can you give a brief answer for this question

Asked by ramhari | 27th Apr, 2010, 02:14: PM

Expert Answer:

Dear Student,

The answer to your queston is (a) 0.

Reason:

the given number 1216451*0408832000 is 19!

So, the given number must be divisible by 3.

The divisibility test for 3 states that a number is divisible by 3 if and only if the sum of all the digits is a multiple of three.

Let the * digit be equal to x.

 

Sum of all the digits = 1+2+1+6+4+5+1+x+0+4+0+8+8+3+2+0+0+0 = 45 + x

Now, for divisiblity by 3, we must have (45 + x) as a multiple of 3.

Among the four options given, x=0 only makes (45 + x) equal to a multiple of three.

For x=0, 45 + x = 45 (multiple of three.)

For x=4, 45 + 4 = 49 (not a multiple of three.)

For x=0, 45 + 2 = 47 (not a multiple of three.)

For x=0, 45 + 5 = 50 (not a multiple of three.)

For x=0, 45 + 7 = 52 (not a multiple of three.)

 

Hence the correct answer of this question is (a).

Answered by  | 27th Apr, 2010, 08:16: PM

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