Let the number be 476ab0
476ab0 is divisible by 3
=> 4 + 7 + 6 + a + b + 0 is divisible by 3
=> 17 + a + b is divisible by 3 ------------------------(i)
476ab0 is divisible by 11
[(4 + 6 + b) -(7 + a + 0)] is 0 or divisible by 11
=> [3 + (b - a)] is 0 or divisible by 11 --------------(ii)
Substitute the values of a and b with the values given in the choices and select the values which satisfies both Equation 1 and Equation 2.
if a=6 and b=2,
17 + a + b = 17 + 6 + 2 = 25 which is not divisible by 3 --- Does not meet equation(i).Hence this is not the answer
if a=8 and b=2,
17 + a + b = 17 + 8 + 2 = 27 which is divisible by 3 --- Meet equation(i)
[3 + (b - a)] = [3 + (2 - 8)] = -3 which is neither 0 nor divisible by 11---Does not meet equation(ii).Hence this is not the answer
if a=6 and b=5,
17 + a + b = 17 + 6 + 5 = 28 which is not divisible by 3 --- Does not meet equation (i) .Hence this is not the answer
if a=8 and b=5,
17 + a + b = 17 + 8 + 5 = 30 which is divisible by 3 --- Meet equation 1
[3 + (b - a)] = [3 + (5 - 8)] = 0 ---Meet equation 2
Since these values satisfies both equation 1 and equation 2, this is the answer
The pattern is ,
The next number= = 4964
Let the number be x.Then
60% of of x=36.
=>
=> => x=
Required number is 100.
Let the required fraction be x. Then | 1 | - x = | 9 |
x | 20 |
∴ | 1 - x2 | = | 9 |
x | 20 |
⟹ 20 - 20x2 = 9x
⟹ 20x2 + 9x - 20 = 0
⟹ 20x2 + 25x - 16x - 20 = 0
⟹ 5x(4x + 5) - 4(4x + 5) = 0
⟹ (4x + 5)(5x - 4) = 0
x = | 4 |
5 |
The pattern is -45, -35, -25, -15
The next number = 20-15= 5
The square of a natural number never ends in 7.
42437 is not the square of a natural number
To find the largest 4 digit number exactly divisible by 88,
We should divide the largest possible 4 digit number by 88, and if we get any remainder than subtract it from that largest number.
The largest possible 4 digit number is 9999
Now,
88) 9999 (113
88
_______
119
88
_______
319
264
_______
55
_______
Therefore, the largest 4 digit number exactly divisible by 88 is given by
9999 - 55 = 9944.
LCM of 2, 3, 7 is 42.
=> (700 ? 300)/42 = 9 22/42 => 9 Numbers.
∴ | a + b | = | 12 | ⟹ | ❨ | 1 | + | 1 | ❩ | = | 12 |
ab | 35 | b | a | 35 |
∴ Sum of reciprocals of given numbers = | 12 |
35 |
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