Data Sufficiency

OG13 DS Q63:
If d denotes a decimal, is d>= 0.5
(1) when d is rounded to near tenth, result is 0.5
(2) when d is rounded to nearest integer , result is 1

According to my analysis, answer is E but OG answer is B

I wanted clarification on rounding theory. I was rounding 1 digit at a time starting from right but that does not seem to be what OG does.

For eg: 1.469 => 1.47 => 1.5 => 2

So do we need to look at entire "469" together and then round? Like Since 469<500 => 1.469 => 1.0

gmatstud wrote:
So do we need to look at entire "469" together and then round? Like Since 469<500 => 1.469 => 1.0

Hi gmatstud:

Yes, you have to look at it together. Whenever you are rounding, you have to consider the overall value, and think about the unit it is rounded to. I will give a few rounding examples which should clarify this once and for all.

Values rounded to integers.

1. 3.499 is rounded to 3.
2. 3.501 is rounded to 4.

Valued rounded to tenths.
1. 3.499 is rounded to 3.5
2. 3.501 is rounded to 3.5

Values rounded to the nearest 10.
1. 4.89 is rounded to 0.
2. 5.01 is rounded to 10.

Values rounded to the nearest 100.
1. 36.1249 is rounded to 0.
2. 148.129 is rounded to 100.
3. 124.148 is rounded to 100.
4. 150.001 is rounded to 200.

And finally here's an example of rounding a number to the nearest hundreth, tenth, integer, 10 and 100. Try doing it yourself.

147.4836, when rounded to:
a. nearest hundredth is 147.48
b. nearest tenth is 147.5
c. nearest integer is 147
d. nearest 10 is 150
e. nearest 100 is 100

Let me know if this helps

eagleeye wrote:
147.4836, when rounded to:
a. nearest hundredth is 147.48
b. nearest tenth is 147.5
c. nearest integer is 147
d. nearest 10 is 150
e. nearest 100 is 100

Let me know if this helps

Awesome...thanks a ton for the detailed explanation.

One question: for the full. number: 147.4846 and if we need to round to nearest hundredth, will it become 147.485 => 147.49 OR will it be 147.48

From the explanation , I summarize as:
- look at the first digit to right of the digit till which you need to round (forgot about other digits).
- if that digit on right is >=5, increase the digit to where rounding is required by 1 else leave it as it is.

Hi Gmatstud:

Just for ease of explanation, I will write down an easier example.

If you have something like 1.5 and you want to round it to the nearest integer, you can't do it without additional information. because 1.5 is the mean and median of 1 and 2, we don't know whether it rounds to 1 or 2.

So, to rehash.

1. Look to the digit to the right of the one you want to round to:
a. If the digit to the right is 0,1,2,3, or 4, round down.
b. If the digit to the right is 6,7,8,9 round up.
c. If the digit is 5, then you need to consider, if there is any non-zero digit at any place after 5. If there is one, round up. If there isn't, we need additional information from the question to decide.

Example:

For rounding to the nearest integer:

a. 1.5000000001 rounds to 2.
b. 1.43452384023984902830 rounds to 1.
c. 1.500000000, we can't round without more info. Depending on the author, it may be rounding down or up.

Let me know if this helps

eagleeye wrote: c. If the digit is 5, then you need to consider, if there is any non-zero digit at any place after 5. If there is one, round up. If there isn't, we need additional information from the question to decide.

Example:

For rounding to the nearest integer:

c. 1.500000000, we can't round without more info. Depending on the author, it may be rounding down or up.

Let me know if this helps

Hi,

I'm more confused now

i quite did not understand the line: "if the digit is 5...." . As per my understanding 1.50000 => 2 by rounding to nearest integer

gmatstud wrote:

eagleeye wrote: c. If the digit is 5, then you need to consider, if there is any non-zero digit at any place after 5. If there is one, round up. If there isn't, we need additional information from the question to decide.

Example:

For rounding to the nearest integer:

c. 1.500000000, we can't round without more info. Depending on the author, it may be rounding down or up.

Let me know if this helps

Hi,

I'm more confused now

i quite did not understand the line: "if the digit is 5...." . As per my understanding 1.50000 => 2 by rounding to nearest integer

even i have read that 1.5 will round up to 2 since digit preceding decimal is odd
had it been even number then round down
2.5 will round down to 2

sandeep_thaparianz wrote:

gmatstud wrote:

eagleeye wrote: c. If the digit is 5, then you need to consider, if there is any non-zero digit at any place after 5. If there is one, round up. If there isn't, we need additional information from the question to decide.

Example:

For rounding to the nearest integer:

c. 1.500000000, we can't round without more info. Depending on the author, it may be rounding down or up.

Let me know if this helps

Hi,

I'm more confused now

i quite did not understand the line: "if the digit is 5...." . As per my understanding 1.50000 => 2 by rounding to nearest integer

even i have read that 1.5 will round up to 2 since digit preceding decimal is odd
had it been even number then round down
2.5 will round down to 2

gmatstud, sandeep_thaparianz:

Don't be confused. There are at least 10 different ways of tie-breaking when value is in the middle.
Since 1.50 is the median of 1 and 2, that's why I wrote that there needs to be additional information about which rule to use. One of the most common ones is rounding up when the value is 1.5 or 2.5 or 3.5 etc.

https://en.wikipedia.org/wiki/Rounding gives a number of ways of rounding, and breaking the tie at median points.

Just skim over it to see the different ways of rounding. Anyway, we don't need to be too technical about rounding. There are more important things in GMAT to focus on.
As sandeep_thaparianz wrote, he or she has been taught the even, odd round up or down rule.

So the whole reason I wrote about 1.5 being either rounded up to 2 or down to 1 was that there are several tie-breaking ways. Let me know if this helps