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

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.

Answer: D.

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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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.



Hope it helps.
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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

Thank you for the clarification Bunuel. Highly appreciated.

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

Answer: D

#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

Answer ends up being D.

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

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?

GMAT assassins aren't born, they're made,
Rich
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Then I'd say that it lets us explicitly answer the question and makes D the answer

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.

GMAT assassins aren't born, they're made,
Rich
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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

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

Answer D

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.

Answer (D)
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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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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

Answer: D

Cheers,
Brent
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GMAT OFFICIAL EXPLANATION

The value of d, rounded to the nearest tenth, is 0.3 for h > 5 and 0.2 for h < 5. Statement (1) can be written d < 0.250, so h < 5. Thus, (1) alone is not sufficient, and the answer must be A or D. Statement (2) gives the information that h < 5 directly, so (2) alone is also sufficient. The best answer is D.

Thank you, Bunuel
Just to confirm my understanding
0.256 rounded to nearest tenth = 0.3
0.256 rounded to nearest hundredth = 0.26
and so on.
Since the statement 1 says d<1/4 i.e. d<0.25 the nearest tenth is 0.2, therefore, Statement 1 is sufficient
Same with statement 2.

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Yes, that's correct.
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(1) Given d=d=0.2h6, so, d < 1/4(.25) can't be \(10^{th}\) digit less then 0.2 and rounding to nearest tenth will be 0.20 Sufficient.

(2) Same logic as (1) applied here. even is 0 the \(0.20\).. will be \(0.20\) after rounding up to the nearest \(10^{th}\). Sufficient.

The answer is \(D\)
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1. We are asked to find value of d=0.2h6 rounded to the tenth place (in bold red font)

(1) \(d < \frac{1}{4}\) - Sufficient
a. Values of \(d\) can be \(0.20\), \(0.21\), \(0.22\), \(0.23\), \(0.24\)
b. If we round any of the above to the tenth place then we get a single value for \(d\) i.e. \(0.2\)

(2) h < 5 - Sufficient
a. If \(h < 5\) then value of \(d\) will be \(0.20\), \(0.21\), \(0.22\), \(0.23\), \(0.24\)
b. If we round any of the above to the tenth place then we get a single value for \(d\) i.e. \(0.2\)

Ans. D
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