A cow costs more than 4 goats but less than 5 goats. If a goat costs between ₹ 600 and ₹ 800, which of the following is a most valid conclusion ?

(a) A cow costs more than ₹ 2,500.
(b) A cow costs less than ₹ 3,600.
(c) A cow costs between ₹ 2,600 and ₹ 3,800.
(d) A cow costs between ₹ 2,400 and ₹ 4,000. ✓ UPSC's answer

Why the answer is (d)

• Let the cost of a goat be $G$, where $600 < G < 800$.

• The cost of a cow ($C$) is given by $4G < C < 5G$.

• To find the minimum possible cost of the cow, use the lower bound of $G$: $4 \times 600 = 2400$. Since $G > 600$, $C > 2400$.

• To find the maximum possible cost of the cow, use the upper bound of $G$: $5 \times 800 = 4000$. Since $G < 800$, $C < 4000$.

• Therefore, the cost of the cow must lie strictly between ₹ 2,400 and ₹ 4,000.

• Option (d) correctly identifies this full range of validity.

Why the other options are wrong

(a) A cow costs more than ₹ 2,500.: A cow can cost as low as just above ₹ 2,400 (e.g., if a goat costs ₹ 601, the cow costs > ₹ 2,404), so it is not necessarily more than ₹ 2,500.
(b) A cow costs less than ₹ 3,600.: A cow can cost up to just below ₹ 4,000 (e.g., if a goat costs ₹ 799, the cow costs < ₹ 3,995), so it is not necessarily less than ₹ 3,600.
(c) A cow costs between ₹ 2,600 and ₹ 3,800.: The range ₹ 2,600 to ₹ 3,800 is too narrow; a cow can validly cost between ₹ 2,400 and ₹ 2,600 or between ₹ 3,800 and ₹ 4,000.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2015, held on 23 August 2015. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.