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

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DS Forum Moderator
Joined: 22 Aug 2013
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Which digit is at the [b]hundredth[/b] place of a positive number X?  [#permalink]

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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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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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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.

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