CAT4MBA

Consider a real number x such that x  = ab.cd, where a, b, c and d are the digits of the number . Also, a and d is not equal to 0.

[x] = The greatest integer less than or equal to x and {x} = x – [x]
if [10{p}] = 8 and {10{p}}=9
Also, [p] is 5 less than the sum of the digits of the quantity 100{p}. Find p
a. 21.89
b. 89.12
c. 12.89
d. None of the above

We can always work with options.

Suppose option (a) is the correct answer.

x = 21.89

[x] = [21.89] = 21

{x} = x - [x] = 21.89 - 21 = 0.89

Now, note that:

[10{p}] = [10(0.89)] = [8.9] = 8

{10{p}} = {10(0.89)} = {8.9} = 8.9 - [8.9] = 8.9 - 8 = 0.9

which does not satisfy the given condition of the problem.

Hence option (a) is not the correct answer.

Next suppose option (b) is the correct answer.

x = 89.12

[x] = [89.12] = 89

{x} = x - [x] = 89.12 - 89 = 0.12

Now, note that:

[10{p}] = [10(0.12)] = [1.2] = 1

which does not satisfy the given condition of the problem.

Hence option (b) is not the correct answer.

Now suppose option (a) is the correct answer.

x = 12.89

[x] = [12.89] = 12

{x} = x - [x] = 12.89 - 12 = 0.89

Now, note that:

[10{p}] = [10(0.89)] = [8.9] = 8

{10{p}} = {10(0.89)} = {8.9} = 8.9 - [8.9] = 8.9 - 8 = 0.9

which does not satisfy the given condition of the problem.

Hence option (c) is also not the correct answer.

Therefore, option (d) is correct.

Ravi Raja

Thanks Ravi for explaining it in details.