Free Practice Question
PS · Problem Solving
705-805
Fractions/Ratios/Decimals
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?
Answer Choices
Correct answer marked belowA
0.005
B
0.0055
0.05
Correct
D
0.0505
E
0.0555
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Explanation
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Official Explanation
Official
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).…
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).…
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What it tests
Your ability to convert between fractions, ratios, and decimals and to reason proportionally.
Common trap
Cross-multiplying incorrectly or mixing up the ratio parts — a part:part ratio is not a fraction of the whole.
Details
Difficulty
705-805
Type
PS
Category