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Statement 1: If Biology Not then Chemistry Not, which is logically equivalent to If Chemistry then Biology

Therefore, Chemistry is a sufficient condition for Biology, which means Chemistry is a subset of Biology

Now, since Chemistry has more than 25 students, there must be >25 students who are also in Biology.

Statement 1 is Sufficient

Statement 2: This directly states the logical chain that we derived earlier, i.e., if Chemistry then Biology

hence Statement 2 is also Sufficient

Answer (D)
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Answer D

1) every student not in biology is also not in chemistry. Meaning if your in chemistry you must also be in biology. there are students enrolled in both. sufficent

2) Every student in chemistry is also in biology. so students in both
Bunuel
At a certain university, each of two advanced courses, Biology and Chemistry, has more than 25 students enrolled. Is there at least one student enrolled in both courses?

(1) Every student who is not enrolled in Biology is also not enrolled in Chemistry.

(2) Every student enrolled in Chemistry is also enrolled in Biology.

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Bunuel
At a certain university, each of two advanced courses, Biology and Chemistry, has more than 25 students enrolled. Is there at least one student enrolled in both courses?

(1) Every student who is not enrolled in Biology is also not enrolled in Chemistry.

(2) Every student enrolled in Chemistry is also enrolled in Biology.

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Each course has more than 25 hence n(c)>25 n(b)>25

Let's look at the options.

1- re wording it - Every student who is enrollled in biology is also enrolled in chemistry. Biology is a subset of Chemistry. Hence Sufficient .

2 - Same thought process of statement one. Hence sufficient.

Hence option D
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We know there are more than 25 students that are part of each course i.e Biology(B) and Chemistry(C)

1. The statement 1 which is of the form If Not B then Not C can be written as If C then B, since we know there are students in C, there will be students in B.
Sufficient

2. The statement 2 is of the form if C then B, since we know there are students in C, there will be students in B
Sufficient

Answer D
Bunuel
At a certain university, each of two advanced courses, Biology and Chemistry, has more than 25 students enrolled. Is there at least one student enrolled in both courses?

(1) Every student who is not enrolled in Biology is also not enrolled in Chemistry.

(2) Every student enrolled in Chemistry is also enrolled in Biology.

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Bunuel
At a certain university, each of two advanced courses, Biology and Chemistry, has more than 25 students enrolled. Is there at least one student enrolled in both courses?

(1) Every student who is not enrolled in Biology is also not enrolled in Chemistry.

(2) Every student enrolled in Chemistry is also enrolled in Biology.

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1) this neither imply there are common students, nor imply opposite.
2)this clearly says there common students. and since chemistry has more than 25, it implies at least 1 student is there in both chem and biology.

hence answer is B
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here we have to check whether the intersection value of the two given sets exist?
1.talks nothing relevant to the intersection value----insufficient
2. is sufficient, even if one student is enrolled in chemistry he is also enrolled in biology---sufficient
B
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Q - Is there at least 1 student enrolled in both courses?

(1) This means that Chemistry students are subset of Biology students.
Since there are more than 25 students enrolled in both, there would be some enrolled in both courses.
Hence (1) is sufficient.

(2) This also means same as one.

Hence both are individually sufficient to answer the question.
(D) is the answer
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We need atleast 1 student enrolled in both courses

B) is pretty straightforward. Every student enrolled in chem is also in bio, hence more than 25 sts in both. Sufficient

A) In CR we have, If A, then B, then only option true is If not B, then not A.

Here we have, if not in Bio, then not in Chem, then this is true: if in Chem, then in Bio, which is basically same as A.

Ans D
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bio >25
chem > 25
find- at least one person in both class?

s-1 if not in bio then not in chem.
basically it means if you are in chem then you must be in bio.
so they are in both class. and we know each class has 254 students.
sufficient

s-2 every chem is in bio. so obviously they are in both class.
sufficient

option D

Bunuel
At a certain university, each of two advanced courses, Biology and Chemistry, has more than 25 students enrolled. Is there at least one student enrolled in both courses?

(1) Every student who is not enrolled in Biology is also not enrolled in Chemistry.

(2) Every student enrolled in Chemistry is also enrolled in Biology.

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Need to find is at least one student has enrolled in both Bio and Chemistry.

Statement 1. It is a classic case of contraposition statement.
If NOT enrolled in BIO, then NOT enrolled in chemistry means that if enrolled in Chemistry then enrolled in BIO also.

sufficient

Statement 2. Direct statement. sufficient.

Answer is D

Bunuel
At a certain university, each of two advanced courses, Biology and Chemistry, has more than 25 students enrolled. Is there at least one student enrolled in both courses?

(1) Every student who is not enrolled in Biology is also not enrolled in Chemistry.

(2) Every student enrolled in Chemistry is also enrolled in Biology.

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(1) This is equal to Every student who enrolled in Biology is also enrolled in Chemistry. SUFFICIENT
(2) SUFFICIENT

Answer: D
Bunuel
At a certain university, each of two advanced courses, Biology and Chemistry, has more than 25 students enrolled. Is there at least one student enrolled in both courses?

(1) Every student who is not enrolled in Biology is also not enrolled in Chemistry.

(2) Every student enrolled in Chemistry is also enrolled in Biology.

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We know that each of Biology and Chemistry is not a null set and having students enrolled greater than 25. Let's look at first statement:

(1) It says every students who is not enrolled in Biology is also not enrolled in chemistry. This means that Chemistry set will be inside Biology set. So Biology will be acting as superset. Then if Biology is not a null set then , there will be atleast one student enrolled in both Chemistry and Biology. So statement 1 is sufficient.
(2) It says student enrolled in Chemistry is also enrolled in Biology. This means that there will be atleast one student enrolled in both Chemistry and Biology since Chemistry is not a null set. So , statement 2 is sufficient.

SO the correct answer is D.
Bunuel
At a certain university, each of two advanced courses, Biology and Chemistry, has more than 25 students enrolled. Is there at least one student enrolled in both courses?

(1) Every student who is not enrolled in Biology is also not enrolled in Chemistry.

(2) Every student enrolled in Chemistry is also enrolled in Biology.

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Given Biology and Chemistry each have >25
1) Every student not enrolled in Biology is also not enrolled in Chemistry- gives us no information on number of children enrolled either one of the courses or both hence NOT SUFFICIENT

2) Every student enrolled in chemistry is also enrolled in biology- This looks at the number if students common to both sets Chemistry and Biology.
Total students - Only Biology + Students enrolled in both + Only Chemistry + Students enrolled in None
Statement means Only Chemistry = 0 and question states that each Chemistry and Biology has>25. So since Chemistry has >25, these >25 of chemistry belong to the group containing students enrolled in both subjects. Since this is greater than 1,it answers the question stem of atleast 1. SUFFICIENT

Ans=Statement 2 alone is sufficient
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From the stem we know that
Biology> 25
Chemistry > 25
ST 1 : Every student who is not enrolled in Biology is not enrolled in Chemistry
If not B -- not C
LOGICAL equivalent of this is IF C --- B , Every student in Chemistry is also in Biology.
We know more than 25 are in chemistry and since all of them are in Biology . There must be atleast 25 students in both. Sufficient

ST 2 : Exact same info we derived from 1 . There is definitely at least one student in both.

Each statement alone is sufficient.
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(1) The translates to everyone who is enrolled in Biology is also enrolled in Chemistry, and we know that at least 25 students are enrolled in each course, so yes, there is at least one student enrolled in both courses (to understand better, one can use venn diagram and see what exactly this simplifies to).
Or, for example, if there are 100 students in total, assume 26 are enrolled in Biology, then 74 are not enrolled in Biology. Now these 75 students are also not enrolled in Chemistry. The question stem states that more than 25 students are enrolled in Chemistry as well. Then it must be the same 26 students who are enrolled in Biology are also enrolled in Chemistry.

(2) Same as 1, sufficient.

Option D.
Bunuel
At a certain university, each of two advanced courses, Biology and Chemistry, has more than 25 students enrolled. Is there at least one student enrolled in both courses?

(1) Every student who is not enrolled in Biology is also not enrolled in Chemistry.

(2) Every student enrolled in Chemistry is also enrolled in Biology.

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We are asked if atleast one student is in both the courses:
Statement 1: Anyone not in Biology is not in chemistry; -Biology then -Chemistry (Sufficient)
Statement 2: Everyone in Chemistry are also in Biology; +Chemistry then +Biology (Sufficient)

ANS: D Sufficient
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Given

No. of student enrolled in Biology >25 and No. of students enrolled in chem is >25
So, Not enrolled in Biology <=25 and Not enrolled in chem <=25

and we need to find whether bio and chem has atleast 1 or not

Also we dont know about the Total.

Let's see with the matrix

B -B |

C a b | >25

-C d c |<=25
_______________
>25 <=25

St-1 c is less than equal to 25, a+b>25, a has to be atleast 1. Sufficient
St-2 we already know in chem there are more than 25, and with the statement it says these are also enrolled in bio. hence a>25. So sufficient

Option D
Bunuel
At a certain university, each of two advanced courses, Biology and Chemistry, has more than 25 students enrolled. Is there at least one student enrolled in both courses?

(1) Every student who is not enrolled in Biology is also not enrolled in Chemistry.

(2) Every student enrolled in Chemistry is also enrolled in Biology.

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