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Find the greatest number of 5 digits, that will give us remainder of 5, when divided by 8 and 9 respectively.
- a)99921
- b)99931
- c)99941
- d)99951
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Find the greatest number of 5 digits, that will give us remainder of 5...
Greatest 5-Digit number = 99999
LCM of 8 and 9,
8 = 2 × 2 × 2
9 = 3 × 3
LCM = 2 × 2 × 2 × 3 × 3 = 72
Now, dividing 99999 by 72, we get
Quotient = 1388
Remainder = 63
So, the greatest 5-digit number divisible by 8 and 9 = 99999 - 63 = 99936
Required number = 99936 + 5 = 99941
Most Upvoted Answer
Find the greatest number of 5 digits, that will give us remainder of 5...
Given, the number should give a remainder of 5 when divided by both 8 and 9.
Solution:
We know that if a number gives a remainder of ‘r’ when divided by ‘n’, then the number can be written as follows:
Number = nq + r
where q is the quotient obtained on dividing the number by n.
Let the required number be ‘x’.
Therefore, x = 8a + 5 and x = 9b + 5, where ‘a’ and ‘b’ are integers.
Solving these equations, we get:
8a + 5 = 9b + 5
8a = 9b
We can see that ‘b’ must be divisible by 8, as 8a and 9b are both multiples of 8.
Let ‘b’ be 8c. Then, we get:
a = 9c
Therefore, x = 8a + 5 = 8(9c) + 5 = 72c + 5
We need to find the greatest 5-digit number of this form.
The greatest 5-digit number of this form will be obtained by taking the maximum possible value of ‘c’.
When ‘c’ is maximum, the value of ‘x’ is also maximum.
The greatest 5-digit number is 99999.
Therefore, we need to find the maximum value of ‘c’ such that 72c is less than or equal to 99994.
We get, c = 1388.
Therefore, the required number is:
x = 72c + 5 = 72 × 1388 + 5 = 99941
Hence, option (c) is the correct answer.
Solution:
We know that if a number gives a remainder of ‘r’ when divided by ‘n’, then the number can be written as follows:
Number = nq + r
where q is the quotient obtained on dividing the number by n.
Let the required number be ‘x’.
Therefore, x = 8a + 5 and x = 9b + 5, where ‘a’ and ‘b’ are integers.
Solving these equations, we get:
8a + 5 = 9b + 5
8a = 9b
We can see that ‘b’ must be divisible by 8, as 8a and 9b are both multiples of 8.
Let ‘b’ be 8c. Then, we get:
a = 9c
Therefore, x = 8a + 5 = 8(9c) + 5 = 72c + 5
We need to find the greatest 5-digit number of this form.
The greatest 5-digit number of this form will be obtained by taking the maximum possible value of ‘c’.
When ‘c’ is maximum, the value of ‘x’ is also maximum.
The greatest 5-digit number is 99999.
Therefore, we need to find the maximum value of ‘c’ such that 72c is less than or equal to 99994.
We get, c = 1388.
Therefore, the required number is:
x = 72c + 5 = 72 × 1388 + 5 = 99941
Hence, option (c) is the correct answer.
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Community Answer
Find the greatest number of 5 digits, that will give us remainder of 5...
Hey see
Lcm of 8 and 9 is 72
greatest 5 digit number is 99999
divide it by 72.
u get 63 as remainder
now subtract 63 from 99999.
99936 it is divisible by 8 and 9 now add 5
it is 99941 so it give remainder 5
Lcm of 8 and 9 is 72
greatest 5 digit number is 99999
divide it by 72.
u get 63 as remainder
now subtract 63 from 99999.
99936 it is divisible by 8 and 9 now add 5
it is 99941 so it give remainder 5
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Find the greatest number of 5 digits, that will give us remainder of 5, when divided by 8 and 9 respectively.a)99921b)99931c)99941d)99951Correct answer is option 'C'. Can you explain this answer?
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