UPSC Prelims 2022 · CSAT
Question 54: Basic Numeracy
Let A, B and C represent distinct non-zero digits. Suppose x is the sum of all possible 3-digit numbers formed by A, B and C without repetition. Consider the following statements :
- 1.The 4-digit least value of x is 1332.
- 2.The 3-digit greatest value of x is 888.
Which of the above statements is/are correct?
AnswerUPSC’s answer is (a).
In the six three-digit numbers formed from A, B and C, each digit appears twice in every place, so the sum is x = 222 (A + B + C). A + B + C ranges from 1 + 2 + 3 = 6 to 7 + 8 + 9 = 24. The least x is 222 × 6 = 1332, a 4-digit number, so statement 1 is correct. Every x is at least 1332, so no x is a 3-digit number, and statement 2 is false.
- 1. Least x = 222 × 6 = 1332, a 4-digit number.
- 2. x is never below 1332, so no 3-digit value exists.
How you could have got this
- If you were sure statement 1 is correct, (b) and (d) go: each of them leaves 1 out.
What you needed to know: Least x = 222 × 6 = 1332, a 4-digit number.
- Then, if you were sure statement 2 is not correct, (c) goes: it includes 2.
What you needed to know: x is never below 1332, so no 3-digit value exists.
Only (a) is left. This one needs every statement.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) Correct: 1332 is the least x, and statement 2 is false.
- (b) Wrong: no value of x is three-digit.
- (c) Wrong: statement 2 fails.
- (d) Wrong: statement 1 holds.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2022, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.