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

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If y is a nonzero integer, what is the value of |y|?  [#permalink]

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29 May 2015, 05:33
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If y is a nonzero integer, what is the value of |y|?

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

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Re: If y is a nonzero integer, what is the value of |y|?  [#permalink]

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29 May 2015, 06:47
1
Hello all

My attempt:

We need to find $$|y|$$ where $$y$$ is a non zero integer

Statement 1:

$$y^2 = |y|$$
$$y^2 - |y| = 0$$
Assume $$y$$ is $$+ve$$ then
$$y^2 - y = 0$$
Gives two solutions $$y = 0$$ and $$y = 1$$ we drop $$y = 0$$ as it is not valid. Therefore $$y = 1$$ is a solution for $$y>0$$
Now assume $$y$$ is $$-ve$$ then
$$y^2 + y = 0$$
This too gives two solutions $$y = 0$$ and $$y = -1$$ and again we drop $$y = 0$$. Therefore $$y = -1$$ is a solution for $$y<0$$
Overall two solutions are valid $$y = 1$$ and $$y = -1$$ and both have absolute values as $$y = 1$$
Hence solvable from this statement.

Statement 2:

$$|y| = |y|!$$
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.

I will go with option $$A$$
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Re: If y is a nonzero integer, what is the value of |y|?  [#permalink]

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29 May 2015, 07:55
2
My Ans - A

Explanation :

(1) y^2 = |y|

This is true for only one value of y i.e. 1

Hence, this is sufficient to determine the value alone.

(2) |y| = |y|!

This is true for y=1 & y=2 . Hence, not sufficient to determine the value of |y|.
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Re: If y is a nonzero integer, what is the value of |y|?  [#permalink]

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29 May 2015, 09:18
1
Quote:
If y is a nonzero integer, what is the value of |y|?

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

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).
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Re: If y is a nonzero integer, what is the value of |y|?  [#permalink]

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29 May 2015, 10:13
Bunuel wrote:
If y is a nonzero integer, what is the value of |y|?

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

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
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Re: If y is a nonzero integer, what is the value of |y|?  [#permalink]

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29 May 2015, 10:31
2
heylookitskarl wrote:
Bunuel wrote:
If y is a nonzero integer, what is the value of |y|?

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

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

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.
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Re: If y is a nonzero integer, what is the value of |y|?  [#permalink]

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29 May 2015, 11:29
2
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

GMAT assassins aren't born, they're made,
Rich
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Re: If y is a nonzero integer, what is the value of |y|?  [#permalink]

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31 May 2015, 10:25
A
(1) y= -1 or +1; |y| = 1
(2) y = 1 or 2
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Re: If y is a nonzero integer, what is the value of |y|?  [#permalink]

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01 Jun 2015, 04:10
Bunuel wrote:
If y is a nonzero integer, what is the value of |y|?

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

OFFICIAL SOLUTION:

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

(1) y^2 = |y|. Since y^2 = |y|^2, then we have that |y|*|y| = |y|. y is nonzero, so we can reduce by it: |y| = 1. Sufficient.

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

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Re: If y is a nonzero integer, what is the value of |y|?  [#permalink]

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01 Jun 2015, 05:02
apoorv601 wrote:
A
(1) y= -1 or +1; |y| = 1
(2) y = 1 or 2

For (2) y can also equal -1 and -2, my bad!!
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Re: If y is a nonzero integer, what is the value of |y|?  [#permalink]

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24 Jul 2016, 06:52
Bunuel wrote:
If y is a nonzero integer, what is the value of |y|?

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

Statement 1. Since both parts are non-negative we can square both sides. Hence we have y^4 = y .Since y is not equal to zero we can divide both parts by y to get y^3 = 1 Hence y=1 Sufficient
Statement 2. Both 1 and 2 satisfy this condition. Hence not sufficient.
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Re: If y is a nonzero integer, what is the value of |y|?  [#permalink]

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Re: If y is a nonzero integer, what is the value of |y|?   [#permalink] 13 Mar 2018, 04:53
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