Consider five people: Mita, Ganga, Rekha, Lakshmi, and Sana. Ganga is taller than both Rekha and Lakshmi. Lakshmi is taller than Sana. Mita is taller than Ganga. Which of the following conclusions are true? 1. Lakshmi is taller than Rekha 2. Rekha is shorter than Mita 3. Rekha is taller than Sana 4. Sana is shorter than Ganga A. 1 and 3 B. 3 only C. 2 and 4 D. 1 only
GATE 2019 · General Aptitude · Logical Reasoning · medium
Answer: C. 2 and 4
- Build the height chain: Given: Mita > Ganga, Ganga > Rekha, Ganga > Lakshmi, Lakshmi > Sana. By transitivity: Mita > Ganga > Rekha, so Mita > Rekha. Mita > Ganga > Lakshmi > Sana, so Ganga > Sana. Rekha and Sana are not connected by any given chain — we cannot determine their relative order.
- Check Conclusion 1: Lakshmi is taller than Rekha: We know Ganga > Rekha and Ganga > Lakshmi, but there is no direct or transitive chain between Lakshmi and Rekha. Lakshmi could be taller or shorter than Rekha — both are consistent with the given facts. Conclusion 1 is NOT necessarily true.
- Check Conclusion 2: Rekha is shorter than Mita: Chain: Mita > Ganga > Rekha. By transitivity, Mita > Rekha, i.e., Rekha is shorter than Mita. Conclusion 2 is TRUE.
- Check Conclusion 3: Rekha is taller than Sana: We know Ganga > Rekha and Ganga > Lakshmi > Sana. There is no established comparison between Rekha and Sana. Rekha could be taller or shorter than Sana. Conclusion 3 is NOT necessarily true.
- Check Conclusion 4: Sana is shorter than Ganga: Chain: Ganga > Lakshmi > Sana. By transitivity, Ganga > Sana, i.e., Sana is shorter than Ganga. Conclusion 4 is TRUE.
- Select the answer: Conclusions that are necessarily true: 2 and 4. This corresponds to option C.