Question

if a, b, c are three distinct integers from 2 to 10 (both inclusive). exactly one of ab, bc and ca is odd. abc id a multiple of 4. the arithmetic mean of a&b is an integer and so is the arithmetic mean of a, b and c. how many such triplets are possible(unordered triplets)? a. 8 b.2 c. 6 d. none e.4

Answer 1

The correct answer is option E

Exactly one of ab, bc and ca is odd  

Two are odd and one is even  

abc is a multiple of 4  

the even number is a multiple of 4  

The arithmetic mean of a and b is an integer  

a and b are odd  

and so is the arithmetic mean of a, b and c.

a+ b + c is a multiple of 3  

c can be 4 or 8.  

c = 4; a, b can be 3, 5 or 5, 9  

c = 8; a, b can be 3, 7 or 7, 9

Answer 2

Answer:

correct answer is option E

Step-by-step explanation:

exactly one of ab,bc and ca is odd

Two are odd and one is even

abc is a multiple of 4

The arthimetic mean of a and b is an integer

a and b are odd

and so is the arthimetic mean of a,b and

c

a+b+c is a multiple of 3

c can be 4 or 8 .

c = 4; a,b can be 3,5 or 5,9

c = 8; a,b can be 3,7 or 7,9