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Given a positive integer p, how many integers are greater th

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Given a positive integer p, how many integers are greater th [#permalink]  09 Apr 2019, 02:09
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Question Stats:

50% (00:45) correct 50% (02:07) wrong based on 8 sessions
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. $$3p-3$$
[Reveal] Spoiler: OA

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

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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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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
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