Data Sufficiency

Hi ,

Can someone help me with this... Its a real simple question , but I am still confused . The concept of rounding GMAC follows is not what I leart in my math classes...


For Ex: round ..4545 to the nearest hundredth - = .46 . IS what I did correct ?

is the OA a?

OA is C

When possible, please type out the question instead of posting a link. Makes it much easier to respond.

Q: what is the result when X is rounded to the nearest hundredth?

(1) when x is rounded to the nearest thousandth, the result is .455

let's pick x = .4546 If we round to the nearest hundredth we get .45

let's pick x = .4554 If we round to the nearest hundredth we get .46

Two possible answers, therefore (1) is insufficient.

(2) the thousandths digit of x is 5

We have no clue what the hundredths digit is, so (2) is insufficient.

Let's try together:

We know that roudned off our number is .455 and we know that the thousandths digit is 5.

So, we could have started with:

.4550
.4551
.4552
.4553
.4554

For all 5 of those possibilities, if we round to the nearest hundredth, we get .46

Together the statements lead to only one answer, so they're sufficient: choose (c).

Stuart ,

Thanks for responding .. I have an additional question for you .

in the example you stated : .4546 ... If I had to round to the nearest hundred , wont it be 0.46. My understanding was u start at the last digit and round your way back up . That being said , my logic was

0.4546 --> 0.0455 --0.046

Do I make any sense ? I could have my fundamentals wrong and I would appreciate if you can help me out.

Thanks for your response. I was hoping you respond.

cheers,
T

what about rounding 0.456 to units digit? does it go like this 0.456 -> 0.46 -> 0.5 -> 1???

Stuart Kovinsky wrote:When possible, please type out the question instead of posting a link. Makes it much easier to respond.

Q: what is the result when X is rounded to the nearest hundredth?

(1) when x is rounded to the nearest thousandth, the result is .455

let's pick x = .4546 If we round to the nearest hundredth we get .45

let's pick x = .4554 If we round to the nearest hundredth we get .46

Two possible answers, therefore (1) is insufficient.

(2) the thousandths digit of x is 5

We have no clue what the hundredths digit is, so (2) is insufficient.

Let's try together:

We know that roudned off our number is .455 and we know that the thousandths digit is 5.

So, we could have started with:

.4550
.4551
.4552
.4553
.4554

For all 5 of those possibilities, if we round to the nearest hundredth, we get .46

Together the statements lead to only one answer, so they're sufficient: choose (c).

Arawamis ,

That would be my understanding.

You round off based on as much information as you have.

So, if we're rounding .4546 to the nearest hundredth, we're 46/100 points between .45 and .46. Since we're less than halfway there, we round down (to .45).

In general, we don't do double (or triple) rounding - we use all the info at our disposal.

So, .456 is 456/1000 of the distance between 0 and 1. 456 is less than 1/2 of 1000, so we'd round down to 0.

neat explanation Stuart !

Stuart Kovinsky wrote:When possible, please type out the question instead of posting a link. Makes it much easier to respond.

Q: what is the result when X is rounded to the nearest hundredth?

(1) when x is rounded to the nearest thousandth, the result is .455

let's pick x = .4546 If we round to the nearest hundredth we get .45

let's pick x = .4554 If we round to the nearest hundredth we get .46

Two possible answers, therefore (1) is insufficient.

(2) the thousandths digit of x is 5

We have no clue what the hundredths digit is, so (2) is insufficient.

Let's try together:

We know that roudned off our number is .455 and we know that the thousandths digit is 5.

So, we could have started with:

.4550
.4551
.4552
.4553
.4554

For all 5 of those possibilities, if we round to the nearest hundredth, we get .46

Together the statements lead to only one answer, so they're sufficient: choose (c).

Hi Stuart,

Thanks for your help. I have a doubt regarding what you explained.

You end up with a list of numbers which is as follows:

.4550
.4551
.4552
.4553
.4554

And you say that "For all 5 of those possibilities, if we round to the nearest hundredth, we get .46". Actually .4550 is as close to .45 as to .46... why do we assume that it should be rounded to .46 instead of .45?

Many thanks!

Pablo

Stuart Kovinsky wrote:When possible, please type out the question instead of posting a link. Makes it much easier to respond.

Q: what is the result when X is rounded to the nearest hundredth?

(1) when x is rounded to the nearest thousandth, the result is .455

let's pick x = .4546 If we round to the nearest hundredth we get .45

let's pick x = .4554 If we round to the nearest hundredth we get .46

Two possible answers, therefore (1) is insufficient.

(2) the thousandths digit of x is 5

We have no clue what the hundredths digit is, so (2) is insufficient.

Let's try together:

We know that roudned off our number is .455 and we know that the thousandths digit is 5.

So, we could have started with:

.4550
.4551
.4552
.4553
.4554

For all 5 of those possibilities, if we round to the nearest hundredth, we get .46

Together the statements lead to only one answer, so they're sufficient: choose (c).

And you say that "For all 5 of those possibilities, if we round to the nearest hundredth, we get .46". Actually .4550 is as close to .45 as to .46... why do we assume that it should be rounded to .46 instead of .45?

...for the same reason that we round 0.5 to 1 rather than to 0 (even though 0.5 is as close to 1 as it is to 0).

Testluv wrote:

And you say that "For all 5 of those possibilities, if we round to the nearest hundredth, we get .46". Actually .4550 is as close to .45 as to .46... why do we assume that it should be rounded to .46 instead of .45?

...for the same reason that we round 0.5 to 1 rather than to 0 (even though 0.5 is as close to 1 as it is to 0).

So basically whenever we have a decimal that is as close to one as to the other we should round up. Is that correct, Testluv?

Many thanks!

Yep. And the only time a number is as close to one end as it is to the other is when that number is 5.