If y is a nonzero integer, what is the value of |y|?

Note that we need to find value of |y| not y.
Now read both the points again.
Point (1) clearly gives a single value of |y| = 1.

Hi All,

This question is a great example of how sometimes you're NOT really being tested on high-level "math" skills - you're really being tested on the thoroughness of your thinking, your ability to see more than just the obvious answer and your attention to the question that is ASKED.

Here, we're told that Y is a NON-ZERO INTEGER. We're asked for the value of |Y|. It's worth remembering that the absolute value symbol turns negative results into positive ones....

Fact 1: Y^2 = |Y|

Since we're dealing with a squared term, there will likely be more than one solution to this equation (but not that many). As Y gets "more positive" or "more negative", the squared term will clearly become bigger than the |Y|, so the solution(s) must be fairly close to 0 (although remember that 0 is NOT allowed here).

IF....
Y = 1
1^2 = |1|
The answer to the question is |1| = 1

IF...
Y = -1
(-1)^2 = |-1|
The answer to the question is |-1| = 1
Fact 1 is SUFFICIENT

Fact 2: |Y| = |Y|!

Here, we're dealing with a factorial, so we also should be looking for relatively "small" answers (since a bigger Y would lead to a bigger Y!).

IF....
Y = 1
|1| = |1|!
The answer to the question is |1| = 1

IF....
Y = 2
|2| = |2|!
The answer to the question is |2| = 2
Fact 2 is INSUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich

My Approach:

(1.) y^2 = |y|
Since, y is not zero. and is an integer, the only values of y which satisfy this are y=1 and y=-1. For both |y|=1.
So, Sufficient.

(2.)|y| = |y|!
Now, y can be -1,1,-1, or 2. And |y| can be 1 or 2.
So Insufficient.

Hence (A).

Dear Yogita25

St. 2 says |y| = |y|!

Now, the factorial of a positive integer n is defined as n(n-1)(n-2)(n-3) . . .1

For example, 4! = 4*3*2*1

Now, let |y| = n.

So, as per St. 2, n = n!

What can be the possible values of n?

If n = 1, then n! = 1. So, n = n!
If n = 2, then n! = 2*1 = 2. So, n = n!
If n = 3, then n! = 3*2*1 = 6. So, n! > n
For all values greater than 3 also, n! > n

So, we see that the only possible values of n are: 1 and 2.

That is, Either |y| = 1
Or, |y| = 2

So, from St. 2, we get two possible values of |y|. Since we could not find a unique value of |y|, St. 2 is not sufficient.

I hope this helped clarify your doubt!

Best Regards

Japinder

I would say E, right? we are looking for the value of y and none of these gives us the true value… it could be 23422 or 2

I am new to this but none of the statements gives me the clue as to what the "value" of y is

can you please reexplain why 2nd statement is not sufficient?

Hello Yogita25

Please note that the statement 2 is giving two values

\(|y| = |y|!\)
Lets assume for case \(y\) is \(+ve\)
\(y = y!\)
\(y*[(y-1)! - 1] = 0\)
Here the solutions are \(y = 0\), \(y = 1\), \(y = 2\) we drop \(y = 0\) and hence leftover solutions are \(y = 1\) and \(y = 2\)
Now if \(y\) is \(-ve\) then again we will be reducing the equation to the same expression.
Hence absolute value of \(y\) can take \(1\) or \(2\).
Thus not solvable from this statement.

Hi Yogita25,

DS questions test you on a variety of skills - one of those skills is your ability to determine if an answer remains CONSISTENT or not. If, when including the information in Fact 1 or Fact 2, the answer to a given DS question CHANGES, then the data in the Fact is INSUFFICIENT to answer the question.

In this DS question, I used the data in Fact 2 to prove that the answer CHANGES depending on the value of Y. Thus, Fact 2 is INSUFFICIENT.

GMAT assassins aren't born, they're made,
Rich

If \(y\) is a nonzero integer, what is the value of \(|y|\)?

(1) \(y^2 = |y|\)

Since \(y^2 = |y|^2\), we can rewrite the above equation as \(|y| * |y| = |y|\). Given that \(y\) is nonzero, we can divide both sides by \(|y|\) to get \(|y| = 1\). Sufficient.

(2) \(|y| = |y|!\)

By testing values, we find this holds true for \(y = +/-1\) as well as for \(y = +/-2\). Thus, \(|y| = 1\) or 2. Not sufficient.


Answer: A