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J = x rounded to the nearest TENTH, and

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J = x rounded to the nearest TENTH, and [#permalink] New post 31 May 2018, 05:41
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66% (02:45) correct 33% (01:28) wrong based on 3 sessions
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
[Reveal] Spoiler: OA

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Re: J = x rounded to the nearest TENTH, and [#permalink] New post 31 May 2018, 22:51
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Value of x when not rounded is somewhere between 0 and 1.

We know that J can have a value of 0.1 to 0.9 because x is rounded to tenth.
But we are also required to find J-K when it is maximum we need to make sure that J is maximum so J can only be 0.9

Coming to K, K can have a value such as 0.abc where a,b and c are placeholders. Because J is rounded to thousandth.
But we should make sure that K is as small as possible for J-K to be maximum.
How can we round O.abc to O.a such that O.a is 0.9 ?

we know that 0.85 is the least number when rounded that gives us 0.9 hence 0.abc can be rewritten as 0.85c
at this point we should make sure that c is least as well that way K is least hence c = 0
Therefore, K = 0.850
Hence, J-K = 0.9-0.850 = 0.05
option C
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Re: J = x rounded to the nearest TENTH, and   [#permalink] 31 May 2018, 22:51
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