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10th digit of x

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10th digit of x

by saisree » Sat Oct 29, 2011 7:50 am
What is the value of the tenths digit of number x?

(1) The hundredths digit of x is 5
(2) Number x, rounded to the nearest tenth, is 54.5

Please help me with an example. I am not able to figure it out :(((

OA is C.
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by GmatMathPro » Sat Oct 29, 2011 7:58 am
Statement 1: tells us the number is of the form _._5_______... No info about tenths digit. INSUFFICIENT.

Statement 2: Two of many possibilities are: x=54.51 and x=54.47. Each value rounded to the nearest tenth gives x=54.5, but the tenths digit is 5 in the first number and 4 in the second number. INSUFFICIENT.

Statements 1&2: If we know for sure that the hundredth's digit is 5 and that the number rounds to 54.5 to the nearest tenth, the tenths digit MUST be 4. x=54.45.... Remember that if the hundredths digit is 5, you would always round UP to the next highest tenths value if you are rounding to the nearest tenth. Thus, if the tenths value is anything besides 4, it would round to something besides 54.5. SUFFICIENT
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by mankey » Tue Nov 01, 2011 11:04 am
It is given tenths and hundredths, how does one come to know to know that they are being referred to the numbers after decimals, they could also be before decimal?

Please clarify.

Thanks.
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by shankar.ashwin » Tue Nov 01, 2011 11:15 am
I remember from school where we were taught, a decimal like say AB.CD

A-tens
B-units
C- tenths
D -hundredths
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by GmatMathPro » Tue Nov 01, 2011 11:27 am
mankey wrote:It is given tenths and hundredths, how does one come to know to know that they are being referred to the numbers after decimals, they could also be before decimal?

Please clarify.

Thanks.
Yeah, the "ths" at the end mean they are to the right of the decimal point. It boils down to place value in a base-ten counting system. For example, the number 145.657 can be expanded as follows:

1*10^2 + 4*10^1 + 5*10^0 + 6*10^-1 + 5*10^-2 + 7*10^-3

on the right side, 10^-1=1/10, 10^-2=1/100, 10^-3=1/1000.

These fractions are read as "one tenth" "one hundredth" and "one thousandth", giving rise to "tenth's digit", "hundredth's digit", and "thousandth's digit"

Whereas the ones to the left are 10^2=100, 10^1=10, and 10^0=1,

and these are read as "one hundred" "ten" and "one", giving rise to "hundred's digit", "ten's digit" and "one's digit" (or sometimes "unit's digit").
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