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.
If t> 1
[#permalink]
13 Jul 2020, 07:44
13 Jul 2020, 07:44
Expert Reply
00:00
Question Stats:
80% (00:52) correct
19% (00:37) wrong based on 31 sessions
Hide Show timer Statistics
\(t>1\)
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
Quantity A |
Quantity B |
\(\frac{1}{1+\frac{3}{2^t}}\) |
\(\frac{1}{1+\frac{3}{3^t}}\) |
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
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1115
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Re: If t> 1
[#permalink]
16 Jul 2020, 09:53
16 Jul 2020, 09:53
Both the Quantities have similar looking fraction but their denominators are bit different. As both are positive fractions so we just need to figure out whose denominator is smaller (=> Fraction is bigger). We also know that t > 1
=> \(2^t\) and \(3^t\) will be greater than 1
and \(3^t\) > \(2^t\) as 3 > 2 and t > 1
=> \(\frac{1}{3^t}\) < \(\frac{1}{2^t}\) [Property: In case of two +ve fractions with same numerator, the fraction with larger denominator is smaller ]
=> \(\frac{3}{3^t}\) < \(\frac{3}{2^t}\) [Property: Multiplying with a +ve number on both the sides of an inequality DOES NOT change the sign of the inequality]
=> 1 + \(\frac{3}{3^t}\) < 1 + \(\frac{3}{2^t}\)
=> \(\frac{1}{1+\frac{3}{3^t}}\) > \(\frac{1}{1+\frac{3}{2^t}}\)
=> Quantity B > Quantity A
So, Answer will be B
Hope it helps!
=> \(2^t\) and \(3^t\) will be greater than 1
and \(3^t\) > \(2^t\) as 3 > 2 and t > 1
=> \(\frac{1}{3^t}\) < \(\frac{1}{2^t}\) [Property: In case of two +ve fractions with same numerator, the fraction with larger denominator is smaller ]
=> \(\frac{3}{3^t}\) < \(\frac{3}{2^t}\) [Property: Multiplying with a +ve number on both the sides of an inequality DOES NOT change the sign of the inequality]
=> 1 + \(\frac{3}{3^t}\) < 1 + \(\frac{3}{2^t}\)
=> \(\frac{1}{1+\frac{3}{3^t}}\) > \(\frac{1}{1+\frac{3}{2^t}}\)
=> Quantity B > Quantity A
So, Answer will be B
Hope it helps!
gmatclubot
Re: If t> 1 [#permalink]
16 Jul 2020, 09:53
Moderators:
