Brent@GMATPrepNow wrote:J = x rounded to the nearest TENTH, and K = x rounded to the nearest THOUSANDTH. If 0 < x < 1, what is the greatest possible value of J - K?
A) 0.005
B) 0.0055
C) 0.05
D) 0.0505
E) 0.0555
Since J = x rounded to the nearest tenth, J = 0.a (where a is a digit 0-9).
Since K = x rounded to the nearest thousandth,
K = 0.bcd (where b, c and d are any digits 0-9).
The value of K implies that J-K can have at most three digits to the right of the decimal.
Eliminate B, D and E.
To maximize J-K, we want x to round UP to the nearest tenth (so that J is as big as possible) but round DOWN to the nearest thousandth (so that K is as small as possible).
One option:
x = 0.0501. with the result that J = 0.1 and K = 0.050.
In this case, J-K = 0.1 - 0.05 = 0.05.
Since option C can be the value of J-K, eliminate A, which is smaller.
The correct answer is
C.
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