Question 6 Exercise 3.3
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Answer:
SOLUTION:
Let the required unknown digit be x Then,
Sum of digits at odd places from right = 9 + 3 + 2 = 14 Sum of digits at even places from right = 8 + x +9 = 17 + x
∵ Number is divisible by 11.
∴ Difference of digits will be 0 or 11.
⇒ (17+x)−14= 0 or 11
⇒ 17+x−14=0 or 11
⇒ x+3= 0or 11 Taking difference 0,
0,x+3=0
⇒ x=03=−3 (not possible) Taking difference 11,
x=3=11 So, required digit to write in the blank space is 11
(b) Let the required unknown digit be x. Then, number be
Sum of digits at odd places from right = 4 + 4 + x = 8 + x
Sum of digits at even places from right = 8 + 9 + 8 = 25
∵ Number is divisible by 11.
∴ Difference of digits will be 0 or 11.
⇒ 25−(8+x) = 0 or 11
⇒ 258x = 0 or 11
⇒ 17x = 0 or 11 Taking difference 0,
17−x=0
⇒x=17+0
⇒x=17
but 17 is not a single digit number, so it is not possible
Taking difference 11,
17-x =11
⇒ x = 17-11= 6
So, required digit to write in the blank space is 6
Video transcript
hello guys welcome to leader homework today we're doing question number six write a digit in the blank space of each of the following numbers so that the number formed is divisible by 11. so to do this uh first of all let's identify uh understand what is the divisibility test of 11. so for 11 what you have to do is let me just write this number down with the blank space i'm writing as x okay so the blank number is x for now and 3 8 9. so for 11 what we have to do is we have to first of all identify all the numbers at the events places so all the numbers at events place is 2 3 and 9 okay so not even numbers the numbers are the even places that is second place fourth is and the sixth place so they are two three and nine next step uh you have to add them so after adding two 3 and 9 the answer is going to be 5 plus 9 which is 14 right now identify all the numbers at the odd places which is the first place third place and the fifth place so the first place has the digit or nine okay so 9 plus x plus uh yeah 9 plus x plus 18 so 9 plus x plus 18 9 plus 18 is 17 so it is going to be 17 plus x right i hope you're following now the next step is that when you subtract both of them your answer should either be 0 or the answer should be 11. so 17 plus x minus 14 should be equal to 11 or should be equal to 0 i'm sorry or 11 it's up to you but we have to find the smaller one so i suppose we should leave it as 11 right so leave it as 0 so 17 minus 14 is 3 and 3 plus x is equal to 0 therefore your x will be 3 right i hope you're following let's move on to the next question which is 8 x um sorry eight x nine four eight four same procedure again uh add all the numbers of the odds place one so i thought this we have eight nine and eight so eight plus 9 plus 8 will give you 26 right now add all the places that evens place at the events place it's x plus 4 plus 4 which is going to be 8 plus x 26 minus 8 plus x should be equal to 11 which or 0 it's up to you now 26 minus 8 will give you 16 okay so 16 plus x is equal to 11 right therefore your answer for x is equal to five okay thank you guys for watching the video if you yet have any doubts please let me know in the comments below and i'll get back to you as soon as possible also please like the video and subscribe the channel thank you so much
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