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Write a digit in the blank space of each of the following numbers so that the number formed is divisible by 11:(a) 92___389(b) 8 ___ 9484. |
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Answer» (a) 92 ___ 389:- Let a be placed in the blank. sum of the digits at odd places = 9 + 3 + 2 = 14 Sum of the digits at even places = 8 + a = 9 = 17a Difference = 17 + a – 14 = 3 + a For a number to be divisible by 11, this difference should be zero or a multiple of 11. If 3 + a = 0, then a = -3 However, It cannot be negative. A closest multiple of 11, which is near to 3, has to be taken. It is 11 itself 3 + a = 11 a = 11 – 3 a = 8 Therefore, the required digits is 8 (b) 8__9484:- Let a be placed in the blank. Sum of the digits at odds places = 4 + 4 + a = 8 + a Sum of the digits at even place = 8 + 9 + 8 = 25 Difference = 25 – 8 + a = 17 – a For a number to be divisible by 11, this difference should be zero or a multiple of 11. If 17 – a = 0, then a = 17 This is not possible A multiple of 11 has to be taken. Taking 11 we obtained 17 – a = 11 a = 6 Therefore the required digit is 6. |
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