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Re: Given a positive integer p, how many integers are greater th [#permalink]
10 Apr 2019, 12:22

1

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Expert's post

Carcass wrote:

Given a positive integer p, how many integers are greater than \(2p\) and less than \(4p − 1\)?

A. \(\frac{p}{2}\)

B. \(p\)

C. \(p+1\)

D. \(2p-2\)

E. \(3p-3\)

On option is to apply the input-output approach

Let's see what happens when p = 4

The question becomes: How many integers are greater than 2(4) and less than 4(4) − 1? In other words, How many integers are greater than 8 and less than 15? The integers are 9, 10, 11, 12, 13 and 14 (6 integers) So, when p = 4, the answer to the question is 6

Now we'll check each answer choice to see which one yields an OUTPUT of 6 when we INPUT p = 4

A. p/2 = 4/2 = 2. No good. We want an output of 6

B. p = 4 = 4. No good. We want an output of 6

C. p+1 = 4 + 1 = 5. No good. We want an output of 6

D. 2p-2 = 2(4) - 2 = 6. PERFECT!

E. 3p-3 = 3(4) - 3 = 9. No good. We want an output of 6

Answer: D

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Re: Given a positive integer p, how many integers are greater th [#permalink]
11 Apr 2019, 14:13

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answer: D

2p < {x} < 4p-1

{x} is the sequence of numbers between 2p and 4p-1. For instance: if p =1 then 2 < {} < 3, So no integer is between 2 and 3. if p =2 then 4 < {5,6} < 7, So 2 numbers are between 4 and 7.

We can both try the options or use the formula for gap between two numbers: The total numbers between 2p and 4p-1 are : 4p-1 - 2p -1 = 2p-2
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Re: Given a positive integer p, how many integers are greater th
[#permalink]
11 Apr 2019, 14:13