एक अंक n > 3 भाज्य है 3 से लेकिन 6 से भाज्य नहीं है। निम्नलिखित में से कौन-सा एक 4 से भाज्य है?
सही उत्तर: (c) 2n + 4
दिया गया है कि n > 3 एक अंक है (अर्थात n, 4 से 9 के बीच का एक एकल-अंक पूर्णांक है), n, 3 से भाज्य है लेकिन 6 से भाज्य नहीं है। 3 से भाज्य एकल-अंक संख्याएं 3, 6, 9 हैं। चूंकि n, 6 से भाज्य नहीं है, इसलिए 6 को हटा दिया जाता है। चूंकि n > 3 है, इसलिए 3 को भी हटा दिया जाता है। इस प्रकार, n का एकमात्र संभावित मान 9 है। आइए n = 9 के लिए विकल्पों की जांच करें: (a) 2n = 2 x 9 = 18, जो 4 से भाज्य नहीं है। (b) 3n = 3 x 9 = 27, जो 4 से भाज्य नहीं है। (c) 2n + 4 = 2(9) + 4 = 22, जो 4 से भाज्य नहीं है। (d) 3n + 1 = 3(9) + 1 = 27 + 1 = 28, जो 4 से पूरी तरह भाज्य है (28/4 = 7)। अतः विकल्प (d) सही उत्तर है।
In English (Question & Model Answer)
A digit n > 3 is divisible by 3 but not divisible by 6. Which one of the following is divisible by 4?
Correct Option: (c) 2n + 4
Given that n > 3 is a digit (meaning n is a single-digit integer from 4 to 9), n is divisible by 3 but not divisible by 6. The possible single-digit numbers divisible by 3 are 3, 6, 9. Since n is not divisible by 6, 6 is eliminated. Since n > 3, 3 is also eliminated. Thus, the only possible value for n is 9. Let us check the options with n = 9: (a) 2n = 2 x 9 = 18, which is not divisible by 4. (b) 3n = 3 x 9 = 27, which is not divisible by 4. (c) 2n + 4 = 2(9) + 4 = 18 + 4 = 22 + 4 = 22... wait, 2(9) + 4 = 18 + 4 = 22, not divisible by 4? Let us recheck: 2n + 4 for n = 9 is 2(9) + 4 = 22. Wait, let us test all single-digit numbers for n where n is a multiple of 3 and not 6. The numbers are 9. Wait, what about other values if n is not strictly a single digit? The question says 'A digit n > 3'. In mathematical terminology, a digit is strictly from 0 to 9. Thus n = 9. Let us re-verify option c: 2n + 4 = 2(9) + 4 = 22. Wait, 22 is not divisible by 4. Let us check if there is any other interpretation or if n can be 9 and 2n+4 is not divisible by 4. Wait, let us check option c expression: if n is any number satisfying the condition, say n = 9, then 2n = 18 (even, not divisible by 4 because n is odd since it's a multiple of 3 not divisible by 6, so n must be odd, i.e., 9). Since n = 9 is odd, 2n is 2 x odd = twice an odd number, which is 4k + 2, meaning it is divisible by 2 but not 4. Adding 4 to 2n gives 2n + 4 = 4k + 2 + 4 = 4k + 6, which is also not divisible by 4. Wait, let us re-evaluate the options carefully or check standard UPSC key. For n = 9, 3n + 1 = 3(9) + 1 = 28, which is divisible by 4! Let us check option d: 3n + 1 = 3(9) + 1 = 28, and 28 divided by 4 is 7, which is completely divisible by 4. Therefore, option d is correct.