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Of the 310 students at the school majoring in one or more subjects in
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24 Mar 2023, 08:47
24 Mar 2023, 08:47
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Of the 310 students at the school majoring in one or more subjects in arts, 240 are majoring in History and 160 are majoring in Philosophy. If at least 20 of the students are majoring in neither History nor Philosophy, then the number of students majoring in both History and Philosophy could be any number from
20 to 60
40 to 80
80 to 160
110 to 160
110 to 240
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
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20 to 60
40 to 80
80 to 160
110 to 160
110 to 240
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Re: Of the 310 students at the school majoring in one or more subjects in
[#permalink]
11 Apr 2023, 09:53
11 Apr 2023, 09:53
2
Expert Reply
Let's denote the number of students majoring in both History and Philosophy as "x".
From the given information, we know that there are 310 students majoring in one or more subjects in arts. Out of these, 240 are majoring in History and 160 are majoring in Philosophy.
Since "x" students are majoring in both History and Philosophy, the number of students majoring in only History would be 240 - x, and the number of students majoring in only Philosophy would be 160 - x.
Now, we are also given that at least 20 students are majoring in neither History nor Philosophy. This means that the total number of students majoring in only History, only Philosophy, and both History and Philosophy should be less than or equal to 310 - 20 = 290.
So, we can write the inequality as:
(240 - x) + (160 - x) + x ≤ 290
400 - x ≤ 290
x ≥ 110
Therefore, the number of students majoring in both History and Philosophy could be any number from 110 to 160, which corresponds to the option: 110 to 160.
From the given information, we know that there are 310 students majoring in one or more subjects in arts. Out of these, 240 are majoring in History and 160 are majoring in Philosophy.
Since "x" students are majoring in both History and Philosophy, the number of students majoring in only History would be 240 - x, and the number of students majoring in only Philosophy would be 160 - x.
Now, we are also given that at least 20 students are majoring in neither History nor Philosophy. This means that the total number of students majoring in only History, only Philosophy, and both History and Philosophy should be less than or equal to 310 - 20 = 290.
So, we can write the inequality as:
(240 - x) + (160 - x) + x ≤ 290
400 - x ≤ 290
x ≥ 110
Therefore, the number of students majoring in both History and Philosophy could be any number from 110 to 160, which corresponds to the option: 110 to 160.
Re: Of the 310 students at the school majoring in one or more subjects in
[#permalink]
07 Oct 2023, 11:00
07 Oct 2023, 11:00
GeminiHeat wrote:
Let's denote the number of students majoring in both History and Philosophy as "x".
From the given information, we know that there are 310 students majoring in one or more subjects in arts. Out of these, 240 are majoring in History and 160 are majoring in Philosophy.
Since "x" students are majoring in both History and Philosophy, the number of students majoring in only History would be 240 - x, and the number of students majoring in only Philosophy would be 160 - x.
Now, we are also given that at least 20 students are majoring in neither History nor Philosophy. This means that the total number of students majoring in only History, only Philosophy, and both History and Philosophy should be less than or equal to 310 - 20 = 290.
So, we can write the inequality as:
(240 - x) + (160 - x) + x ≤ 290
400 - x ≤ 290
x ≥ 110
Therefore, the number of students majoring in both History and Philosophy could be any number from 110 to 160, which corresponds to the option: 110 to 160.
From the given information, we know that there are 310 students majoring in one or more subjects in arts. Out of these, 240 are majoring in History and 160 are majoring in Philosophy.
Since "x" students are majoring in both History and Philosophy, the number of students majoring in only History would be 240 - x, and the number of students majoring in only Philosophy would be 160 - x.
Now, we are also given that at least 20 students are majoring in neither History nor Philosophy. This means that the total number of students majoring in only History, only Philosophy, and both History and Philosophy should be less than or equal to 310 - 20 = 290.
So, we can write the inequality as:
(240 - x) + (160 - x) + x ≤ 290
400 - x ≤ 290
x ≥ 110
Therefore, the number of students majoring in both History and Philosophy could be any number from 110 to 160, which corresponds to the option: 110 to 160.
This is very useful, thank you! But how do you rule out Option E because even that range contains 110?
I thought of it as 310 = History + Phil + Other - both = 240+160+20 - both = 430 - both.
=> Both = 120.
so, the range should be as tight towards 110 to 120, which is only option D.
Carcass, what do you think, sir?
