Question

# From a two digit number N, we subtract the number with the digits reversed and find that the result is a positive perfect cube. Then:

A
N cannot end in 5
B
N can end in any digit other than 5
C
N does not exist
D
there are exactly 7 values for N
E
there are exactly 10 values for N

Solution

## The correct option is D there are exactly 7 values for NLet the two digit number be 10a+bN = 10a+bN' = reversed number = 10b+aN-N' = 9(a-b)N-N' is positive perfect cube.$$\therefore$$ a>bFor 9(a-b) be perfect cube, a-b = 3$$\therefore$$ b $$\epsilon$$ [0, 6] $$\longrightarrow$$ 7 values$$\therefore$$ a $$\epsilon$$ [3, 9] $$\longrightarrow$$ 7 values$$\therefore$$ Total 7 values are possible for N.Mathematics

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