At a certain school, is the number of biology students greater than

Question

At a certain school, is the number of biology students greater than the number of chemistry students?

(1) Of the biology students, 30 percent are also chemistry students.
(2) Of the chemistry students, 40 percent are also biology students.

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onlyPlanA · Answer

IMO, answer is E.

Need to find if number of biology students > number of chemistry students
Total number of students  not  given.

Statement-1:

Out of all biology students, 30% are chemistry.
That means 70% are  only  biology students.
But, 70% of what?
Also, we don't know how many chemistry students are there.
Hence, insufficient.

Statement-2:
Out of all chemistry students, 40% are biology students.
That means, 60% are only chemistry students, but again, 60% of what?
We do not know how many biology and chemistry students are there.
Hence, insufficient.

Combining the two statements, we still don't have total number of students, nor the number of bio or chem students.
Hence, both statements together are also insufficient.

ShresthKhandelwal · Answer

I think answer should be C.
As, Equating the two expressions: 0.3 X B = 0.4 X C. Both statements describe the exact same group of overlapping students (those taking both biology and chemistry). So, we can say that Biology students are 4/3 of Chemistry students.

quosaperiam · Answer

I set B as the number of biology students, C as the number of chemistry students, and X as the students taking both.

From (1): 0.30B=X
This alone is not enough because we do not know C.

From (2): 0.40C=X
This alone is also not enough because we do not know B.

Together:
0.30B=0.40C
so
3B=4C⇒B=4/3C

Therefore, the number of biology students is definitely greater than the number of chemistry students.

Answer: C.

counterclash1 · Answer

Correct Answer: C (BOTH statements TOGETHER are sufficient)

QUESTION:
Is Biology students (B) > Chemistry students (C)?

STATEMENT (1):
- Overlap (B ∩ C) = 0.30 * B
- C can be any number >= 0.30 * B.
- If B = 100, C could be 30 (Yes) or 200 (No).
- INSUFFICIENT.

STATEMENT (2):
- Overlap (B ∩ C) = 0.40 * C
- B can be any number >= 0.40 * C.
- If C = 100, B could be 40 (No) or 200 (Yes).
- INSUFFICIENT.

TOGETHER (1) + (2):
- Since the overlap (B ∩ C) represents the exact same group:
 0.30 * B = 0.40 * C
 3 * B = 4 * C
 B = (4/3) * C = 1.33 * C
- Since C > 0, B is always greater than C.
- Definitive YES.
- SUFFICIENT.

Conclusion: Answer Choice C.

officiisnobis · Answer

I choose C and this is my reasoning - 
If there are 100 students in bio then 30 are in chemistry and 30= 40% of chemistry (from statement 2)
So in chemistry we only have 75 students.

At a certain school, is the number of biology students greater than

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At a certain school, is the number of biology students greater than