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18 Jun 2022, 17:30
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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.
Are You Up For the Challenge: 700 Level Questions
(1) k and p are distinct and positive.
(2) k = 1 and |p|>1.
Are You Up For the Challenge: 700 Level Questions
19 Jun 2022, 03:18
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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
=> 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
20 Jun 2022, 04:19
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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.
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.
