In the decimal, 2.4d7, d represents a digit from 0-9. If : GMAT Problem Solving (PS)
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# In the decimal, 2.4d7, d represents a digit from 0-9. If

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In the decimal, 2.4d7, d represents a digit from 0-9. If [#permalink]

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09 Dec 2010, 21:01
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In the decimal, 2.4d7, d represents a digit from 0-9. If the value of the decimal rounded to the nearest tenth is less than 2.5, what are the possible values of d?

Hi ppl..I always get confused about rounding the digit Questions in PS..

Can some one explain me the above Q

Last edited by Bunuel on 09 Feb 2012, 06:29, edited 1 time in total.
Edited the question
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09 Dec 2010, 22:24
krishireddy wrote:
Hi ppl..I always get confused about rounding the digit Questions in PS..

Can some one explain me the below Q

In the decimal, 2.4d7, d represents a digit from 0-9. If the value of the decimal rounded to the nearest tenth is less than 2.5, what are the possible values of d?

REMEBER:
In XYZ.abc
Z - Units digit
y - tens
x - hundreds

a - Tenths
b - hundredths
c - thousandths

ROUNDING concept

Important: THE ROUNDING SHUD TAKE PLACE FROM RIGHT TO LEFT

if the above # is getting rounded to Thenth (a), then the value of "a" depends on the value of "b" (the hundredths place) in the below way.

$$a ==> a+1 , if b>=5$$
$$a ==> a , if b<5$$

Original qtn

given # is $$2.4d7$$
(as per the above concept, the tenths place value depends upon the value in hundredths place i.e. d)

and as given the resultant # is < 2.5 ==> 2.4 (after rounding to tehnths)
so for the 4 (in the tenths place) not to be changed d has to be < 5
==> d has to be < 5
==> posiible values for d are $$0,1,2,3, and 4$$

Regards,
Murali
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Last edited by muralimba on 09 Dec 2010, 23:11, edited 1 time in total.
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09 Dec 2010, 22:50
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muralimba, I'm not sure if that's right.

If a decimal is to round to the tenth, then you need the hundredth greater than or equal to 0.05 to round up, or less than 0.05 to round down.

The thousandths value doesn't directly contribute in this question.

Since we want to round to the tenth and less than 2.5, d can be 0, 1, 2, 3 and 4. 4 is included because 0.047 is less than 0.05.
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09 Dec 2010, 23:12
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Mypatpat. You are right. Edited my post.
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09 Dec 2010, 23:37
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krishireddy wrote:
Hi ppl..I always get confused about rounding the digit Questions in PS..

Can some one explain me the below Q

In the decimal, 2.4d7, d represents a digit from 0-9. If the value of the decimal rounded to the nearest tenth is less than 2.5, what are the possible values of d?

Rounding rules

Rounding is simplifying a number to a certain place value. To round the decimal drop the extra decimal places, and if the first dropped digit is 5 or greater, round up the last digit that you keep. If the first dropped digit is 4 or smaller, round down (keep the same) the last digit that you keep.

Example:
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.

BACK TO THE ORIGINAL QUESTION:
In the decimal, 2.4d7, d represents a digit from 0-9. If the value of the decimal rounded to the nearest tenth is less than 2.5, what are the possible values of d?

So, in order 2.4d7 rounded to the nearest tenth to be less than 2.5, d must be less than 5: 0, 1, 2, 3, or 4. In this case 2.4d7 rounded to the nearest tenth will be 2.4 which is less than 2.5.

For more on number properties check: math-number-theory-88376.html

Hope it helps.
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10 Dec 2010, 08:02
Thanks for the explanations Muralimba,mypatpat and Bunnel…

I was under the impression that if d = 4 then

2.447 rounded to nearest tenth is (I was coming from right most digit rounding each preceding digit)
2.45 (since 7>5)
2.5 (since 5=5)

Hence I thght d=4 is also an invalid option…

But now I understand that whenever a digit is rounded we should consider only the digit to the right of our digit .We shall not be worrying about the rest of the digits.

Shall add this to my learnings…:-)
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10 Dec 2010, 08:19
thanks for the explanation
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17 Jan 2011, 03:54
Bunuel,I disagree with u .in case 4372.25 rounded tenth digit(decimal).
in these type of problems we have 2 case
1-If the preceding digit(2) is odd and hundred digit is equal to 5. then we increase tenth digit by 1. and n.m. become 4372.3
2-If the preceding digit is even ( in this case),then we left the n.m. unchanged and n.m. become 4372.2
hope you got my point
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17 Jan 2011, 05:21
rojans wrote:
Bunuel,I disagree with u .in case 4372.25 rounded tenth digit(decimal).
in these type of problems we have 2 case
1-If the preceding digit(2) is odd and hundred digit is equal to 5. then we increase tenth digit by 1. and n.m. become 4372.3
2-If the preceding digit is even ( in this case),then we left the n.m. unchanged and n.m. become 4372.2
hope you got my point

The above is not correct for GMAT. Anyway number x.25 rounded to the nearest tenth is x.3.

Again, check rounding rules:

Rounding is simplifying a number to a certain place value. To round the decimal drop the extra decimal places, and if the first dropped digit is 5 or greater, round up the last digit that you keep. If the first dropped digit is 4 or smaller, round down (keep the same) the last digit that you keep.

Example:
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.

BACK TO THE ORIGINAL QUESTION:
In the decimal, 2.4d7, d represents a digit from 0-9. If the value of the decimal rounded to the nearest tenth is less than 2.5, what are the possible values of d?

So, in order 2.4d7 rounded to the nearest tenth to be less than 2.5, d must be less than 5: 0, 1, 2, 3, or 4. In this case 2.4d7 rounded to the nearest tenth will be 2.4 which is less than 2.5.

For more on number properties check: math-number-theory-88376.html

Hope it's clear.
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17 Jan 2011, 08:17
I am saying 4327.254 ----will be 4327.2 in tenth decimal place.
and 4327.354 will be 4327.4 in tenth decimal place
value will depend what is coming before 5.It's true.
I agree with you.Except in this case.
usually -above 5 we increase the n.m.by 1 in decimal digit and below 5 we unchanged the digit. such as 4327.567--- 4327.6
and 4327.435---4327.4 in rounding tenth in decimal digit
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17 Jan 2011, 08:33
rojans wrote:
I am saying 4327.254 ----will be 4327.2 in tenth decimal place.
and 4327.354 will be 4327.4 in tenth decimal place
value will depend what is coming before 5.It's true.
I agree with you.Except in this case.
usually -above 5 we increase the n.m.by 1 in decimal digit and below 5 we unchanged the digit. such as 4327.567--- 4327.6
and 4327.435---4327.4 in rounding tenth in decimal digit

For GMAT if the first dropped digit is 5 or more you ROUND UP the last digit that you keep and if the first dropped digit is less than 5 you KEEP THE SAME the last digit that you keep.

4327.254 rounded to the nearest tenth will be 4327.3 since the dropped 5 is equal to 5;
4327.354 rounded to the nearest tenth will be 4327.4 since the dropped 5 is equal to 5.
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17 Jan 2011, 18:13
Same here...I was thinking exactly the same...thanks for the explanation
krishireddy wrote:
Thanks for the explanations Muralimba,mypatpat and Bunnel…

I was under the impression that if d = 4 then

2.447 rounded to nearest tenth is (I was coming from right most digit rounding each preceding digit)
2.45 (since 7>5)
2.5 (since 5=5)

Hence I thght d=4 is also an invalid option…

But now I understand that whenever a digit is rounded we should consider only the digit to the right of our digit .We shall not be worrying about the rest of the digits.

Shall add this to my learnings…:-)
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22 Jan 2011, 05:38
Bunuel wrote:
For GMAT if the first dropped digit is 5 or more you ROUND UP the last digit that you keep and if the first dropped digit is less than 5 you KEEP THE SAME the last digit that you keep..

Hi Bunuel, where did you get the statement above ? OG10, 11, or 12? I am trying to look for it. Here is what I found from a math website, please read Rule Three carefully:

Rule One. Determine what your rounding digit is and look to the right side of it. If the digit is 0, 1, 2, 3, or 4 do not change the rounding digit. All digits that are on the right hand side of the requested rounding digit will become 0.

Rule Two. Determine what your rounding digit is and look to the right of it. If the digit is 5, 6, 7, 8, or 9, your rounding digit rounds up by one number. All digits that are on the right hand side of the requested rounding digit will become 0.

Rounding with decimals: When rounding numbers involving decimals, there are 2 rules to remember:

Rule One Determine what your rounding digit is and look to the right side of it. If that digit is 4, 3, 2, or 1, simply drop all digits to the right of it.

Rule Two Determine what your rounding digit is and look to the right side of it. If that digit is 5, 6, 7, 8, or 9 add one to the rounding digit and drop all digits to the right of it.

Rule Three: Some teachers prefer this method:

This rule provides more accuracy and is sometimes referred to as the 'Banker's Rule'. When the first digit dropped is 5 and there are no digits following or the digits following are zeros, make the preceding digit even (i.e. round off to the nearest even digit). E.g., 2.315 and 2.325 are both 2.32 when rounded off to the nearest hundredth. Note: The rationale for the third rule is that approximately half of the time the number will be rounded up and the other half of the time it will be rounded down.
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22 Jan 2011, 07:59
ezinis wrote:
Bunuel wrote:
For GMAT if the first dropped digit is 5 or more you ROUND UP the last digit that you keep and if the first dropped digit is less than 5 you KEEP THE SAME the last digit that you keep..

Hi Bunuel, where did you get the statement above ? OG10, 11, or 12? I am trying to look for it. Here is what I found from a math website, please read Rule Three carefully:

Rule One. Determine what your rounding digit is and look to the right side of it. If the digit is 0, 1, 2, 3, or 4 do not change the rounding digit. All digits that are on the right hand side of the requested rounding digit will become 0.

Rule Two. Determine what your rounding digit is and look to the right of it. If the digit is 5, 6, 7, 8, or 9, your rounding digit rounds up by one number. All digits that are on the right hand side of the requested rounding digit will become 0.

Rounding with decimals: When rounding numbers involving decimals, there are 2 rules to remember:

Rule One Determine what your rounding digit is and look to the right side of it. If that digit is 4, 3, 2, or 1, simply drop all digits to the right of it.

Rule Two Determine what your rounding digit is and look to the right side of it. If that digit is 5, 6, 7, 8, or 9 add one to the rounding digit and drop all digits to the right of it.

Rule Three: Some teachers prefer this method:

This rule provides more accuracy and is sometimes referred to as the 'Banker's Rule'. When the first digit dropped is 5 and there are no digits following or the digits following are zeros, make the preceding digit even (i.e. round off to the nearest even digit). E.g., 2.315 and 2.325 are both 2.32 when rounded off to the nearest hundredth. Note: The rationale for the third rule is that approximately half of the time the number will be rounded up and the other half of the time it will be rounded down.

The part in red is correct.

And again: For GMAT if the first dropped digit is 5 or more you ROUND UP the last digit that you keep and if the first dropped digit is less than 5 you KEEP THE SAME the last digit that you keep.

Check this: http://www.manhattangmat.com/fdps-digits-decimals.cfm
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23 Jan 2011, 14:30
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Banker's rounding (Round half to even) is one of them many tie breaking rules that can be used in case of .5
They are Round half to odd, Round up, Round down, Round towards 0, Round away from 0 etc etc etc (Check http://en.wikipedia.org/wiki/Rounding for explanation of each method.)

As Bunuel mentioned, GMAT uses Round Up by default. (Inferred from the solution they provided for OG12, Data Sufficiency, Q64, Page 309... When d is rounded to the nearest tenth, the result is 0.5. The value of d could range from 0.45 to 0.54.
0.45 is made 0.5 i.e. rounding up is used, not banker's rounding)

Note: Banker's rounding is more accurate since it doesn't have the upward bias but we have to use what GMAT uses.
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24 Jan 2011, 06:13
Thanks veritas for the GMAT reference, +1. That's exactly what I am looking for.
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