DS - fraction (explanation reqd.)

[karthikpandian19]

Mildred wove scarves with different combinations of yellow, blue, green, and red thread. Of the scarves that Mildred wove, one fourth contain no red thread. What fraction of the scarves that Mildred wove contain both red and blue thread?

1. Mildred wove 120 scarves in total, of which 60 contain no blue thread.
2. One third of the scarves with red thread contain no blue thread.

[eagleeye]

Mildred wove scarves with different combinations of yellow, blue, green, and red thread. Of the scarves that Mildred wove, one fourth contain no red thread. What fraction of the scarves that Mildred wove contain both red and blue thread?

1. Mildred wove 120 scarves in total, of which 60 contain no blue thread.
2. One third of the scarves with red thread contain no blue thread.

Hi karthikpandian19:

Let the total number of scarves be x. We are told that 1/4 have no red thread. So 3x/4 have red thread. We need to find the fraction of x that contains both red and blue. With that in mind, let's look at the statements.


1. Mildred wove 120 scarves in total, of which 60 contain no blue thread.
We are told that x=120, and that 60 have no blue thread. so x/2 have no blue thread. We are told nothing about the red thread here. Insufficient.

2. One third of the scarves with red thread contain no blue thread.
We are told that 1/3*(red) have no blue thread. so 2/3*(red) have blue thread. But we know that red = 3x/4. Hence red and blue both are in: 2/3*(3x/4). So we get the fraction of red and blue in x. Sufficient.

Hence the final answer is B.

Let me know if this helps

[karthikpandian19]

Eagleeye,


We are told that x=120, and that 60 have no blue thread. so x/2 have no blue thread. We are told nothing about the red thread here. Insufficient.
But we are told about the red thread in the main sentence. Cant we refer that?
Pls explain

Mildred wove scarves with different combinations of yellow, blue, green, and red thread. Of the scarves that Mildred wove, one fourth contain no red thread. What fraction of the scarves that Mildred wove contain both red and blue thread?

1. Mildred wove 120 scarves in total, of which 60 contain no blue thread.
2. One third of the scarves with red thread contain no blue thread.

Hi karthikpandian19:

Let the total number of scarves be x. We are told that 1/4 have no red thread. So 3x/4 have red thread. We need to find the fraction of x that contains both red and blue. With that in mind, let's look at the statements.


1. Mildred wove 120 scarves in total, of which 60 contain no blue thread.
We are told that x=120, and that 60 have no blue thread. so x/2 have no blue thread. We are told nothing about the red thread here. Insufficient.

2. One third of the scarves with red thread contain no blue thread.
We are told that 1/3*(red) have no blue thread. so 2/3*(red) have blue thread. But we know that red = 3x/4. Hence red and blue both are in: 2/3*(3x/4). So we get the fraction of red and blue in x. Sufficient.

Hence the final answer is B.

Let me know if this helps

[eagleeye]

Eagleeye,


We are told that x=120, and that 60 have no blue thread. so x/2 have no blue thread. We are told nothing about the red thread here. Insufficient.
But we are told about the red thread in the main sentence. Cant we refer that?
Pls explain

We can, but it will be inconsequential. The big overarching principle here is that we are looking for fractions that talk about both red and blue. In this example, we have threads of four colors. So other possibilities can affect the results of how many red-blue scarfs we get. Let me illustrate this by examples.

We are told that there are 120 scarfs. We know from question stem that 3/4 contain red. Hence 90 have red. We are also told that 60 have blue in them. The only inference we can make here is that "at least" 30 scarfs are red-blue. However, we can have possibly up to 60 scarfs as red-blue. So the fraction ranges from 30/120 to 60/120, a total of 31 possible values. Since there is more than a single befitting value, the statement is insufficient.

Now, I rejected this statement without doing any such calculation because unless it is said that all threads are blue, any value of blue, without any mention of red will provide more than one answer.

Conceptually this comes from:

Total = Red + Blue -(Red AND Blue) + (Other options).
We know the fraction of red. But if we are told only about the Blue, we can have many combinations of (Red AND Blue) and (Other options) to give a myriad of values for (Red AND Blue) case.

Did this help?

[karthikpandian19]

Yeah,........now i understood

Thanks

Eagleeye,


We are told that x=120, and that 60 have no blue thread. so x/2 have no blue thread. We are told nothing about the red thread here. Insufficient.
But we are told about the red thread in the main sentence. Cant we refer that?
Pls explain

We can, but it will be inconsequential. The big overarching principle here is that we are looking for fractions that talk about both red and blue. In this example, we have threads of four colors. So other possibilities can affect the results of how many red-blue scarfs we get. Let me illustrate this by examples.

We are told that there are 120 scarfs. We know from question stem that 3/4 contain red. Hence 90 have red. We are also told that 60 have blue in them. The only inference we can make here is that "at least" 30 scarfs are red-blue. However, we can have possibly up to 60 scarfs as red-blue. So the fraction ranges from 30/120 to 60/120, a total of 31 possible values. Since there is more than a single befitting value, the statement is insufficient.

Now, I rejected this statement without doing any such calculation because unless it is said that all threads are blue, any value of blue, without any mention of red will provide more than one answer.

Conceptually this comes from:

Total = Red + Blue -(Red AND Blue) + (Other options).
We know the fraction of red. But if we are told only about the Blue, we can have many combinations of (Red AND Blue) and (Other options) to give a myriad of values for (Red AND Blue) case.

Did this help?