If 545A is a multiple of 11 , where A is a digit , what is the value of A?
Please give the correct answer by step by step method
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If 545A is a multiple of 11 , where A is a digit , what is the value of A?
Please give the correct answer by step by step method
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Answer:
6
Step-by-step explanation:
From the test of divisibility by 11, we know that, a number is divisible by 11, if the difference between the sum of digits at odd places and the sum of digits at even places is either 0 or a multiple of 11.
For 545A, sum of digits at even places 5+5=10
and sum of digits at odd places = 4+A
Hence, 10−4-A=6-A or A-6 must be either 0 or some multiple of 11.
∴ 6−A=0⇒A=6
or 6−A=11⇒A=-5
or 6−A=22⇒A=−16
and so on.
Also,
A−6=0⇒A=6
or A−6=11⇒y=17
or A−6=22⇒A=28
and so on.
But, we observe that when the difference is 0, we get A=6
and if it is any multiple of 11, the value is either negative or more than one digit, which are both not possible.
Hence, the value of the difference must be 0.
∴ A=6
Hence, the value of y for which 545A is divisible by 11, is 6.