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Which digit is at the [b]hundredth[/b] place of a positive number X?

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Which digit is at the [b]hundredth[/b] place of a positive number X?  [#permalink]

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New post 07 Mar 2018, 03:15
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Difficulty:

  65% (hard)

Question Stats:

45% (01:40) correct 55% (01:38) wrong based on 31 sessions

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Which digit is at the hundredth place of a positive number X?

(1) Y = 10*X, and when Y is rounded off to nearest tenth the result is 2176.5

(2) Z = X/10, and when Z is rounded off to nearest hundredth the result is 21.76
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Which digit is at the [b]hundredth[/b] place of a positive number X?  [#permalink]

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New post 07 Mar 2018, 10:26
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amanvermagmat wrote:
Which digit is at the hundredth place of a positive number X?

(1) Y = 10*X, and when Y is rounded off to nearest tenth the result is 2176.5

(2) Z = X/10, and when Z is rounded off to nearest hundredth the result is 21.76


Statement 1: \(y=10x =>x=\frac{y}{10}\)

therefore, \(x=\frac{2176.5}{10}=217.65\)

Now the hundredths digit \(5\) is a rounded off digit so the original hundredths digit could be \(4\) or \(5\). Insufficient

Statement 2: \(z=\frac{x}{10}=>x=10z\)

therefore, \(x=21.76*10=217.6\). From this we have no idea about hundredths digit. Insufficient

Combining 1 & 2: we get two values of hundredths digit \(4\) or \(5\). Hence Insufficient

Option E
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Which digit is at the [b]hundredth[/b] place of a positive number X?  [#permalink]

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New post 19 Mar 2018, 12:50

SOLUTION



We need to find:
    • The value of digit at the hundredths place of X.

Statement-1\(Y = 10*X\), and when \(Y\) is rounded off to nearest tenth, the result is \(2176.5\)”.

If \(Y=10*X\) then:
    • \(X\)= \(\frac{Y}{10}\)
      o Thus, \(X = 217.65\)

When \(Y\) is rounded off to the nearest tenth, the result is \(2176.5\).
Thus, \(Y\) can have two different possibilities:
    • \(Y= 2176.5a\), where \(a <4\).
      o \(X= 217.65a\), the hundredths digit of \(X\) is \(5\).

    • \(Y= 2176.4a\), where \(a >=5\).
      o \(X= 217.64a\), the hundredths digit of \(X\)is \(4\).

Since we do not have a unique answer, statement 1 alone is not sufficient to answer the question.

Statement-2 “\(Z\) = \(\frac{X}{10}\), and when \(Z\) is rounded off to nearest hundredth the result is \(21.76\)

If \(Z\)= \(\frac{X}{10}\) then:

    • \(X=10*Z\).
      o Thus, \(X=217.6\)\(\)

When \(Z\) is rounded off to the nearest hundredth, the result is \(21.76\)\(\).
Thus, \(Z\) can have various possibilities:
    • \(Z=21.76a\), where \(a <4\).
      o \(X= 217.6a\), the hundredth digit of \(X\) is less than \(4\).

    • \(Z= 21.75a\), where \(a >=5.\)
      o \(X= 217.5a\), then hundredth digit of \(X\) is greater or equal to \(5\).

We don’t need to look for other cases as \(X\) does not have a unique value.
Hence, Statement 2 alone is not sufficient to answer the question.

Combining both the statements:
After combining both the statements, the hundredth digits of x has 2 different values, 4 and 5.
Hence, statement (1) and (2) together are not sufficient to answer the question.

Answer: E
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