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# If d denotes a decimal, is d >= 0.5?

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If d denotes a decimal, is d >= 0.5? [#permalink]

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11 Dec 2005, 10:54
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If d denotes a decimal, is $$d \ge 0.5$$ ?

(1) When d is rounded to the nearest tenth, the result is 0.5.
(2) When d is rounded to the nearest integer, the result is 1.
[Reveal] Spoiler: OA

Last edited by blshah on 11 Dec 2005, 18:08, edited 1 time in total.
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Re: DS: d denotes a decimal [#permalink]

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11 Dec 2005, 17:41
blshah wrote:
If d denotes a decimal, is d >= 5?

(1) When d is rounded to the nearest tenth, the result is 0.5.
(2) When d is rounded to the nearest integer, the results is 1.

This question is from OG 11th #58

There seems to be a typo in the question...I think you meant d >= 0.5

(1) When d is rounded to the nearest tenth, the result is 0.5 ==> d could be 0.49 or 0.52 ==> Insufficient

(2) When d is rounded to the nearest integer, the result is 1 ==> d ranges from 0.51 to 1.49 ==> Sufficient
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11 Dec 2005, 18:10
Thanks for pointing out the typo. I have corrected it now.

I think that the answer is E.
(1) d could be anywhere from 0.45 to 0.54. Thus some of the values are greater than 0.5 and some are less than 0.5.
(2) d could be anywhere from 0.45 to 1.44. This is because 0.45 when rounded, gives 0.5 which when further rounded gives 1.

Can someone explain?
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11 Dec 2005, 18:24
Quote:
(2) d could be anywhere from 0.45 to 1.44. This is because 0.45 when rounded, gives 0.5 which when further rounded gives 1.

When 0.45 is rounded to the nearest integer, it would be 0. For a decimal to be rounded to 1, it has to be between 0.50 ~ 1.49 ==> which are >= than 0.50
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Re: DS: decimals (OG11- #58) [#permalink]

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03 Sep 2008, 00:08
droopy57 wrote:
If d denotes a decimal, is d≥0.5?

(1) When d is rounded to the nearest tenth, the result is 0.5

(2) When d is rounded to the nearest integer, the result is 1

B.

for 1 , the d can be 0.45 to 0.54, so may or may not be true

for 2, d has to be d≥0.5
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Re: DS: decimals (OG11- #58) [#permalink]

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03 Sep 2008, 13:51
Ok I agree when d>0.5 and it is rounded to nearest integer then it is 1.
But what about d=0, it an be rounded to 0 as it does lie at equal distance from 0 as well as 1.
I am confused
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Re: DS: decimals (OG11- #58) [#permalink]

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03 Sep 2008, 21:27
OA is B

Here's the problem I had w/ this question:

(2) can't 0.459 rounded to nearest integer = 1? Or 0.4999, etc etc?
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Re: DS: decimals (OG11- #58) [#permalink]

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03 Sep 2008, 21:31
droopy57 wrote:
OA is B

Here's the problem I had w/ this question:

(2) can't 0.459 rounded to nearest integer = 1? Or 0.4999, etc etc?

0.459 or 0.4999 near to integer 0 than integer 1
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Re: DS: decimals (OG11- #58) [#permalink]

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03 Sep 2008, 21:58
sorry for the typo in previous post

Ok I agree when d>0.5 and it is rounded to nearest integer then it is 1.
But what about d=0.5, it can be rounded to 0 as it does lie at equal distance from 0 as well as 1.
So why it should be 1 instead of 0.
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Re: DS: decimals (OG11- #58) [#permalink]

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04 Sep 2008, 00:06
While rounding, one looks at only the immediate next digit.....if that digit is 5 or more....rounding is to 1....if that digit is less than 5 then rounded to 0.

Thus, 0.499999 will be rounded to 0 and 0.500000 will be rounded to 1.
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Re: DS: decimals (OG11- #58) [#permalink]

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04 Sep 2008, 08:42
Thanks SCthakur for the explanation.
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01 Apr 2011, 08:20
Statement 1:
d can be equal to 0.49 which when rounded off to the nearest 10th place would be 0.5

d can be equal to 0.51 which when rounded off to the nearest 10th place would be 0.5

In the former case d < 0.5 in the later case d > 0.5

Therefore, the statement is not sufficient!

Statement 2:
If d is rounded off to the nearest integer and the result is 1, then the tenth place is greater than or equal to 5.
Thus, d must be greater or equal to 5.
Sufficient!

Ans - 'B'
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01 Apr 2011, 08:42
mirzohidjon wrote:
If d denotes a decimal,is d≥0.5?
I. When d is rounded to the nearest tenth, the result is 0.5.
II. When d is rounded to the nearest integer, the result is 1.

A. Statement I alone is sufficient
B. Statement II alone is sufficient
C. Both statements I and II together are sufficient
D. Each statement alone is sufficient
E. Statements I and II are not sufficient

I know the OA is B. However, my question is could answer be E?

I know that statement I is insufficient.

If we look at Statement II, it says that when d is rounded to the nearest integer, the result is 1. I think that the values from 0.45 till 1.44 would fit the statement II, hence the Statement should be incorrect. For example, let's round 0.49 to nearest integer. Because hundredth digit is 9, we round it to 0, now tenth digit 4 turns to 5, since it is 5, we round it to 1. Am I correct?

If d denotes a decimal,is d≥0.5?
I. When d is rounded to the nearest tenth, the result is 0.5.
Range: 0.45Anything<=d<=0.54Anything

II. When d is rounded to the nearest integer, the result is 1.
Range: 0.5Anything<=d<=1.4Anything
d is always more than or equal to 0.5.
Hence Sufficient.

Ans: "B"

********************
Descriptive:

When we talk about rounding a certain place value of the decimal; we mark that place and place immediately right to that.
I. When d is rounded to the nearest tenth, the result is 0.5.
We need to the see the "tenths place" and the "hundredths place"(hundredths place is right to tenths)
Rounding to 0.5 will result if the tenths place is 5 and hundredths place is from 0 to 4. The moment hundredths place digit become 5, the tenths place will become one more.

0.51 rounds to 0.5
0.52 rounds to 0.5
0.539999 rounds to 0.5
0.549999 rounds to 0.5
0.55000 rounds to 0.6(Here hundredths place is 5 i.e. more than 4 thus the tenths place become one more)

Similarly; if tenths place of the decimal is 4 i.e. a decimal such as 0.4768768768, we need to see the hundredths place to decide whether tenths place decimal become one more;

0.49=0.5
0.48999=0.5
0.47032=0.5
0.467685868=0.5
0.45342432=0.5
0.4499999999=0.4(Here hundredths place is 4 thus the tenths place remain as is)

Range: 0.45Anything<=d<=0.54Anything
d can 0.48<0.5 or d can be 0.51>0.5. Not Sufficient.

II. When d is rounded to the nearest integer, the result is 1.
We need to the see the "units place" and the "tenths place"(tenths place is right to units place if we ignore the "." in between)
Rounding to 1 or 1.0 will result if the units place is 1 and tenths place is from 0 to 4. The moment tenths place digit become 5, the units place will become one more.

1.1=1
1.23232=1
1.345545=1
1.454545=1
1.500089=2.0(Here tenths place is 5 i.e. more than 4 thus the units place become one more)

Similarly; if units place of the decimal is 0 i.e. a decimal such as 0.7576, we need to see the tenths place to decide whether units place decimal become one more;

0.9999=1
0.899=1
0.78=1
0.67=1
0.50=1
0.4999999=0(Here tenths place is 4 i.e. less than 5, the units place remain as is)

Range: 0.5Anything<=d<=1.4Anything
d is always more than or equal to 0.5.
Sufficient.

Ans: "B"
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01 Apr 2011, 08:47
Thank you very much. It was a nice brush up of rounding topic! I got where is my mistake!!!
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03 Apr 2011, 07:10
I. following are the decimals when rounded to tenth would yield 0.5

0.45,046...05.0,0.51....0.54

on observing the above decimals , we can say some are less than 0.5,some greater than 0.5. so not enough to
Not sufficient.

2. here the decimals could be any of the following
0.5,0.6.....1.4 and all of them are greater than or equal to 0.5
Sufficient

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04 Apr 2011, 18:09
it should be B. anything greater than .500000.... and less than 1.499999.... will be 1. But i had a question. if we say d >= .5, does this means d can be anything greater than .5, i.e. can d be more than 1.5000 as well? in this case II is not sufficient.
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05 Apr 2011, 02:52
brandy96 wrote:
it should be B. anything greater than .500000.... and less than 1.499999.... will be 1. But i had a question. if we say d >= .5, does this means d can be anything greater than .5, i.e. can d be more than 1.5000 as well? in this case II is not sufficient.

Statement 2 says: d must be between 0.50000 and 1.499999. Thus, d can't be more than or equal to 1.5. We must consider the statements as true. The statements may be relevant or irrelevant/ sufficient or insufficient to answer the question asked in the stem but they are always true.
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