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UPSC Prelims 2025CSATGeneral Mental AbilityNumber System - Divisibility

Q50. 50. The difference between any two natural numbers is 10. What can be said about the natural numbers which are divisible by 5 and lie between these two numbers?

A. There is only one such number.
B. There are only two such numbers.
C. There can be more than one such number.✓ Correct
D. No such number exists.

Detailed Solution

✓ Correct Answer: Option C

Let the two natural numbers be N1 and N2, with N2 - N1 = 10. We are looking for numbers divisible by 5 that lie strictly between N1 and N2. Let's test different pairs of numbers with a difference of 10: * Case 1: N1 = 1, N2 = 11.

Numbers between 1 and 11 that are divisible by 5 are 5 and 10. In this case, there are two such numbers. * Case 2: N1 = 5, N2 = 15. The only number between 5 and 15 that is divisible by 5 is 10.

In this case, there is only one such number. * Case 3: N1 = 2, N2 = 12. Numbers between 2 and 12 that are divisible by 5 are 5 and 10. In this case, there are two such numbers. Since we found cases where there is one such number (e.g., between 5 and 15) and cases where there are two such numbers (e.g., between 1 and 11), we can conclude that there can be more than one such number.

Option (c) "There can be more than one such number" correctly captures this variability. Options (a) and (b) are too restrictive, and (d) is clearly false. This question tests logical reasoning and number properties through examples.

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