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Decimals

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Decimals

by DHRJ007 » Mon Sep 21, 2020 9:37 am

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In the number 1.4ab5, a and b represent single positive digits. If x = 1.4ab5, what is the value of 10– x?

(1) If x is rounded to the nearest hundredth, then 10 – x = 8.56.

(2) If x is rounded to the nearest thousandth, then 10 – x = 8.564.
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Source: — Data Sufficiency |
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Re: Decimals

by Neha sharma » Mon Sep 21, 2020 7:43 pm

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Given: X = 1.4ab5

Statement 1: If x is rounded to the nearest hundredth, then 10 – x = 8.56
10 - 1.44 = 8.56
So, x rounded to the nearest HUNDREDTH = 1.44
So, x COULD equal 1.4355, 1.4365, 1.4375, 1.4385, 1.4395, 1.4405, 1.4415, 1.4425, 1.4435 OR 1.4445
Given all of the different possible values of x, 10 - x could have MANY different values.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: If x is rounded to the nearest thousandth, then 10 - x = 8.564
10 - 1.436 = 8.564
In other words, x rounded to the nearest THOUSANDTH = 1.436
This tells us that a must equal 3, leaving us with 1.43b5
If 1.43b5 rounded to the nearest THOUSANDTH = 1.436, then b MUST equal 5
So, x must equal 1.4355, which means 10 - x MUST equal 8.5645
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
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