Question

The sum of all the numbers formed by the digits x,y and z of the number xyz is divisible by​

Answer 1

The correct answer is option (c) 37

EXPLANATION:-

It is known that, three numbers which can be formed by the using the digits x, y and z are xyz, yzx and zxy.

It is known that, three numbers which can be formed by the using the digits x, y and z are xyz, yzx and zxy.The general form of xyz = 100x + 10y + z.

It is known that, three numbers which can be formed by the using the digits x, y and z are xyz, yzx and zxy.The general form of xyz = 100x + 10y + z.The general form of yzx = 100y + 10z + x.

It is known that, three numbers which can be formed by the using the digits x, y and z are xyz, yzx and zxy.The general form of xyz = 100x + 10y + z.The general form of yzx = 100y + 10z + x.The general form of zxy = 100z + 10x + y.

It is known that, three numbers which can be formed by the using the digits x, y and z are xyz, yzx and zxy.The general form of xyz = 100x + 10y + z.The general form of yzx = 100y + 10z + x.The general form of zxy = 100z + 10x + y.Add the three numbers, we will get

It is known that, three numbers which can be formed by the using the digits x, y and z are xyz, yzx and zxy.The general form of xyz = 100x + 10y + z.The general form of yzx = 100y + 10z + x.The general form of zxy = 100z + 10x + y.Add the three numbers, we will getxyz + yzx + zxy = (100x + 10y + z) + (100y + 10z + x) + (100z + 10x + y).

It is known that, three numbers which can be formed by the using the digits x, y and z are xyz, yzx and zxy.The general form of xyz = 100x + 10y + z.The general form of yzx = 100y + 10z + x.The general form of zxy = 100z + 10x + y.Add the three numbers, we will getxyz + yzx + zxy = (100x + 10y + z) + (100y + 10z + x) + (100z + 10x + y).xyz + yzx + zxy = 100x + 10x + x + 100y + 10y + y + 100z + 10z + z

It is known that, three numbers which can be formed by the using the digits x, y and z are xyz, yzx and zxy.The general form of xyz = 100x + 10y + z.The general form of yzx = 100y + 10z + x.The general form of zxy = 100z + 10x + y.Add the three numbers, we will getxyz + yzx + zxy = (100x + 10y + z) + (100y + 10z + x) + (100z + 10x + y).xyz + yzx + zxy = 100x + 10x + x + 100y + 10y + y + 100z + 10z + zxyz + yzx + zxy = 111x + 111y + 111z.

SIMPLIFYING:-

xyz + yzx + zxy = 111(x + y + z).

xyz + yzx + zxy = 111(x + y + z).Now, it is clear that 111 is the common factor. So,

xyz + yzx + zxy = 111(x + y + z).Now, it is clear that 111 is the common factor. So,xyz + yzx + zxy is divisible by 111

xyz + yzx + zxy = 111(x + y + z).Now, it is clear that 111 is the common factor. So,xyz + yzx + zxy is divisible by 111Also xyz + yzx + zxy will be divisible by factors of 111.

FINAL ANSWER:-

• From the given options, 11, 33, and 74 are not the factors of 11 whereas 37 is the factor of 111.