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Find the least of value of ‘x’ so that the number 73818x4 is divisible by 8
Answer : B
Explanation:A number is exactly divisible by 8, then the last 3 digits of the numbers must be divisible by 83
Here the last 3 digits are 8x4.
Put each value in given options in the place of x and check whether it is divisible by 8 or not .
Option b , 824 which is exactly divisible by 8.
So answer is option b.
Divisibility Rules Solved Problem 7.Find the least of value of ‘*’ so that the number 37*124 is divisible by 9 ?
Answer : A
Explanation:
if a number is divisible by 9, the sum of its digits must be a multiple of 9.
Here, 3+7+*+1+2+4=17+*
Here the value of * must be 1 because the next multiple of 9 is 18.
Divisibility Rules Solved Problem 8.For a number to be divisible by 88 it should be:
Answer: C
Explanation:
For a number to be divisible by 88, the number must be divisible by 8 and 11.
Write 88 as product of two factors : 22 ,2
11 ,8
44,2
Of these pairs , 11 and 8 are co primes.
So the number must be divisible by 8 and 11.
Divisibility Rules Solved Problem 9.What is the smallest number which must be added to 8261955 so as to obtain a sum which is divisible by 11?
Answer : B
Explanation:
For divisibility by 11, the difference of sums of digits at even and odd places must be either zero or divisible by 11.
For 8261955, Difference =(8+6+9+5) (2+1+5)=288=20.
The units digit is at odd place. So we add 2 to the number
=> 8261955 +2 = 8261957
Now , (8+6+9+7) (2+1+5)=308=22 => 22 is a multiple of 11 and hence 8261957 is also divisible by 11.
What is the missing digit which makes the number 9724* exactly divisible by 6?
Answer : A
Explanation:
Divisibility by 6 requires that the number be divisible by 2 as well as 3 , i.e, the following 2 conditions must be met
i) Unit digit be Zero or even
ii) Sum of digits be divisible by 3
The given number is 9724*
Sum of the digits =9 +7 +2 +4 +* =22+*
The digit which on being added to 22 will give the sum divisible by 3 are
22+2 =24 and 22 +5=7.
2 and 7 satisfy the condition ii.
The blank space is at unit's place. So the missing digit must satisfy the condition (i) also
Out of 2 and 5, only 2 is even.
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