If the 8 digit number 179x091y is divisible by 88 then what is the value of (x-y)?
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Answers
Answer:
- 179x091y is completely divisible by 88
- Find the vale of (x - y)
We can write 88 as (8 × 11), so If the number is divisible by 8 and 11 then it is divisible by 88 too.
Before heading to the question, let's know divisibility rule of 8 and 11
- If Last three digit of the given number is divisible by 8, then number is completely divisible by 8
- Difference of sum of Odd places and Even places digits is either 0 or multiple of 11, then number is completely divisible by 11
First we will check divisibility by 8, and for that we will take Last Three Digits i.e. 91y. Will check by putting different number at the place of y
⇒ y = 0 ; 910 isn't divisible by 8
⇒ y = 1 ; 911 isn't divisible by 8
⇒ y = 2 ; 912 is divisible by 8
⇒ y = 3 ; 913 isn't divisible by 8
⇒ y = 4 ; 914 isn't divisible by 8
⇒ y = 5 ; 915 isn't divisible by 8
⇒ y = 6 ; 916 isn't divisible by 8
⇒ y = 7 ; 917 isn't divisible by 8
⇒ y = 8 ; 918 isn't divisible by 8
⇒ y = 9 ; 919 isn't divisible by 8
Only value which satisfy y is 2, hence our number will be : 179x0912
Last we will check divisibility of 11, and for that we will sum odd places and even places separately.
Sum of even places = (1 + 0 + 9 + 1) = 11
Sum of odd places = (2 + 9 + x + 7) = (18 + x)
Now we can't subtract (18 + x) from 11 as it is greater number, hence we take the next multiple of 11.
⇒ (18 + x) = 11 × 2
⇒ (18 + x) = 22
⇒ x = 22 - 18
⇒ x = 4
- Required Number = 17940912
∴ Value of x & y are 4 & 2 respectively.
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Q. Find the Value of (x - y) ?
Answer : (x - y) = (4 - 2) = 2
∴ Hence, the correct option is (d) 2.
Answer:
x - y = 2
Step-by-step explanation:
Now at first glance its might be impossible to solve, but thinking further all Questions eventually gets an Answer.
Lets take the Divisor first.
Divisor = 88
Now,
88 = 8 × 11
And if a number is divisible by 88, then logically it should be divisible by 8 and 11 right?
Yes.
So,
179x091y should be divisible by 8 and 11.
So, now what.
Now, here is when divisibility rule of numbers becomes crucial.
Divisibility rule of 8 tells us that, A number is divisible by 8 only if its last 3 digits are divisible by 8.
Hence,
179x091y is divisible by 8, only if 91y is divisible by 8, and since we know that 179x091y is divisible by 8, again logically, 91y should also be divisible by 8.
Now, let's divide 91y with 8,
11
________
8 | 91y
- 8
——
11
- 8
——
3y
So, now we are left with 3y as the remainder.
Here,
3y is a two digit number starting with 3.
Thus, we know that, in 8's table only 32 is divisible by 8.
Hence,
3y = 32
y = 2
Thus,
The number becomes 179x0912.
Again, this number is also divisible by 11.
The divisibility rule of 11 says that, a number is divisible by 11, if its alternate sum of digits are a multiple of 11.
Thus,
1 - 7 + 9 - x + 0 - 9 + 1 - 2 = 11k
where k is an integer.
-7 - x = 11k
x = -7 - 11k
Let k = 0,
x = -7 - 11(0)
x = (-7)
x = (-7)
Since the digit of a number can't be negative, x ≠ (-7).
Let k = (-1)
x = -7 - 11(-1)
x = -7 + 11
x = 4
Thus,
x = 4 is the smallest and the only solution for x,
So, The original number is 17940912.
Hence,
x = 4 and y = 2
Now, we must find what (x - y) is,
So,
x - y = 4 - 2
= 2
Hence,
x - y = 2
Hope it helped and believing you understood it. All the best.