If x + y + z = 6 and z is an odd digit, then the three-digit number xyz is
(a) an odd multiple of 3
(b) odd multiple of 6
(c) even multiple of 3
(d) even multiple of 9
Solution:
Since x + y + z = 6 and z is a odd digit it means that z is either 1 or 3 or 5
If z = 5 then x + y =1 which means that x = 1 and y = 0 because xyz is a three digit number because x cannot be zero. So z can be 5. The three digit number is 105.
If z = 3 then x + y = 3 which means that both x and y can be either 1 or 2. So the possible three digit numbers can be 123 or 213.
If z = 1 then x + y = 5 which means x and y both can take values 1, 2, 3, or 4. The possible three digit numbers are 141, 411, 231, and 321.
It can be seen that all numbers formed are odd multiples of 3 because the sum of digits will be 6, which is divisible by 3.
Hence the number xyz is an odd multiple of 3.
The correct choice is (a)
✦ Try This: If x + y + z = 4 and z is an odd digit, then the three-digit number xyz is (a) may be a multiple of 11, (b) may not be a multiple of 11, (c) will be an odd number, (d) will be an odd number ending in one, (e) Both (a) & (d)
Since x + y + z = 4 and z is a odd digit it means that z is either 1 or 3 because
If z = 3 then x + y =1 which means that either x = 1 and y = 0. X cannot be zero because xyz is a three digit number. So z can be 3. The three digit number will be 103
If z = 1 then x + y = 3 which means that both x and y can be either 1 or 2
Since z is 1 and x, y could be either 1 or 2. The numbers possible are 111, 121, 221 and 211
Hence the correct answer is (e).
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 16
NCERT Exemplar Class 8 Maths Chapter 13 Problem 12
If x + y + z = 6 and z is an odd digit, then the three-digit number xyz is (a) an odd multiple of 3, (b) odd multiple of 6, (c) even multiple of 3, (d) even multiple of 9
Summary:
If x + y + z = 6 and z is an odd digit, then the three-digit number xyz is an odd multiple of 3
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