UPSC Prelims 2021 · CSAT
Question 60: Basic Numeracy
Consider the following multiplication problem : (PQ) × 3 = RQQ, where P, Q and R are different digits and R ≠ 0. What is the value of (P + R) ÷ Q ?
AnswerUPSC’s answer is (b).
Write (10P + Q) × 3 = 100R + 11Q, so 30P + 3Q = 100R + 11Q, which gives 15P = 50R + 4Q. The units digit of 3Q equals Q, so 2Q ends in 0, making Q = 0 or 5. Q = 0 forces 3P = 10R, impossible with R ≠ 0 and a one-digit P. So Q = 5: 3P = 10R + 4, which gives R = 2 and P = 8. Check: 85 × 3 = 255. Then (P + R) ÷ Q = 10 ÷ 5 = 2. Remember: use the units-digit condition to narrow candidates before solving.
Why each option is right or wrong
- (a) P + R = 10 and Q = 5, so the value is 2, not 1.
- (b) Right: P = 8, Q = 5, R = 2 gives 85 × 3 = 255 and (8 + 2) ÷ 5 = 2.
- (c) 5 would need P + R = 25, impossible with single digits.
- (d) The conditions fix a single solution, so the value can be determined.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2021, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.