past gate question

Question

A number is represented as m in base 10,p in base 2, q in base 3

p - q = 990 where subtraction is performed in base 10

then 

(a) m>=14

(b) 9<=m<=13

(c) 6<=m<=8

(d) m<6

Comments

What does it mean -> m₁₀ = p₂ = q₃  (m in base 10,p in base 2, q in base 3)

* Does it mean m, p and q look alike

  if yes then m will only contain 0 and 1, & p will never greater than q i,e. p₁₀ - q₁₀ = 990 is wrong.

* Does it mean m₁₀, p_{2 and} q₃ will give same value in their base

  if yes then p₁₀ and q₁₀ will be equal i,e. p₁₀ - q₁₀ = 990 is wrong.

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Sorry, i phrased the question wrong.....Now it is updated

Answer 1

To get a decimal difference 990 of p and q, p must have 4 digits. i,e In decimal p>=8

So the option C and D are wrong.

Now, A or B may be correct but If we choose m>=15, p-q=990 become wrong.

So Option A is incorrect

Option B is the closest Answer. m=12 or m=13 it is true that p-q=990.

Comments

ok .... Thanx :)