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AnkurGMAT20
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­For all real numbers x, let x denote the number obtained by rounding 13 Aug 2024, 07:43
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35% (medium)

Question Stats:

75% (01:28) correct 25% (01:45) wrong based on 520 sessions

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­For all real numbers x, let \(\overline{x}\) denote the number obtained by rounding x to the nearest hundredth. If x = 21.9445, what is the value of \(10x−10\overline{x}\) ?

A. 0.005
B. 0.045
C, 0.095
D. 0.45
E. 0.95­

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B
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Bunuel
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­For all real numbers x, let x denote the number obtained by rounding 13 Oct 2024, 02:16
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dhruv1108
­For all real numbers x, let \(\overline{x}\) denote the number obtained by rounding x to the nearest hundredth. If x = 21.9445, what is the value of \(10x−10\overline{x}\) ?
A. 0.005
B. 0.045
C, 0.095
D. 0.45
E. 0.95­

Did anyone else find the language of this question problematic? Nearest 100th would naturally direct one to assuming something like 21.9445 -> 0 or 100. While in the question they mean rounding of the decimals.
Show more

There is a difference between the hundredth digit and the hundreds digit.




1234.567

1 - THOUSANDS
2 - HUNDREDS
3 - TENS
4 - UNITS
. - decimal point
5 - TENTHS
6 - HUNDREDTHS
7 - THOUSANDTHS

Hope it helps.
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Bunuel
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­For all real numbers x, let x denote the number obtained by rounding 13 Aug 2024, 10:55
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AnkurGMAT20
­For all real numbers x, let \(\overline{x}\) denote the number obtained by rounding x to the nearest hundredth. If x = 21.9445, what is the value of \(10x−10\overline{x}\) ?

A. 0.005
B. 0.045
C, 0.095
D. 0.45
E. 0.95­
Show more
Since \(\overline{x}\) denote the number obtained by rounding x to the nearest hundredth, \(\overline{21.9445}=21.94\). Thus:


\(10x−10\overline{x}=\)

\(=10(x−\overline{x})=\)

\(=10(21.9445 - 21.94)=\)

\(=10(0.0045)=\)

\(=0.045\)

Answer: B.­
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­For all real numbers x, let x denote the number obtained by rounding 12 Oct 2024, 12:00
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Did anyone else find the language of this question problematic? Nearest 100th would naturally direct one to assuming something like 21.9445 -> 0 or 100. While in the question they mean rounding of the decimals.
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­For all real numbers x, let x denote the number obtained by rounding 24 Mar 2025, 08:34
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Hello Bunuel,

While rounding the hundredth number do you not round off the thousandth number as well?
I rounded 21.9445 as 21.95, since I had rounded the thousandth number "4".


Thank you
Bunuel
AnkurGMAT20
­For all real numbers x, let \(\overline{x}\) denote the number obtained by rounding x to the nearest hundredth. If x = 21.9445, what is the value of \(10x−10\overline{x}\) ?

A. 0.005
B. 0.045
C, 0.095
D. 0.45
E. 0.95­
Since \(\overline{x}\) denote the number obtained by rounding x to the nearest hundredth, \(\overline{21.9445}=21.94\). Thus:


\(10x−10\overline{x}=\)

\(=10(x−\overline{x})=\)

\(=10(21.9445 - 21.94)=\)

\(=10(0.0045)=\)

\(=0.045\)

Answer: B.­
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Bunuel
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­For all real numbers x, let x denote the number obtained by rounding 24 Mar 2025, 08:54
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SamCodes
Hello Bunuel,

While rounding the hundredth number do you not round off the thousandth number as well?
I rounded 21.9445 as 21.95, since I had rounded the thousandth number "4".


Thank you
Bunuel
AnkurGMAT20
­For all real numbers x, let \(\overline{x}\) denote the number obtained by rounding x to the nearest hundredth. If x = 21.9445, what is the value of \(10x−10\overline{x}\) ?

A. 0.005
B. 0.045
C, 0.095
D. 0.45
E. 0.95­
Since \(\overline{x}\) denote the number obtained by rounding x to the nearest hundredth, \(\overline{21.9445}=21.94\). Thus:


\(10x−10\overline{x}=\)

\(=10(x−\overline{x})=\)

\(=10(21.9445 - 21.94)=\)

\(=10(0.0045)=\)

\(=0.045\)

Answer: B.­
Show more

21.9445 rounded to the nearest hundredth is 21.94. Only the first dropped digit is considered when rounding — rounding is not cumulative.

Rounding means simplifying a number to a certain place value. To round a decimal, look at the first digit being dropped:

  • If it is 5 or greater, round up the last digit you keep.
  • If it is 4 or less, keep the last digit as is.

Examples:

  • 5.3485 rounded to the nearest tenth = 5.3, since the dropped 4 is less than 5.
  • 5.3485 rounded to the nearest hundredth = 5.35, since the dropped 8 is greater than 5.
  • 5.3485 rounded to the nearest thousandth = 5.349, since the dropped 5 is equal to 5.

So, according to this, 21.944x rounded to the nearest tenth will be 21.94 regardless of the value of x.
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