Question : Which of the numbers amongst 25560, 35751, 48168, and 49608 is NOT divisible by 24?
Option 1: 35751
Option 2: 48168
Option 3: 25560
Option 4: 49608
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Correct Answer: 35751
Solution : Given Numbers = 25560, 35751, 48168, and 49608 For a number to be divisible by 24, it should be divisible by both 3 and 8. Divisibility rule for 3 = A number is completely divisible by 3 if the sum of its digits is divisible by 3. Divisibility rule for 8 = A number is completely divisible by 8 if the last three digits of the number are divisible by 3. (i) 25560 For 3: 2 + 5 + 5 + 6 + 0 = 18 18 is divisible by 3 which means the number is divisible by 3. For 8: the last three digits = 560, when divided by 8 gives 0 as the remainder. $\therefore$ 25560 is divisible by 24 (ii) 35751 For 3: 3 + 5 + 7 + 5 + 1 = 21, divisible by 3 For 8: The last 3 digits = 751, which is not divisible by 8. (iii) 48168 For 3: 4 + 8 + 1 + 6 + 8 = 27, divisible by 3 For 8: Last 3 digits = 168, when divided by 8 gives the remainder 0. $\therefore$ 48168 is divisible by 24 (iv) 49608 For 3: 4 + 9 + 6 + 0 + 8 = 27, divisible by 3 For 8: Last 3 digits = 608, divisible by 8 Hence, the correct answer is 35751.
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