Let k and p be nonzero integers. Is k - 1/p = 1/p?

Question

Let k and p be nonzero integers. Is  k - \frac{1}{p} \geq \frac{1}{p} ?
 
(1) k and p are distinct and positive.
(2) k = 1 and |p|>1.

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BrushMyQuant · Answer

Given that k and p be nonzero integers and we need to find if \(k - \frac{1}{p} \geq \frac{1}{p}\)
=> If \(k \geq \frac{1}{p} + \frac{1}{p} \)
=> If \(k \geq \frac{2}{p} \)

STAT 1: k and p are distinct and positive

Since k and p are distinct and positive so for any value of k and p, k will always be \(\geq \frac{2}{p} \)

Let's take some values to understand

k = 1 , p = 2
=> \(1 \geq \frac{2}{2} \) => \(1 \geq 1 \) (which is true)

k = 2, p = 1
=> \(2 \geq \frac{2}{1} \) => \(2 \geq 2 \) (which is true)
=> SUFFICIENT

STAT 2: k = 1 and |p|>1

Now, |p|>1 => p > 1 or p < -1 [ As |x| > a => x > a or x < -a ]
(Watch this video to understand basics of Absolute Value)

Let's take some values to check

for k = 1 and p < -1, \(k \geq \frac{2}{p} \) will always be true
as k is positive and \(\frac{2}{p}\) will be negative

for k = 1 and p > 1, \(k \geq \frac{2}{p} \) will always be true
as k =1 and \(\frac{2}{p}\) will be \(\leq\) 1
=> SUFFICIENT

So, Answer will be D
Hope it helps!

Watch the following video to learn the Basics of Absolute Values

Suberwoman · Answer

BrushMyQuant  
I have a doubt. Since the statement 1 says k and p are distinct positive integers, cant I use k=1 and p=1.
That way k>=2/p will not be true, as 1 is not greater than 2. Please let me know.

sauravhippargi · Answer

Suberwoman

Statement 1 says k and p are  distinct , so you cannot use k=1 and p=1.

BrushMyQuant · Answer

Suberwoman  : as k and p are distinct positive integers so they both cannot be equal to 1

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Let k and p be nonzero integers. Is k - 1/p >= 1/p?

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