Question

1. If the number 65 x 5 is divisible by 3 then the least digit to replace 'x'is
a) 1
b) 2
c) 0
d) 3

2. If the number 6702 x is divisible by 4 then the least digit to replace 'x' is
a) 2
b) 0
c) 4
d) 6

3. The number of possible digits for x such that 123456 x is divisible by 2 is
a) 1
b) 3
c) 5
d) 8

4. Number of possible digits for x such that 198 x 2 in divisble by 4 is
a) 1
b) 3
c) 5
d) 7

5. Number of possible digits for x such that 10 x 78 x is divisble by 3 is
a) 1
b) 3
c) 5
d) 7​

Answer 1

Answer:

hope it helps...........

Answer 2

Concept

A divisibility rule is a shortcut and useful way of ascertaining whether a given number is divisible by a fixed divisor by examining its digits,  without performing division.

Solution

1. if a number is divisible by three then the sum of its digits must also be divisible by 3

Therefore, in 65x5

6 + 5 + x + 5 must be divisible by 3

= 16 + x

here, the least value x can take is 2 by which sum becomes 18 and divisible by 3.

Thus, least digit to replace 'x' is 3

2.   If a number is divisible by 4 then its last two digits must be divisible by 4

here, the last two digits are 2x

the least value x can take is 0 as 20 is divisible by 4.

Thus, least digit to replace 'x' is 0

3. If a number is divisible by 2 then its last digit must be even.

The last digit of the number is x and from the options 8 is the only even integer.

Thus, least digit to replace 'x' is 8

4. If a number is divisible by 4 then its last two digits must be divisible by 4

here, the last two digits are x2

the least value x can take is 1 as 12 is divisible by 4.

Thus, least digit to replace 'x' is 1

5. if a number is divisible by three then the sum of its digits must also be divisible by 3

Therefore, in 10x78x

10 + x + 7+ 8+ x must be divisible by 3

= 25 + 2x

here, the least value x can take is 1 by which sum becomes 27 and divisible by 3.

Thus, least digit to replace 'x' is 1

#SPJ3