|y|<=1 (y less than or equal to 1), what does this mean?

[benjiboo]

|y|<=1 (y less than or equal to 1), what does this mean?

Does it mean that y can only be 0,1,-1, or does it mean Y could be anything

Thinking about this one is confusing me, because cant it be:

|y|<=1 =
-----
y <=1
y=>-1

So y could be anything?

Please provide explanation with your answer Thanks

[pemdas]

|y|<=1 think about y as the distance on the number line between 0 and a value, number (discreet or continuous) here discreet and 1, that's exactly what the sign of modulus tells us the distance on the number line within the brackets | |

now it also tells us that the distance is equal or less than 1. This means that we can have our y within the range of -1 _____0______1 where -1 and 1 are also included.

we are having the continuous value's range as we have no restriction set, such as y must be integer

|y|<=1 (y less than or equal to 1), what does this mean?

Does it mean that y can only be 0,1,-1, or does it mean Y could be anything

Thinking about this one is confusing me, because cant it be:

|y|<=1 =
-----
y <=1
y=>-1

So y could be anything?

Please provide explanation with your answer Thanks

[benjiboo]

Ok, I was confusing myself after studying too much in one day!

I am putting together an absolute value/inequality DS guide.

Thanks.
Benjiboo

[Javoni]

Here we go, as per the gist of absolute value, i.e. module of number or |y|<=1 means following:
y<=1 and y>=-1 and this means that y belongs to the segment [-1;1], hence, y could be one of infinite numbers from the segment set forth above. If, y is an integer so it could be either -1, 0 or 1.

In general |x| means x if x>=0 and -x if x<0

Please, correct me if I went awry

[Brent@GMATPrepNow]

|y|<=1 (y less than or equal to 1), what does this mean?

Does it mean that y can only be 0,1,-1, or does it mean Y could be anything

Thinking about this one is confusing me, because cant it be:

|y|<=1 =
-----
y <=1
y=>-1

So y could be anything?

Here's one way to look at it:

In general, the statement: |x-k| can be thought of as the distance between x and k on the number line.
Example: |1-8| = 7 because, on the number line, the distance between 1 and 8 is 7.
Similarly, |(-3) - 2| = 5 because, on the number line, the distance between -3 and 2 is 5.

Different example: If we're told that |x-5| = 2, then we know that, on the number line, the distance between x and 5 is 2. So, x can equal either 7 or 3, since 7 and 3 are both 2 units away from 5 on the number line.

Now, the question at hand: |y| < 1
We can rewrite this as: |y - 0| < 1
This tells us that, on the number line, between y and 0 is less than or equal to 1.
So, which numbers are such that their distance from 0 is less than or equal to 1?
Well, all numbers between (and including) -1 and 1 are such that their distance from 0 is less than or equal to 1.

So, |y| < 1 is telling us that: -1 < y < 1

Cheers,
Brent