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

SOLUTION

If d denotes a decimal, is \(d\geq{0.5}\) ?

(1) When d is rounded to the nearest tenth, the result is 0.5. This statement implies that \(0.45\leq{d}<0.55\). Not sufficient.

(2) When d is rounded to the nearest integer, the result is 1. d cannot be less than 0.5 because in this case 1 won't be the nearest integer. Sufficient.

Answer: B.
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1) d can be any number between 0.45 to .54 --- >Insufficient
2) d can be any number greater than or equal to 0.5-->Sufficient
Answer B

Video solution from Quant Reasoning:

These one are always tricky for me

We have to know id d is < = or >= 0,5

1) if the number is 0,45 to 0,54 we have the decimal that cuold be 4 or 5 (0,4 or 0,5)

2) if the numbe must be 1 the number ranging from 0,5 to 0,9 but always the decimal will be >= 0,5

B is the answer
_________________

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

so if we pick d=0.48 then in this case the answer to is d>=0.5 is NO

but if we pick d=0.53 then in this case it is YES

2 situations YES / NO ambiguity hence insufficient


When d is rounded to the nearest integer, the result is 1.

so for example if d=0.2 then the decimal would be rounded to nearest integer which is 0

but we have been given that it is rounded to 1 so the range is 0.5 to 1.4 in all of those cases it is rounded to 1 hence B is sufficient

Answer is B

Statement 1:
round(d,0.1) = 0.5
=>
0.45<=d<=0.54
Not suff as d can have values less than 0.5 as well as greater than 0.5

Statement 2:
round(d,1) =1
=>
0.5 <=d<=1.49
for any value of d here, it is sufficient to answer.

Ans B

Its B.. was confused .49 wud be included in option or not...then i thought no..because .51 to1.49 wud b nearest integer 1..
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Solution:

We are given that d is a decimal, and we need to determine whether d is greater than or equal to 0.5.

Statement One Alone:

When d is rounded to the nearest tenth, the result is 0.5.

Using the information in statement one, we can get a multitude of values for d.

For example, d can be 0.51, and 0.51 is greater than or equal to 0.5.

In another case, d can be 0.49, but 0.49 is not greater than or equal to 0.5.

Statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

When d is rounded to the nearest integer, the result is 1.

In order for d to be rounded to 1 (when rounded to the nearest integer), the value of d must be at least 0.5. Statement two is sufficient to answer the question.

The answer is B.
_________________

Target question: Is d ≥ 0.5?

Statement 1: When d is rounded to the nearest tenth, the result is 0.5.
There are several values of d that satisfy statement 1. Here are two:
Case a: d = 0.51 (we get 0.5 when 0.51 is rounded to the nearest tenth). In this case, the answer to the target question is YES, it IS the case that d ≥ 0.5
Case b: d = 0.49 (we get 0.5 when 0.49 is rounded to the nearest tenth). In this case, the answer to the target question is NO, it is NOT the case that d ≥ 0.5
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: When d is rounded to the nearest integer, the result is 1
If we get 1 when d is rounded to the nearest integer, then we know that 0.5 ≤ d < 1.5[/color]
So, it MUST be the case that d ≥ 0.5
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

When the question says "If d denotes a decimal", can that mean that d is for instance 6.1? Isn't 6.1 a decimal? Or is it only 0.XXXXXXX ? I am confused as to the definition of "a decimal". Thank you!

A decimal is a fraction that is written in the form of a dot followed by one or more numbers which represent tenths, hundredths, and so on. For example, 0.1, 5.1, ... So, to answer your question, yes, 6.1 is also a decimal.
_________________

Hi Bunuel

I am confused with respect to Statement 1, if result is 0.5 when d is rounded to nearest tenth range would be 0.45 to 0.49 (instead of 0.54)

Then ST 1 would mean definite No. Can you please help me out?

Let me ask you: what is, say, 0.53 rounded to the nearest tenth?
_________________

Statement 2:
If \(d≤0.5\), there is no chance to be the nearest integer 1. The answer is Yes----> Sufficient.

Statement 1:
We should not try for finding Yes answer here because we've an automatic Yes in the statement 2 (as statements don't contradict each other). So, if d=0.45, then No. So, it gives YES and NO answer at a time.-->Insufficient.

The correct choice is
_________________

Answer: Option B

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Bunuel

Hi Bunuel,

I am confused with st2 and decimal rounding concept

Why can't we consider d=0.487?
When we roundup 0.487 = 0.5 = 1
Is it because in case of round up to integer, we consider decimal upto tenth? So 0.487 is not a valid case.

Also rounded up to tenth means we will consider decimal upto hundredth digit (0.49 or 0.51). Is my understanding correct?
Even in this case, can we consider 0.485?

Thanks!

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.

So, when rounding to the nearest tenth, only hundredths digit is important, you can ignore all other digits.
When rounding to the nearest integer, only tenths digit is important, you can ignore all other digits.

Back to your example. When rounding 0.487 to the integer, you should pay attention to the tenths digit, which is 4. 4 < 5, so 0.487 rounded to the integer is 0.
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Is d>= 0.5?

1. rounding to the nearest decimal we get 0.5, d could be 0.45 or 0.51. (Insufficient)
2. rounding to the nearest integer, we get 1, d could be 1.49 or 0.51. TF>=0.5 (Sufficient)
Ans B