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If digit h is the hundredths' digit in the decimal d=0.2h6,  [#permalink]

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Question Stats: 61% (01:15) correct 39% (01:33) wrong based on 813 sessions

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If digit h is the hudredths' digit in the decimal d=0.2h6, what is the value of d, rounded to the nearest tenth?

(1) d < 1/4
(2) h < 5

Originally posted by vanidhar on 30 Sep 2010, 01:24.
Last edited by Bunuel on 20 Sep 2012, 03:55, edited 1 time in total.
Edited the question.
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If digit h is the hudredths' digit in the decimal d=0.2h6, what is the value of d, rounded to the nearest tenth?

Given: $$d=0.2h6$$.

(1) d < 1/4 --> 1/4 = 0.25 --> $$0.2h6<0.25$$ --> $$h<5$$ ($$0.2<d<0.25$$)--> $$d$$, rounded to the nearest tenth will be $$0.2$$. Sufficient.

(2) h < 5 --> the same as above: $$d$$, rounded to the nearest tenth will be $$0.2$$. Sufficient.

Note:
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.

Also:
1234.567

1 - THOUSANDS
2 - HUNDREDS
3 - TENS
4 - UNITS
. - decimal point
5 - TENTHS
6 - HUNDREDTHS
7 - THOUSANDTHS
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Hi Bunuel,

You mean to say that we completely ignore the 1000th digit ("6" in this question) and irrespective of it being more than 5, we will use the 100th digit and answer the question according to that. I thought we look at "6", so if we assume the 100th digit to be 4 (less than "5") it becomes 0.246, which first rounds off to 0.25 (because 6 is greater than 5) and then answer becomes is 0.3, rounding off 0.25->0.3. I think this was the wrong way (however, we were taught this in primary school).
This is a learning for me. Please confirm.

Looking forward to hearing from you.

Thanks and regards,

Eshan
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Eshan wrote:
Hi Bunuel,

You mean to say that we completely ignore the 1000th digit ("6" in this question) and irrespective of it being more than 5, we will use the 100th digit and answer the question according to that. I thought we look at "6", so if we assume the 100th digit to be 4 (less than "5") it becomes 0.246, which first rounds off to 0.25 (because 6 is greater than 5) and then answer becomes is 0.3, rounding off 0.25->0.3. I think this was the wrong way (however, we were taught this in primary school).
This is a learning for me. Please confirm.

Looking forward to hearing from you.

Thanks and regards,

Eshan

Yes, when rounding to the nearest tenth, we only need to know the hundredth: when rounding we are interested in the first dropped digit. So, 0.246 rounded to the tenth is 0.2, not 0.3.

All DS Fractions/Ratios/Decimals questions: search.php?search_id=tag&tag_id=36
All PS Fractions/Ratios/Decimals questions: search.php?search_id=tag&tag_id=57

Hope it helps.
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Bunuel wrote:
Eshan wrote:
Hi Bunuel,

You mean to say that we completely ignore the 1000th digit ("6" in this question) and irrespective of it being more than 5, we will use the 100th digit and answer the question according to that. I thought we look at "6", so if we assume the 100th digit to be 4 (less than "5") it becomes 0.246, which first rounds off to 0.25 (because 6 is greater than 5) and then answer becomes is 0.3, rounding off 0.25->0.3. I think this was the wrong way (however, we were taught this in primary school).
This is a learning for me. Please confirm.

Looking forward to hearing from you.

Thanks and regards,

Eshan

Yes, when rounding to the nearest tenth, we only need to know the hundredth: when rounding we are interested in the first dropped digit. So, 0.246 rounded to the tenth is 0.2, not 0.3.

All DS Fractions/Ratios/Decimals questions: search.php?search_id=tag&tag_id=36
All PS Fractions/Ratios/Decimals questions: search.php?search_id=tag&tag_id=57

Hope it helps.

Thank you for the clarification Bunuel. Highly appreciated.
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Re: If digit h is the hundredths digit in the decimal n = 0.2h6, what is t  [#permalink]

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Bunuel wrote:
If digit h is the hundredths digit in the decimal n = 0.2h6, what is the value of n, rounded to the nearest tenth?

(1) n < 1/4
(2) h < 5

Kudos for a correct solution.

1. n<0.25
n (rounded to the nearest tenths)=0.2
Sufficient

2. h<5
n (rounded to the nearest tenths)=0.2
Sufficient

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If digit h is the hundredths digit in the decimal n = 0.2h6, what is t  [#permalink]

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1
#1 n< 1/4 implies that n < 0,25 which explicitly lets us round it down to 0,2 coz the hundredth digit in this case is 4 at max(which rounds down). SUFFICIENT
#2 h<5. Lets look at our number: n = 0.2h6 rounds to n = 0.2(h+1). If h = 4 we get n = 0,25 which rounds up to 0,3, if h < 4 then the result is 0,2
INSUFFICIENT

A

edit:
#2 h<5. Since 6 is not the factor due to the fact that we are rounding to tenths, h being below 5 (0 1 2 3 or 4) lets us explicitly answer our question thus SUFFICIENT

Thanks for ur comemnt rich! Every day learning something new, huh.

Originally posted by Zhenek on 17 Apr 2015, 05:17.
Last edited by Zhenek on 17 Apr 2015, 11:11, edited 2 times in total.
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Re: If digit h is the hundredths digit in the decimal n = 0.2h6, what is t  [#permalink]

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1
Hi Zhenek,

When rounding a decimal to the 'nearest tenth", the thousandth's digit has NO EFFECT on the rounding. So in this question, the '6' is NOT a factor - only the H is. Knowing that, what would you do differently with Fact 2?

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If digit h is the hundredths digit in the decimal n = 0.2h6, what is t  [#permalink]

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Then I'd say that it lets us explicitly answer the question and makes D the answer
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Re: If digit h is the hundredths digit in the decimal n = 0.2h6, what is t  [#permalink]

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Hi Zhenek,

Very good. While explicit "rounding" as a subject isn't something you'll be asked about too often on Test Day (likely just 1-2 times), the rules that govern it are not too complicated. As you 'lock in' more of these rarer categories, you'll see a nice increase in your Quant scores.

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Re: If digit h is the hundredths digit in the decimal n = 0.2h6, what is t  [#permalink]

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n=0.2h6

1) n <1/4

=> n<0.25

so h <5.

so rounded to the nearest tenth, n becomes = 0.2 (as h <5)

Sufficient

2) h <5

n rounded to nearest tenth =0.2 (as h <5)

sufficient

hence D
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Re: If digit h is the hundredths digit in the decimal n = 0.2h6, what is t  [#permalink]

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1
Given n =0.2h6

Statement (1):
n < 1/4 --> n < 0.25, so n ranges between 0.20 and 0.24; n's tenth won't change
Sufficient

Statement (2)
h < 5, so n ranges between 0.206 and 0.246
ONLY considering hundredth's when rounding n to its tenth, n's tenth won't change
Sufficient

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Joined: 02 Sep 2009
Posts: 64101
Re: If digit h is the hundredths digit in the decimal n = 0.2h6, what is t  [#permalink]

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Bunuel wrote:
If digit h is the hundredths digit in the decimal n = 0.2h6, what is the value of n, rounded to the nearest tenth?

(1) n < 1/4
(2) h < 5

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION

Given that n = 0.2h6

We need to find the value of n rounded to the nearest tenth i.e. we need to keep only one digit after the decimal.

Statement 1: n < 1/4

In decimal form, it means n < 0.25

If h were 5 or greater, n would become 0.256 or 0.266 or higher. All these values would be more than 0.25 so h must be less than 5 such as 0.246 or 0.236 etc. In all such cases, n would be rounded to 0.2

This statement alone is sufficient.

Statement 2: h < 5

This is even simpler. Since we have been given that h is less than 5, when we round n to the tenths digit, we will get 0.2

This statement alone is also sufficient.

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GRE 1: Q169 V154 Re: If digit h is the hundredths' digit in the decimal d=0.2h6,  [#permalink]

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vanidhar wrote:
If digit h is the hudredths' digit in the decimal d=0.2h6, what is the value of d, rounded to the nearest tenth?

(1) d < 1/4
(2) h < 5

Rounding decimal to nearest tenths we will get=>
0.2 for h=> {0,1,2,3,4}
0.3 fro h=>{5,6,7,8,9}
so essentially we need to check whether h is <5 or ≥5

statement 1
d<1/4
so d<0.25
hence h can be 0,1,2,3,4
hence sufficient
statement 2
h<5
again sufficient

Hence D
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Re: If digit h is the hundredths' digit in the decimal d=0.2h6,  [#permalink]

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Top Contributor
vanidhar wrote:
If digit h is the hudredths' digit in the decimal d=0.2h6, what is the value of d, rounded to the nearest tenth?

(1) d < 1/4
(2) h < 5

Given: Digit h is the hundredths digit in the decimal d=0.2h6

Target question: What is the value of d, rounded to the nearest TENTH?

Statement 1: d < 1/4
In other words, 0.2h6 < 0.25
This means h = 0, 1, 2, 3 or 4
If h = 0, 1, 2, 3 or 4, then 0.2h6 (aka d) rounded to the nearest TENTH is 0.2
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: h < 5
This means h = 0, 1, 2, 3 or 4
If h = 0, 1, 2, 3 or 4, then 0.2h6 (aka d) rounded to the nearest TENTH is 0.2
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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Re: If digit h is the hundredths' digit in the decimal d =  [#permalink]

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# If digit h is the hundredths' digit in the decimal d=0.2h6,  