किसी पाँच-मंज़िला इमारत को, जिसके I से V तल हैं, चार भिन्न रंगों का इस्तेमाल कर रँगा गया है और एक तल को रँगने में सिर्फ़ एक ही रंग का इस्तेमाल किया गया है ।
निम्नलिखित कथनों पर विचार कीजिए :
- 1.बीच के तीन तलों को भिन्न रंगों में रँगा गया है ।
- 2.दूसरे (II) और चौथे (IV) तलों को भिन्न रंगों में रँगा गया है ।
- 3.पहले (I) और पाँचवें (V) तलों को लाल रंग में रँगा गया है ।
यह सुनिश्चित करने के लिए, कि कोई भी दो क्रमागत तल भिन्न रंगों के हैं :
Read this question in English
A five-storeyed building with floors from I to V is painted using four different colours and only one colour is used to paint a floor.
Consider the following statements:
1. The middle three floors are painted in different colours.
2. The second (II) and the fourth (IV) floors are painted in different colours.
3. The first (I) and the fifth (V) floors are painted red.
To ensure that any two consecutive floors have different colours
(a) Only statement 2 is sufficient · (b) Only statement 3 is sufficient · (c) Statement 1 is not sufficient, but statement 1 along with statement 2 is sufficient · (d) Statement 3 is not sufficient, but statement 3 along with statement 2 is sufficient
उत्तर और व्याख्या · explanation in English
Answer: (b) केवल कथन 3 पर्याप्त है
All four colours are used on five floors, so exactly one colour repeats. If floors I and V are both red, red is that repeat, and floors II, III and IV must take the other three colours, one each — no two neighbours can match. Statements 1 and 2 leave the end floors free to copy a neighbour.
- Five floors, four colours, all four used: one colour appears on two floors, the others once each.
- Statement 3: I and V are red, so red is the repeated colour; II, III and IV take the other three colours, all different and none red.
- Hence I–II, II–III, III–IV and IV–V all differ: statement 3 alone is sufficient.
- Statement 1: II, III, IV differ, but floor I may copy floor II (e.g. blue, blue, green, yellow, red) — not sufficient.
- Statement 2 (II ≠ IV) is already implied by statement 1, so 1 and 2 together are still not sufficient; 2 alone says nothing about any adjacent pair.
- ✗ 1. Not sufficient: it leaves the pairs I–II and IV–V unchecked.
- ✗ 2. Not sufficient: floors II and IV are not neighbours, so it controls no consecutive pair.
- ✓ 3. Sufficient: it forces II, III and IV to be the three non-red colours, all different.
Remember · 'Painted using four different colours' means all four are used; with five floors exactly one colour repeats — build from that count.
Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·