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प्रश्न
The sum of all the numbers formed by the digits x, y and z of the number xyz is divisible by ______.
विकल्प
11
33
37
74
उत्तर
The sum of all the numbers formed by the digits x, y and z of the number xyz is divisible by 37.
Explanation:
We have, xyz + yzx + zxy
= (100x + 10y + z) + (100y + 10z + x) + (100z + 10x + y) ...(i)
= 100x + 10x + x + 10y + 100y + y + z + 100z + 10z
= 111x + 111y + 111z
= 111(x + y + z)
= 3 × 37 × (x + y + z)
Hence, equation (i) is divisible by 37, but not divisible by 11, 33 and 74.
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