KarishmaB wrote:

GMATantidote wrote:

Given k is a nonzero integer, is \(k > 0\) ?

1) \(|k-4| =| k| +4\)

2) \(k>k^3\)

k is a non zero integer so the values it can take are ... -2, -1, 1, 2, 3, ...

Is k > 0?

1) \(|k-4| =| k| +4\)

According to the definition of absolute values,

|k - 4| = k - 4 if (k - 4) >= 0

|k - 4| = -(k - 4) = -k + 4 if (k - 4) < 0

Note that the the right hand side is |k| + 4. This can be equal to the second case only and that too when k < 0. So we know that k must be negative. We can answer the question with 'No'.

Sufficient.

2) \(k>k^3\)

On the number line, where is x greater than x^3? When either 0 < x< 1 or x < -1.

Here, since k must be an integer, it will not lie between 0 and 1. So k must be less than -1 i.e. k must be negative. We can answer the question with 'No'.

Sufficient.

Answer (D)

P.S. - You must know the relation between x, x^2 and x^3 on the number line.

Responding to a pm: Detailing stmnt 1

First, go through this post I wrote for

Veritas Prep:

https://www.veritasprep.com/blog/2014/0 ... -the-gmat/As per definition of absolute values,

|x| = x if x >= 0

|x| = -x is x < 0

Look at the LHS first: Using the definition,

|k - 4| = k - 4 ......... if (k - 4) >= 0 i.e. if k >= 4

|k - 4| = -(k - 4) = -k + 4 .................if (k - 4) < 0 i.e. if k < 4

So |k - 4| can take two values: k - 4 OR -k + 4 depending on some constraints

Now look at the RHS: |k| + 4

|k| = k if k >= 0

|k| = -k if k < 0

So |k| + 4 can take two values: k + 4 OR -k + 4 depending on whether k is positive or negative

The only common value between LHS and RHS is -k + 4 which happens when k < 0.

So for LHS to be equal to RHS, k must be negative.

_________________

Karishma

Veritas Prep GMAT Instructor

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