If a six-digit number 3x9z8y is divisible by 7, 11, 13, then the average value…
2020
If a six-digit number 3x9z8y is divisible by 7, 11, 13, then the average value of x, y, z is:
- A.
23/3
- B.
31/3
- C.
8
- D.
20/3
Attempted by 7 students.
Show answer & explanation
Correct answer: D
Given number:
3x9z8y
The number is divisible by 7, 11 and 13.
Since:
7 × 11 × 13 = 1001
Any number divisible by 7, 11 and 13 together must be divisible by 1001.
Now observe:
A 6-digit number of the form abcdef is divisible by 1001 if:
(abc) = (def)
Given number:
3x9z8y
So,
3x9 = z8y
Comparing digits:
z = 3
8 = x
y = 9
Therefore:
x = 8
y = 9
z = 3
Average of x, y, z:
= (8 + 9 + 3)/3
= 20/3