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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