number of recipes that include basil but do not include either thyme or oregano is how much greater than the number of recipes that include thyme but do not include either oregano or basil?
means we need to check n(B U T' U O') - n(T U O' U B') = ? Lets check given statements.
1st - In the book, the total number of recipes which include basil is equal to the total number of recipes which include thyme.
n(B) = n(T),
But what possible combinations of n(B) and n(T) are possible individually so lets check that first
n(B) = Basil without oregano or thyme + Basil with oregano + Basil with Thyme - Basil with either organo or thyme.
n(B) = n(B U T' U O') + n(B U O) + n(B U T) - n(B U T U O)
Similarly,
n(T) = Thyme without oregano or Basil + Thyme with oregano + Thyme with Basil - Thyme with either oregano or basil.
n(T) = n(T U O' U B') + n(T U O) + n(B U T) - n(B U T U O)
After equating both and cancelling out common terms
n(B U T' U O') + n(B U O) = n(T U O) + n(T U O' U B') ---- (Eq 1)
But we dont have any information about n(B U O) & n(T U O) in this statement Hence Not sufficient.
2nd - In the book, the total number of recipes which include both thyme and oregano is 12 greater than the total number of recipes which include both basil and oregano.
n(T U O) = 12 + n(B U O)
n(T U O) - n(B U O) = 12
This we needed in statement 1 Hence now if put this in eq 1
We will get n(B U T' U O') - n(T U O' U B') = 12
Answer C.
