If the 5-digit number 535ab is divisible by 3, 7 and 11, then what is the value of ( a^2 – b^2+ ab)?
95
83
89
77
Answers
Answer:
First option
95
Step-by-step explanation:
Given:-
The 5-digit number 535ab is divisible by 3, 7 and 11.
To find:-
what is the value of ( a^2 – b^2+ ab)
Solution:-
Given 5-digit number = 535ab
If it is divisible by 3,7 and 11 then it is also divisible by their LCM
LCM of 3 ,7 and 11 = 3×7×11 = 231
Now The greatest possible value of the given number 535ab is 53599
So ,On dividing 53599 by 231
53599 = 232×231+7
=>>53599=53592+7
We get remainder = 7
The required number = 53599-7 = 53592
The number is divisible by 3,7,11
535ab = 53592
We have a = 9 and b= 2
Now , The value of a^2 – b^2+ ab
On Substituting the values of a and b then
=>9^2 - 2^2 +(9×2)
=>81 -4 +18
=>99 - 4
=>95
Answer:-
The value of a^2 – b^2+ ab for the given problem is 95
Used formulae:-
If a number is divisible by two or more numbers then it is also divisible by their LCM.
First option
95
Step-by-step explanation:
Given:-
The 5-digit number 535ab is divisible by 3, 7 and 11.
To find:-
what is the value of ( a^2 – b^2+ ab)
Solution:-
Given 5-digit number = 535ab
If it is divisible by 3,7 and 11 then it is also divisible by their LCM
LCM of 3 ,7 and 11 = 3×7×11 = 231
Now The greatest possible value of the given number 535ab is 53599
So ,On dividing 53599 by 231
53599 = 232×231+7
=>>53599=53592+7
We get remainder = 7
The required number = 53599-7 = 53592
The number is divisible by 3,7,11
535ab = 53592
We have a = 9 and b= 2
Now , The value of a^2 – b^2+ ab
On Substituting the values of a and b then
=>9^2 - 2^2 +(9×2)
=>81 -4 +18
=>99 - 4
=>95
Answer:-
The value of a^2 – b^2+ ab for the given problem is 95
Used formulae:-
If a number is divisible by two or more numbers then it is also divisible by their LCM.