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.
0<p<1
[#permalink]
26 Aug 2021, 01:52
26 Aug 2021, 01:52
1
Expert Reply
1
Bookmarks
00:00
Question Stats:
3% (00:45) correct
96% (01:05) wrong based on 27 sessions
Hide Show timer Statistics
\(0<p<1\)
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
The greatest value of \(p(1-p)\) |
\(\frac{1}{2}\) |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
0<p<1
[#permalink]
30 Aug 2021, 01:12
30 Aug 2021, 01:12
2
Carcass wrote:
pick a number for p that must be a fraction
Now if p=1/2 we do have 1/2*1/2 and the greatest value is still 1/2 and the answer is C
But if we have 1/4 we do have 1/4*3/4 and the greatest value is 3/4 which is > 1/2 and the answer is A
The answer should be D and not C as reported by the book.
I also wait confirm from others mod rx10 KarunMendiratta
Now if p=1/2 we do have 1/2*1/2 and the greatest value is still 1/2 and the answer is C
But if we have 1/4 we do have 1/4*3/4 and the greatest value is 3/4 which is > 1/2 and the answer is A
The answer should be D and not C as reported by the book.
I also wait confirm from others mod rx10 KarunMendiratta
Carcass
The highlighted part would be 1/2*1/2 = 1/4 and 1/4*3/4 = 3/16
The answer must be Col. B
Let us solve this question using Quadratic function (Parabola);
\(f(p) = p(1-p)\)
\(f(p) = -p^2 + p\)
In a Quadratic function with a < 0, the maximum value is y-coordinate of the vertex
x-coordinate of the vertex \(= \frac{-b}{2a} = \frac{-1}{2(-1)} = \frac{1}{2}\)
y-coordinate of the vertex \(= -(\frac{1}{2})^2 + \frac{1}{2} = 1/4\)
Col. A: \(\frac{1}{4}\)
Col. B: \(\frac{1}{2}\)
Hence, option B
Attachments
p(1-p) vs 0.5.png [ 21.6 KiB | Viewed 2776 times ]
General Discussion
Re: 0<p<1
[#permalink]
29 Aug 2021, 23:47
29 Aug 2021, 23:47
greatest value of p(1-p) will be 1/4
[and not 1/2 .. please note it has not asked the value of x at which p(1-p) will be greatest .. which is at x=1/2]
hence, answer should be B
Carcass , please provide your comments.
Thanks!
[and not 1/2 .. please note it has not asked the value of x at which p(1-p) will be greatest .. which is at x=1/2]
hence, answer should be B
Carcass , please provide your comments.
Thanks!
