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What is the value of k such that 70k is divisible by 7
A.6
B.7
C.8
D.9

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Last updated date: 19th Jun 2024
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Answer
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Hint: In 70k the units place is occupied by k . By replacing it with one of our options we need to check the divisibility of the number. With 7 in the place of k , to check the divisibility of 7 multiply the last digit by 2 and subtract it from the number formed by the other two digits. If the difference is 0 or divisible by 7 then the number is divisible by 7.

Complete step-by-step answer:
Step 1:
In 70k the units place is occupied by k
And we need to value for k such that the number is divisible by 7
Step 2:
We know the divisibility rule of 7
We must choose the last digit of the number and multiply it by 2.
And subtract the product from the rest of the number .
And if the difference is zero or divisible by 7 then the whole number is divisible by 7
Step 3
Now let's consider the number 7 from the options.
So our number will be 707
First we need to multiply the last digit by 2
(i.e) 7*2=14
Now let's subtract 14 from the number formed by the other two digits (i.e.)70
Subtracting 14 from 70 , we get
70 – 14 = 56
Now we know that 56 is divisible by 7
Hence the number 707 is divisible by 7

The correct option is B.

Note: Many students tend to think 70k as 70*k but in this problem 70k means that the units place is occupied by k
For divisibility of 2 , the units place must be a even number
And for divisibility of 3 , 9 , 11 the sum of the digits must be the multiples of 3 , 9 and 11 respectively.