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.
Nov 17Live Online Classes with Top GRE Expert Rich Zwelling
08:00 PM EST
-10:00 PM EST
Get live instruction from a top-scoring, industry-recognized GRE teachers + 6 months of access to TTP Self-Study included! Tues/Thur Sept 7, 2026---Feb. 2, 2027, 1:00pm-3:00pm EST
Dec 14Live Online Classes with Top GRE Expert Michael Butville
08:00 PM EST
-10:00 PM EST
Get live instruction from a top-scoring, industry-recognized GRE teachers + 6 months of access to TTP Self-Study included! Mon/Wed Dec. 14, 2026---Feb. 22, 2027, 8:00pm-10:00pm EST
It is given that 0<p<1
[#permalink]
20 Apr 2021, 23:31
20 Apr 2021, 23:31
1
Expert Reply
00:00
Question Stats:
96% (00:57) correct
3% (00:59) wrong based on 52 sessions
Hide Show timer Statistics
It is given that \(0<p<1\)
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Quantity A |
Quantity B |
\(\frac{1}{p^2}\) |
\(\frac{1}{(p+1)^2}\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
Re: It is given that 0<p<1
[#permalink]
21 Apr 2021, 11:18
21 Apr 2021, 11:18
1
Carcass wrote:
It is given that \(0<p<1\)
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given
Quantity A |
Quantity B |
\(\frac{1}{p^2}\) |
\(\frac{1}{(p+1)^2}\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given
\(0<p<1\) mean \(p\) is a positive number
Col. A: \(\frac{1}{p^2}\)
Col. B: \(\frac{1}{(p+1)^2}\)
Cross-multiplying the denominators (Since \(p > 0\));
Col. A: \((p+1)^2\)
Col. B: \(p^2\)
Col. A: \(p^2 + 2p + 1\)
Col. B: \(p^2\)
Subtracting \(p^2\) from both sides;
Col. A: \(2p + 1\)
Col. B: \(0\)
Subtracting \(1\) from both sides and dividing by \(2\);
Col. A: \(p\)
Col. B: \(\frac{-1}{2}\)
Hence, option A
Re: It is given that 0<p<1
[#permalink]
05 May 2021, 22:49
05 May 2021, 22:49
3
If you know the fact that squaring a number between 0 and 1 results in a number smaller than the original number, this question can be solved quickly without any calculations.
We can easily realize that the denominator for :
option A = 1 / (number between 0 and 1)^2;
option B = 1 / (number NOT between 0 and 1)^2;...since you are adding +1 to p, the denominator is greater than 1;
From the fact that squaring a number between 0 and 1 results in a number smaller than the original number, it can be understood that the denominator of option A will be much lesser than option B. Since it is denominator of a fraction, option A will be bigger in value than option B.
Hence, answer is option A.
Hit Kudos if this reply helped!:)
We can easily realize that the denominator for :
option A = 1 / (number between 0 and 1)^2;
option B = 1 / (number NOT between 0 and 1)^2;...since you are adding +1 to p, the denominator is greater than 1;
From the fact that squaring a number between 0 and 1 results in a number smaller than the original number, it can be understood that the denominator of option A will be much lesser than option B. Since it is denominator of a fraction, option A will be bigger in value than option B.
Hence, answer is option A.
Hit Kudos if this reply helped!:)
