Question
How many values can 'x' take if the number 7531xk must be
divisible by 15 for any valid digit 'k'?Solution
ATQ,
Divisible by 15 ⇒ divisible by both 5 and 3
Divisible by 5: last digit k must be 0 or 5
Divisible by 3: sum of digits must be divisible by 3
Case 1: k = 0
Sum = 7 + 5 + 3 + 1 + x + 0 = x + 16
Divisible by 3 ⇒ x = 2, 5, 8
Case 2: k = 5
Sum = 7 + 5 + 3 + 1 + x + 5 = x + 21
Divisible by 3 ⇒ x = 0, 3, 6, 9
Total values of x: 3 (case 1) + 4 (case 2) = 7 values
Find the circumference and area of a circle of radius 7 cm. Take π = 22/7.
The base of the triangular area is two times its height. If the cost of farming area is Rs. 2000 and Rs. 80 per hectare. Find its base (1 hectare = ...
The breadth of a rectangle is increased by 9 cm, it will become twice the length of the rectangle. If the new perimeter is 294 cm, then find the origina...
Two wires A and B are made of the same material and have the same length but different cross-sectional areas. If the resistance of wire A is 9 times the...
The cost of fencing a rectangular field at the rate of Rs. 5/metre is Rs. 350. If the length of the field is 11 metres more than its breadth, then find ...
In a rectangular floor of length and breadth of 19 metres and 6 metres, respectively, square tiles each of 2 metre edge length are to be laid. If the co...
The perimeter of an equilateral triangle is 36√3 cm. Find its height.
The volume of a cuboid is 480 cubic cm. If its length is 10 cm and breadth is 8 cm, find its height.
Find the length of a wire radius 0.40 cm which can completely cover the surface of a cylinder whose height is 1.6m and base radius 21 cm?
A wire, when bent in the form of a square encloses an area of 121 sq. cm. If the same wire is bent in the form of a circle, what is the area enclosed by...
Relevant for Exams:
