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![Which digit is at the [b]hundredth[/b] place of a positive number X?](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "Which digit is at the [b]hundredth[/b] place of a positive number X?"){kind=icon}
07 Mar 2018, 03:15
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
36% (02:05) correct
64%
(02:07)
wrong
based on 72
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
(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
07 Mar 2018, 10:26
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amanvermagmat
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
19 Mar 2018, 12:50
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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
