UPSC Prelims 2017 CSAT Paper II · Q13 of 79 Logical Reasoning medium

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?

  1. (a) Physics
  2. (b) Biology
  3. (c) Mathematics ✓ UPSC's answer
  4. (d) Chemistry

Why the answer is (c)

• Let the four consecutive days be Day 1, Day 2, Day 3, and Day 4.

• The condition 'Chemistry is conducted exactly after two tests are held' means Chemistry is on Day 3 (since two tests precede it).

• The condition 'Physics is held before the test which is conducted after Biology' implies that Biology cannot be on Day 4 (as there is no test after it) and Physics must be on a day earlier than the day following Biology.

• If Biology were on Day 1, the test after it is Day 2; Physics must be before Day 2, so Physics is Day 1, which is impossible as Biology is Day 1. Thus, Biology is not Day 1.

• If Biology were on Day 2, the test after it is Day 3 (Chemistry); Physics must be before Day 3, so Physics is Day 1 or Day 2. Since Biology is Day 2, Physics must be Day 1. This leaves Day 4 for Mathematics. The order is Physics (1), Biology (2), Chemistry (3), Mathematics (4). This satisfies all conditions.

• If Biology were on Day 3, it conflicts with Chemistry being on Day 3. If Biology were on Day 4, there is no test after it, violating the condition. Therefore, the only valid sequence is Physics, Biology, Chemistry, Mathematics, making Mathematics the last test.

Why the other options are wrong

(a) Physics
Physics is held on Day 1 in the only valid sequence, so it is the first test, not the last.
(b) Biology
Biology is held on Day 2 in the only valid sequence, so it is not the last test.
(d) Chemistry
Chemistry is held on Day 3 because it is conducted exactly after two tests, so it is not the last test.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2017, held on 18 June 2017. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.

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