Four tests—Physics, Chemistry, Mathematics and Biology are to be conducted on four consecutive days, not necessarily in the same order. The Physics test is held before the test which is conducted after Biology. Chemistry is conducted exactly after two tests are held. Which is the last test held?

Here's a step-by-step breakdown to determine the last test: 1. **Analyze the second statement:** "Chemistry is conducted exactly after two tests are held." This means Chemistry (C) is the third test in the sequence of four consecutive days. So, the order is: Day 1: \_, Day 2: \_, Day 3: Chemistry, Day 4: \_. 2. **Analyze the first statement:** "The Physics test is held before the test which is conducted after Biology." Let's call the test conducted after Biology as 'X'. So, Biology (B) is held before X (B -> X). The statement says Physics (P) is held before X (P -> X). This implies that both Biology and Physics must occur before X. Since B and P are two distinct tests, X cannot be the 1st or 2nd test in the sequence. Therefore, X must be either the 3rd or the 4th test. 3. **Combine findings from steps 1 and 2:** * We know Chemistry is the 3rd test. * We know X must be the 3rd or 4th test. **Case A: X is the 3rd test.** If X is the 3rd test, then X must be Chemistry. So, the test after Biology is Chemistry (B -> C). And Physics is before Chemistry (P -> C). Since Chemistry is on Day 3, both Biology and Physics must be on Day 1 and Day 2 (in some order). The sequence so far is: Day 1: (P or B), Day 2: (B or P), Day 3: Chemistry, Day 4: \_. The only remaining test is Mathematics (M). So, Mathematics must be on Day 4. Let's verify a possible sequence like Physics, Biology, Chemistry, Mathematics: * Chemistry is 3rd: True (Day 3). * Physics is before the test after Biology: The test after Biology (B on Day 2) is Chemistry (C on Day 3). Physics (P on Day 1) is indeed before Chemistry (C on Day 3). True. This sequence (Physics, Biology, Chemistry, Mathematics) is valid. **Case B: X is the 4th test.** If X is the 4th test, then X must be Mathematics (since P, B, C are already placed or considered for earlier slots). So, the test after Biology is Mathematics (B -> M). And Physics is before Mathematics (P -> M). The sequence is: Day 1: \_, Day 2: \_, Day 3: Chemistry, Day 4: Mathematics. For B -> M and P -> M to hold, Biology and Physics must be on Day 1 and Day 2 (in some order). Let's check the first statement with this setup: "Physics is held before the test which is conducted after Biology." If Biology is on Day 1, the test after Biology is Physics (on Day 2). The statement would then require "Physics is held before Physics," which is impossible. If Biology is on Day 2, the test after Biology is Chemistry (on Day 3). The statement would then require "Physics is held before Chemistry." This would mean Physics is on Day 1. So the sequence would be Physics, Biology, Chemistry, Mathematics. However, in this specific sequence, the test after Biology (Day 2) is Chemistry (Day 3), meaning X is Chemistry, not Mathematics. This contradicts our assumption for Case B (that X is Mathematics). Therefore, Case B is not possible. 4. **Conclusion:** The only consistent sequence is where Chemistry is the 3rd test, and Mathematics is the 4th test. An example of a valid sequence is Physics, Biology, Chemistry, Mathematics. In this sequence, Mathematics is the last test. The final answer is C) Mathematics.