Question
What is the highest possible sum of (m + n) if the
number '9m813n2' is divisible by 12?Solution
ATQ,
A number is divisible by 12 if it is divisible by both 3 and 4.
A number is divisible by 4 when the last two digits of the number are divisible by 4.
'n2' is divisible by 4 when 'n' = 0, 2, 4, 6, or 8.
Since we have to find the maximum value, so 'n' = 8.
A number is divisible by 3 when the sum of its digits is divisible by 3.
So, (9 + m + 8 + 1 + 3 + 8 + 2) = (31 + m) must be divisible by 3.
So, 'm' = 2, 5, or 8.
Since we have to find the maximum value, so 'm' = 8.
Therefore, required value = 8 + 8 = 16 .
The sum of the perimeters of a square and a rectangle is 124 metres. If the sum of the length and breadth of the rectangle is 34 cm, then find the area ...
Which one among the following is the smallest?
A wire is bent to form a square whose sides are of 99 cm. If the same wire is bent to form a circle, then find the area (in cm2) of the circl...
The angle of elevation of the top of an unfinished tower at a point distant 78 m from its base is 30°. How much higher must the tower be raised (in ...
A square has a perimeter of 88 cm. Find its area.
A solid right circular cylinder of radius 7 cm and height 10 cm is melted and recast into small right circular cones each of radius 3.5 cm and height 8 ...
The perimeter of a rectangle is 80 cm. The side of a square is equal to the average of the length and breadth of the rectangle. Find the area of the squ...
Find the total surface area of a cylinder with radius 7 cm and height 10 cm.
Find the volume of a cylinder with radius 7 cm and height 5 cm. Take π = 22/7.
The length of a 744 metre long wire is 12 times the perimeter of a rectangular French garden. Find the area of the rectangular garden given that its len...
