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Joined: 10 Jun 2007
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[0], given: 0

OA=B
x=1+0.01*d, d is a positive integer and d<10
what is the value of d?
1) 2<=d<=4
2) The thousandth digit of 10(x^2)＝ the hundredth digit of x^2
We know from the question that d can be 1,2,3,...,9
For (1) This is obviously INSUFFICIENT since d can be 2, 3, 4
For (2) we know that
If d=1,2,3,4,...,9, then x equals 1.01, 1.02, 1.03, 1.04...,1.09
Then we know that x^2 equals 1.0201, 1.0404, 1.0609, 1.0816, etc...
Therefore, 10*(x^2) will be 10.201, 10.404, 10.609, 10.816, etc...
Now, we can create a table:
(d, thousandth digit of 10*(x^2), hundredth digit of x^2)
(1, 1, 2)
(2, 4, 4)
(3, 9, 6)
(4, 6, 8)
etc...
If you look at the pattern, the question is asking when is the digit unit of d^2 ever equals to 2d knowing that 1<=d<=9. This is only true when d=2. Therefore, B is sufficient.
Cheers.
