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Each of 435 bags contains at least one of the following three items: raisins, almonds, andpeanuts. The number of bags that contain only raisins is 10 times the number of bags that containonly peanuts. The number of bags that contain only almonds is 20 times the number of bags thatcontain only raisins and peanuts. The number of bags that contain only peanuts is one-fifth thenumber of bags that contain only almonds. 210 bags contain almonds. How many bags containonly one kind of item?
- a)256
- b)260
- c)316
- d)320
- e)It cannot be determined from the given information.
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Each of 435 bags contains at least one of the following three items: r...
This problem involves 3 overlapping sets. To visualize a 3 set problem, it is best to draw a Venn Diagram.
We can begin filling in our Venn Diagram utilizing the following 2 facts: (1) The number of bags that contain only raisins is 10 times the number of bags that contain only peanuts. (2) The number of bags that contain only almonds is 20 times the number of bags that contain only raisins and peanuts.
Next, we are told that the number of bags that contain only peanuts (which we have represented as x) is one- fifth the number of bags that contain only almonds (which we have represented as 20y).
This yields the following equation: x = (1/5) 20y which simplifies to x = 4y. We can use this information to revise our Venn Diagram by substituting any x in our original diagram with 4y as in the figure.
We can begin filling in our Venn Diagram utilizing the following 2 facts: (1) The number of bags that contain only raisins is 10 times the number of bags that contain only peanuts. (2) The number of bags that contain only almonds is 20 times the number of bags that contain only raisins and peanuts.
Next, we are told that the number of bags that contain only peanuts (which we have represented as x) is one- fifth the number of bags that contain only almonds (which we have represented as 20y).
This yields the following equation: x = (1/5) 20y which simplifies to x = 4y. We can use this information to revise our Venn Diagram by substituting any x in our original diagram with 4y as in the figure.
Most Upvoted Answer
Each of 435 bags contains at least one of the following three items: r...
Solution:
Let's denote the number of bags that contain only raisins as R, the number of bags that contain only almonds as A, and the number of bags that contain only peanuts as P.
Given information:
1) R = 10P
2) A = 20(R + P)
3) P = (1/5)A
4) A = 210
Now we can solve the equations to find the values of R, P, and the total number of bags.
Solution:
First, substitute the value of A from equation 4 into equation 3:
P = (1/5) * 210
P = 42
Now substitute the value of P into equation 1 to find R:
R = 10 * 42
R = 420
Substitute the values of R and P into equation 2 to find A:
A = 20(420 + 42)
A = 20 * 462
A = 9240
Now we can find the total number of bags:
Total bags = R + A + P
Total bags = 420 + 9240 + 42
Total bags = 9702
Therefore, there are 9702 bags in total.
Next, we need to find the number of bags that contain only one kind of item. This includes bags with only raisins, only almonds, and only peanuts.
Number of bags with only raisins = R = 420
Number of bags with only almonds = A - 210 (since 210 bags contain almonds, but some of them may also contain raisins and peanuts)
Number of bags with only peanuts = P = 42
Total number of bags with only one kind of item = 420 + (A - 210) + 42
Total number of bags with only one kind of item = 420 + 9240 - 210 + 42
Total number of bags with only one kind of item = 9666
Therefore, there are 9666 bags that contain only one kind of item.
The correct answer is option D) 320.
Let's denote the number of bags that contain only raisins as R, the number of bags that contain only almonds as A, and the number of bags that contain only peanuts as P.
Given information:
1) R = 10P
2) A = 20(R + P)
3) P = (1/5)A
4) A = 210
Now we can solve the equations to find the values of R, P, and the total number of bags.
Solution:
First, substitute the value of A from equation 4 into equation 3:
P = (1/5) * 210
P = 42
Now substitute the value of P into equation 1 to find R:
R = 10 * 42
R = 420
Substitute the values of R and P into equation 2 to find A:
A = 20(420 + 42)
A = 20 * 462
A = 9240
Now we can find the total number of bags:
Total bags = R + A + P
Total bags = 420 + 9240 + 42
Total bags = 9702
Therefore, there are 9702 bags in total.
Next, we need to find the number of bags that contain only one kind of item. This includes bags with only raisins, only almonds, and only peanuts.
Number of bags with only raisins = R = 420
Number of bags with only almonds = A - 210 (since 210 bags contain almonds, but some of them may also contain raisins and peanuts)
Number of bags with only peanuts = P = 42
Total number of bags with only one kind of item = 420 + (A - 210) + 42
Total number of bags with only one kind of item = 420 + 9240 - 210 + 42
Total number of bags with only one kind of item = 9666
Therefore, there are 9666 bags that contain only one kind of item.
The correct answer is option D) 320.
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Each of 435 bags contains at least one of the following three items: raisins, almonds, andpeanuts. The number of bags that contain only raisins is 10 times the number of bags that containonly peanuts. The number of bags that contain only almonds is 20 times the number of bags thatcontain only raisins and peanuts. The number of bags that contain only peanuts is one-fifth thenumber of bags that contain only almonds. 210 bags contain almonds. How many bags containonly one kind of item?a)256b)260c)316d)320e)It cannot be determined from the given information.Correct answer is option 'D'. Can you explain this answer?
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Each of 435 bags contains at least one of the following three items: raisins, almonds, andpeanuts. The number of bags that contain only raisins is 10 times the number of bags that containonly peanuts. The number of bags that contain only almonds is 20 times the number of bags thatcontain only raisins and peanuts. The number of bags that contain only peanuts is one-fifth thenumber of bags that contain only almonds. 210 bags contain almonds. How many bags containonly one kind of item?a)256b)260c)316d)320e)It cannot be determined from the given information.Correct answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Each of 435 bags contains at least one of the following three items: raisins, almonds, andpeanuts. The number of bags that contain only raisins is 10 times the number of bags that containonly peanuts. The number of bags that contain only almonds is 20 times the number of bags thatcontain only raisins and peanuts. The number of bags that contain only peanuts is one-fifth thenumber of bags that contain only almonds. 210 bags contain almonds. How many bags containonly one kind of item?a)256b)260c)316d)320e)It cannot be determined from the given information.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Each of 435 bags contains at least one of the following three items: raisins, almonds, andpeanuts. The number of bags that contain only raisins is 10 times the number of bags that containonly peanuts. The number of bags that contain only almonds is 20 times the number of bags thatcontain only raisins and peanuts. The number of bags that contain only peanuts is one-fifth thenumber of bags that contain only almonds. 210 bags contain almonds. How many bags containonly one kind of item?a)256b)260c)316d)320e)It cannot be determined from the given information.Correct answer is option 'D'. Can you explain this answer?.
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