GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Given a positive integer p, how many integers are greater th
[#permalink]
09 Apr 2019, 02:09
09 Apr 2019, 02:09
1
Expert Reply
1
Bookmarks
00:00
Question Stats:
58% (01:27) correct
41% (01:43) wrong based on 63 sessions
Hide Show timer Statistics
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. \(3p-3\)
A. \(\frac{p}{2}\)
B. \(p\)
C. \(p+1\)
D. \(2p-2\)
E. \(3p-3\)
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Given a positive integer p, how many integers are greater th
[#permalink]
10 Apr 2019, 12:22
10 Apr 2019, 12:22
1
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. \(3p-3\)
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
Re: Given a positive integer p, how many integers are greater th
[#permalink]
11 Apr 2019, 14:13
11 Apr 2019, 14:13
2
1
Bookmarks
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
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
