IBPS PO Mains 5 Nov 2023 Paper

Concept:The three-digit number and the multiplier are factor pairs of $2634$. Use the tens-digit condition to identify the correct pair.Explanation:Factorize $2634$: $2634 = 2 \times 3 \times 439$.Possible factor pairs where one factor is a three-digit number: $439 \times 6$ and $878 \times 3$.For $439$ and $X = 6$: the tens digit of $439$ is $3$, and $\frac{X}{2} = \frac{6}{2} = 3$. This satisfies the condition.For $878$ and $X = 3$: the tens digit of $878$ is $7$, but $\frac{3}{2} = 1.5$. This does not match.So the number is $439$ and $X = 6$.Statement I: The unit digit of $439$ is $9$, so it is correct.Statement II: Sum of digits $= 4 + 3 + 9 = 16$, so it is correct.Statement III: $439$ is prime because it is not divisible by any prime up to $\sqrt{439} \approx 20.95$. So it is correct.All three statements are true.Answer:Option C: All I, II, and III.